Suppressed fuzzy-soft learning vector quantization for MRI segmentation by n.rajbharath

VIEWS: 10 PAGES: 11

									                                                            Artificial Intelligence in Medicine 52 (2011) 33–43



                                                             Contents lists available at ScienceDirect


                                                  Artificial Intelligence in Medicine
                                                journal homepage: www.elsevier.com/locate/aiim




Suppressed fuzzy-soft learning vector quantization for MRI segmentation
Wen-Liang Hung a,∗ , De-Hua Chen b , Miin-Shen Yang c
a
  Department of Applied Mathematics, National Hsinchu University of Education, Hsin-Chu 30014, Taiwan
b
  Institute of Statistical Science, Academia Sinica, Taipei 11529, Taiwan
c
  Department of Applied Mathematics, Chung Yuan Christian University, Chung-Li 32023, Taiwan




a r t i c l e         i n f o                          a b s t r a c t

Article history:                                       Objective: A self-organizing map (SOM) is a competitive artificial neural network with unsupervised
Received 12 November 2009                              learning. To increase the SOM learning effect, a fuzzy-soft learning vector quantization (FSLVQ) algorithm
Received in revised form 3 January 2011                has been proposed in the literature, using fuzzy functions to approximate lateral neural interaction of
Accepted 27 January 2011
                                                       the SOM. However, the computational performance of FSLVQ is still not good enough, especially for large
                                                       data sets. In this paper, we propose a suppressed FSLVQ (S-FSLVQ) using suppression with a parameter
Keywords:
                                                       learning schema. We then apply the S-FSLVQ to MRI segmentation and compare it with several existing
Self-organizing map
                                                       methods.
Learning vector quantization
Mean squared error
                                                       Methods and materials: The proposed S-FSLVQ algorithm and some existing methods, such as FSLVQ,
CPU time                                               generalized LVQ, revised generalized LVQ and alternative LVQ, are compared using numerical data and
Magnetic resonance image segmentation                  MRI images. The numerical data are generated by a mixture of normal distributions. The MRI data sets
                                                       are from a 2-year-old female patient who was diagnosed with retinoblastoma of her left eye, a congenital
                                                       malignant neoplasm of the retina with frequent metastasis beyond the lacrimal cribrosa. To evaluate the
                                                       performance of these algorithms, two criteria for accuracy and computational efficiency are used.
                                                       Results: Comparing S-FSLVQ with FSLVQ, generalized LVQ, revised generalized LVQ and alternative LVQ,
                                                       the numerical results indicate that the S-FSLVQ algorithm is better than the other algorithms in accuracy
                                                       and computational efficiency. Moreover, the proposed S-FSLVQ can reduce the computation time and
                                                       increase accuracy compared to existing methods in segmenting these ophthalmological MRIs.
                                                       Conclusions: The proposed S-FSLVQ is a good competitive learning algorithm that is very suitable for seg-
                                                       menting the ophthalmological MRI data sets. Therefore, the S-FSLVQ algorithm is highly recommended
                                                       for use in MRI segmentation as an aid for supportive diagnoses.
                                                                                         Crown Copyright © 2011 Published by Elsevier B.V. All rights reserved.




1. Introduction                                                                         response based on the networks has ability to organize itself. Com-
                                                                                        petitive learning, on the other hand, occurs when artificial neurons
    Artificial neural networks are a data processing system consist-                     compete among themselves, and only the one that yields the best
ing of a large number of simple, highly interconnected processing                       response to a given input modifies its weight to become more like
elements in an architecture inspired by the structure of the cere-                      the input.
bral cortex in the human brain. This system performs two major                               Lippmann [1] presented a good tutorial review on neural com-
functions: learning and recall. Learning is the process of adapting                     puting with six important neural net models that can be used for
connection weights in an artificial neural network to produce the                        pattern classification. Of these neural net models, the Kohonen’s
desired output vector in response to a stimulus vector presented                        self-organizing map (SOM) is one of the most important ones since
to the input buffer. Recall is the process of accepting an input stim-                  it is unsupervised with a competitive learning neural network that
ulus and producing an output response in accordance with the                            uses the neighborhood interaction set to approximate lateral neu-
network weight structure. The learning rules of neural computa-                         ral interaction and discover topological structures hidden in the
tion indicate how connection weights are adjusted in response to                        data [2,3]. Learning vector quantization (LVQ) is the simplest case of
a learning example. In supervised learning, an artificial neural net-                    SOM and its learning rule is the well-known winner-take-all (WTA)
work is trained to give the desired response to a specific input                         principle, which gives crisp excitation states for each neuron. When
stimulus. In unsupervised no specific response is sought, but the                        the data sets under consideration become large, the computation
                                                                                        time of the algorithm is more important. To see the convergence
                                                                                        rate and speed up the learning, Kohonen [2] proposed a batch
    ∗ Corresponding author. Tel.: +886 3 5213132; fax: +886 3 5611128.                  version SOM. Cheng [4] studied the convergence and ordering prop-
      E-mail address: wlhung@mail.nhcue.edu.tw (W.-L. Hung).                            erties of the batch SOM. This motivates us to propose another LVQ

0933-3657/$ – see front matter. Crown Copyright © 2011 Published by Elsevier B.V. All rights reserved.
doi:10.1016/j.artmed.2011.01.004
34                                         W.-L. Hung et al. / Artificial Intelligence in Medicine 52 (2011) 33–43


algorithm. Adopting the ideas of Fan et al. [5] and Hung et al. [6],             tering algorithms are widely used for MRI segmentation, such as
we modified Wu and Yang’s [7] fuzzy-soft LVQ (FSLVQ) algorithm                    brain MRI [15–19] and ophthalmological MRI segmentations [20].
to propose a suppressed FSLVQ (S-FSLVQ). To select the param-                    However, these fuzzy clustering algorithms always suffer from
eter in S-FSLVQ algorithm, we propose a learning process which                   sensitivity to initials, parameters and noise. Thus, various neural
is based on an exponential separation strength between weights                   network approaches have been proposed for the MRI segmentation
with updating at each iteration. Numerical examples are used to                  to overcome these problems. In these neural network approaches,
illustrate the effectiveness of the proposed S-FSLVQ algorithm.                  Kohonen’s SOM is most used in MRI segmentation. Lin et al. [21]
    In oncology, physicians depend on different clinical frameworks,             generalized Kohonen’s SOM with fuzzy and fuzzy-soft types called
different types of anatomical evidence and different theoretical                 fuzzy Kohonen’s competitive learning and fuzzy-soft Kohonen’s
approaches to diagnose patients. Magnetic resonance image (MRI)                  competitive learning. They applied these generalized Kohonen’s
approaches are particularly helpful in clinical oncology to support              competitive learning algorithms to MRI and magnetic resonance
the diagnosis of retinoblastoma, a congenital oncological disease in             angiographies (MRA) ophthalmological segmentations. Recently,
ophthalmology, which usually shows its symptoms in early child-                  Yang et al. [22] applied the FSLVQ algorithm to three MRI data sets of
hood. In this paper, the proposed S-FSLVQ algorithm is applied for               real cases: (i) a 2-year-old girl who was diagnosed with retinoblas-
the segmentation of the MRI of a retinoblastoma patient who was                  toma in her left eye; (ii) a 55-year-old woman who developed
diagnosed using MRI in the ophthalmology field.                                   complete left side oculomotor palsy immediately after a motor
    The rest of this paper is organized as follows. Section 2 is a               vehicle accident; and (iii) an 84-year-old man who was diagnosed
brief survey of related work on LVQ algorithms. In Section 3, we                 with Alzheimer’s disease. Yang et al. [22] also compared the per-
introduce the batch FSLVQ algorithm. In Section 4, the S-FSLVQ                   formance of FSLVQ algorithm with the generalized Kohonen’s SOM
algorithm with a parameter learning schema is proposed and                       algorithms proposed by Lin et al. [21]. The results indicated that the
experimental results in comparison with a variety of data sets are               FSLVQ algorithm is better than these generalized Kohonen’s SOM
presented. In Section 5, we apply the S-FSLVQ to an MRI segmenta-                algorithms.
tion in the case study of a patient diagnosed with retinoblastoma of
her left eye. In comparison with some existing LVQ algorithms for                3. Batch fuzzy-soft LVQ
these MRI segmentation results, we find that the proposed algo-
rithm provides better detection of abnormal tissue than others,                       The SOM [2,3] is a useful tool for visualizing high-dimensional
especially in reducing the CPU time. Finally, discussions and con-               data. Basically, it produces a similarity graph of input data and
clusions are presented in Sections 6 and 7, respectively.                        converts the nonlinear statistical relationships between high-
                                                                                 dimensional data into simple geometric relationships of their
                                                                                 image points on a low-dimensional display, usually a regular
2. Related work                                                                  two-dimensional grid of nodes. That is, SOM is a two-layer feed-
                                                                                 forward competitive learning neural network that can discover a
    Kohonen’s SOM is an unsupervised competitive neural network                  topological structure hidden in the data and display it in one or two-
that uses the neighborhood interaction set to approximate lateral                dimensional space. Assume that Wk in an p-dimensional Euclidean
neural interaction and discovers the topological structure hidden                space Rp with its ordinary Euclidean norm ||·|| is the specified weight
in the data for visual display in one or two dimensional space [3].              of the node k and the feature vector xj ∈ Rp is shown on-line at time
Although Kohonen’s competitive learning network originally was                   t, the winner neuron k among all neurons is produced by the nearest
not a clustering method, it could be used as a prototype gener-                  neighbor condition
ation algorithm called a LVQ [3]. Because LVQ updates only the
winner node, Pal et al. [8] proposed a generalization of LVQ (GLVQ)              ||xj − Wk (t − 1)|| = min||xj − Wi (t − 1)||.                     (1)
                                                                                                            i
that updates all nodes for given input data with the learning rule
depending on the degree of distance match to the winner node.                       Eq. (1) indicates that the weight of node k matches best with xj .
Based on the winner-take-most competing strategy, Karayiannis                    Then the self-organization used the following learning rule:
and Pai [9], Karayiannis [10] and Karayiannis et al. [11] proposed               Wi (t) = Wi (t − 1) + ˛i (t)hi,j,k (xj − Wi (t − 1)),             (2)
some fuzzy generalized LVQ (FGLVQ) algorithms. Zhou et al. [12]
discussed the disadvantages of GLVQ and FGLVQ algorithms and                     where ˛i (t) is the learning rate of the node i and is a monotonically
then proposed a revised generalized LVQ (RGLVQ) algorithm to                     decreasing function of time t. The neighborhood function hi,j,k is the
overcome these disadvantages.                                                    lateral neural interaction phenomenon and the degree of excitation
    Yair et al. [13] applied the stochastic relaxation concept to                of the neuron. Usually, hi,j,k is defined as
modify the learning rate and neighborhood function in SOM and
proposed a soft competitive learning network. Combining the                                   1,   if the node i belongs to Nk (t),
                                                                                 hi,j,k =                                                          (3)
competitive learning with soft competition and fuzzy c-means                                  0,   otherwise.
membership functions, Wu and Yang [7] proposed a batch com-
                                                                                 Nk (t) is called the neighborhood set of the winner neuron k and is
petitive learning method called fuzzy-soft LVQ (FSLVQ). Recently,
                                                                                 a decreasing function of time t because it needs to match the WTA
Wu and Yang [14] discussed the influences of noise and outliers
                                                                                 principle. It means that when t → ∞,
on the SOM quality. To reduce the influence of noise and outliers
on SOM, they proposed an alternative LVQ (ALVQ) algorithm, and                                1,   if i = k,
numerical results have shown ALVQ performs well.                                 hi,j,k =                                                          (4)
                                                                                              0,        /
                                                                                                   if i = k.
    Image segmentation is a way to partition image pixels into dif-
ferent cluster regions with similar intensity image values. Cluster                  It is well-known that LVQ for unlabelled data can be viewed as
analysis is a method of clustering a data set into groups dis-                   a special case of SOM. In LVQ, the neighborhood set of each node
playing similar characteristics. It is an approach to unsupervised               will contain the winner node and hence the vectorial location of the
learning and has become one of the major techniques used in                      node is negligible. This competitive learning rule is called the WTA
pattern recognition. Therefore, clustering algorithms would natu-                and the neighborhood function is defined as Eq. (4). From Eq. (2), we
rally be applied in image segmentation. Because most MRIs present                know that, after an on-line feature vector xj is input, the weights
overlapping gray-scale intensities for different tissues, fuzzy clus-            of the nodes in both SOM and LVQ will update toward the input
                                                                        W.-L. Hung et al. / Artificial Intelligence in Medicine 52 (2011) 33–43                                     35


vector with a step size ˛i (t)hi,j,k . Furthermore, LVQ uses the WTA                                          S1 Initialize Wi (0) for each prototype and set the iteration counter
principle to approximate the neural interaction as Eq. (4), which                                                t = 1. Specify the maximum number of iteration max NI and ε.
shows a crisp labelling for each node. Because the neighborhood                                               S2 Compute i (xj ) using Eq. (9), ∀i, j.
set of the winner neuron k is negligible, the index k in hi,j will be                                         S3 Compute hi,j using Eq. (8), ∀i, j.
deleted. Now we rewrite Eq. (4) as                                                                            S4 Compute Wi (t) using Eq. (12).
                                                                                                                        c     p
                                                                                                              S5 If     i=1   l=1
                                                                                                                                  |Wil (t) − Wil (t − 1)| < ε or t = max NI, THEN stop
                 1, if Wi satisfies (1),                                                                          ELSE t = t + 1 and go to Step 2.
hi,j,k =                                                                                            (5)
                 0, if otherwise.
                                                                                                              4. Suppressed FSLVQ
     To extend this crisp type competition, Yair et al. [13] proposed
hi,j with                                                                                                        When the size of the data set under consideration becomes large,
                                                                                                              the computation time of the FSLVQ algorithm will grow rapidly. A
                                       2                                                                      good algorithm should perform well with a large data set, as often
                 e−ˇ(t)||xj −Wi ||
hi,j =          c
                                               ,                                                    (6)       occurs in real application systems. To speed up the FSLVQ, we adopt
                    e−ˇ(t)||xj −Wk ||
                                     2
                k=1                                                                                           the suppression idea of Fan et al. [5] to the FSLVQ and then create
                                                                                                              the S-FSLVQ algorithm. We first modify hi,j in Eq. (8) to be
where ˇ(t) corresponds to a temperature which can be specified by
                                                                                                                                                    −1
users. Based on the learning formula Eq. (2), Yair et al. [13] created a                                                 (1 − ˛ + ˛ i (xj ))(cf (t)) , if i is winner neuron,
soft competition scheme (SCS). The learning rate in this sequential                                           hi,j =                                                             (13)
                                                                                                                         (˛ i (xj ))f (t)/c ,          otherwise.
learning is
                                                                                                              where 0 ≤ ˛ ≤ 1. Note that (i) when ˛ = 0, hi,j is reduced to the WTA
                 1,                                    if t is a perfect square,                              principle and (ii) when 0 < ˛ ≤ 1, hi,j is also reduced to the WTA
˛i (t) =                    1                                                                       (7)       principle as t → ∞. However, the problem of selecting a suitable
                                        ,              otherwise.
                  [1/˛i (t − 1)] + hi,j                                                                       parameter ˛ in S-FSLVQ constitutes an important part of imple-
                                                                                                              menting the S-FSLVQ algorithm for real applications. Based on the
To solve Yair et al.’s [13] problems such as the selection of the neigh-                                      concept of machine learning, we use the idea of Hung et al. [6]
borhood functions and unstable reinitialization in the SCS, Wu and                                            to solve this problem. That is, the learning process of ˛ is based
Yang [7] apply a fuzzy function to approximate hi,j with                                                      on an exponential separation strength between prototypes with
                                                                                                              updating at each iteration. Therefore, we choose ˛ as follows:
                                               1+f (t)/c
                           i (xj )                                                                                              mini = k ||Wi − Wk ||2
hi,j =                                                     ,                                        (8)       ˛ = exp      −
                                                                                                                                     /
                                                                                                                                                            ,                    (14)
                max1≤k≤c             k (xj )                                                                                                   s

where                                                                                                         where
                                                                                                                       n                            n
                                                               −1                                                      j=1
                                                                                                                           ||xj   − x||2
                                                                                                                                    ¯                  x
                                                                                                                                                    j=1 j
                      c
                           ||xj − Wi       ||2/(m−1)                                                          s=                           ,   x=
                                                                                                                                               ¯            .
            =                                                       ,                                                       n                       n
  i (xj )                                                                                           (9)
                           ||xj − Wk       ||2/(m−1)                                                          Thus, the S-FSLVQ algorithm is summarized as follows:
                   k=1
                                                                                                                S-FSLVQ algorithm
and the inhibition function f(t) > 0 is a monotone strict function of
t that is used to control the degree of inhibition within the neural                                          S1 Initialize Wi (0) for each prototype and set the iteration counter
lateral interaction. They also suggested the learning rate with                                                  t = 1. Specifying the maximum number of iteration max NI and
                                                                                                                 ε.
                       ˛i (t)                                                                                 S2 Compute i (xj ) using Eq. (9), ∀i, j.
˛i (t + 1) =                                                                                      (10)
                    1 + ˛i (t)hi,j                                                                            S3 Compute ˛ using Eq. (14).
                                                                                                              S4 Compute hi,j using Eq. (13), ∀i, j.
which is equivalent to the optimal learning rate in SOM [3]. The                                              S5 Compute Wi (t) using Eq. (12).
constraint of f(t), that is, limt→∞ f(t) = ∞, leads to the learning rule                                                c     p
                                                                                                              S6 If     i=1
                                                                                                                                 W (t) − Wil (t − 1)| < ε or t = max NI, THEN stop
                                                                                                                              l=1 il
of this on-line FSLVQ tending toward WTA as t → ∞.                                                               ELSE t = t + 1 and go to Step 2.
    Assume that the sample size of feature vectors is fixed, the batch
version of FSLVQ is the same construction of batch SOM assum-                                                     In order to examine and compare the performance of S-FSLVQ
ing that the algorithm will converge to a stationary state W*. This                                           with FSLVQ, ALVQ, GLVQ and RGLVQ algorithms, the two criteria
means that the expectation values of Wi (t) and Wi (t − 1) in FSLVQ                                           of accuracy and computational efficiency are used. The accuracy of
must be equal as t → ∞. That is,                                                                              an algorithm is measured by the mean squared error (MSE), that is,
                                                                                                              the average sum of squared error between the true parameter and
E(hi,j (xj − Wi∗ )) = 0.                                                                          (11)        the estimated in N repeated trials. The computational efficiency of
                                                                                                              an algorithm is measured by the average numbers of iterations (NI)
Using the empirical function to solve the above equation, the batch                                           and the CPU time in N repeat trials. Next, we consider the normal
learning formula of FSLVQ is obtained as                                                                      mixture distribution consisting of 2 subpopulations, that is,

                  h x
                 j i,j j                                                                                      pN(0, 1) + (1 − p)N( , 1)
Wi∗ =                      ,                                                                      (12)
                   h
                  j i,j                                                                                       where 0 < p < 1. The data are generated by this distribution with
                                                                                                              sample size n = 100 and the number of trials N = 200. Table 1 shows
where hi,j is defined as Eq. (8). Wi∗ is the weighted mean of all fea-                                         various p and .
ture vectors whose weighted functions are the lateral interaction                                                Similar to Wu and Yang [7], we consider three inhibition func-
                                                                                                                             √
functions. The algorithm of batch FSLVQ is as follows:                                                        tions f(t) with t, t and t2 to control the neural lateral interaction in
   FSLVQ algorithm                                                                                            FSLVQ and S-FSLVQ. According to the three kinds of f(t), these two
36                                                  W.-L. Hung et al. / Artificial Intelligence in Medicine 52 (2011) 33–43

Table 1
Normal mixture distributions for the numerical tests.

 Test A                             A1               A2                          A3

 p                                  0.1              0.1                         0.1
                                    1                1.5                         2.0

 Test B                             B1              B2                           B3

 p                                  0.3             0.3                          0.3
                                    1               1.5                          2.0

 Test C                             C1              C2                           C3

 p                                  0.5             0.5                          0.5
                                    1               1.5                          2.0
                                                                                                                                                                          √
                                                                                              Fig. 2. Values of CPU time for S-FLVQ and FLVQ algorithms with f (t) =       t.

algorithms and the ALVQ, GLVQ and RGLVQ algorithms are imple-
mented under the same specifying initial values Wi (0), ε = 0.001,
max NI = 50 and m = 2. The MSE is defined as
     N     2     (k)            2
     k=1   i=1
               (ˆi     −   i)
               2N
                                                           (k)
where i is the true subpopulation mean and ˆ i is the estimated
value of i for the k-th trial. Tables 2, 3 and 5 show the simula-
tion results of FSLVQ, S-FSLVQ, ALVQ, GLVQ and RGLVQ algorithms,
respectively. To compare the performance of S-FSLVQ, we consider
the ratios of MSE, NI and CPU time. They are defined as follows:
               MSE obtained by S-FSLVQ
r(MSE) =                               ,
               MSE obtained by others
               NI obtained by S-FSLVQ
     r(NI) =                          ,                                                            Fig. 3. Values of MSE for S-FLVQ and FLVQ algorithms with f(t) = t.
                NI obtained by others
               CPU time obtained by S-FSLVQ
r(time) =                                   .
                CPU time obtained by others

   Clearly, if these ratio values are less than 1 then the perfor-
mance of S-FSLVQ is better than others according to the criteria
of accuracy and computational efficiency. Tables 4 and 6 show
these ratio values. From Table 2 (i.e. S-FSLVQ algorithm), f(t) = t
                                                √
has higher accurate than the use of f (t) = t, t 2 and has better
computational efficiency. From√    Table 3 (i.e. FSLVQ algorithm), the
slow increasing rate of f (t) = t, t has also high accuracy than
the use of f(t) = t2 . The fast increasing rate of f(t) = t2 has bet-
ter computational efficiency. The MSEs √      and the CPU times for
S-FLVQ and FLVQ algorithms with f (t) = t, t and t2 are depicted  √
in Figs. 1–6. From these figures, we find that (i) except f (t) = t,
S-FSLVQ algorithm has better accuracy than FSLVQ algorithm for
most of cases and (ii) the S-FSLVQ algorithm has better com-                                    Fig. 4. Values of CPU time for S-FLVQ and FLVQ algorithms with f(t) = t.
putational efficiency than FSLVQ algorithm. Furthermore, it can
be found that the S-FSLVQ algorithm has better computational




                                                                                                  Fig. 5. Values of MSE for S-FLVQ and FLVQ algorithms with f(t) = t2 .
                                                                           √
       Fig. 1. Values of MSE for S-FLVQ and FLVQ algorithms with f (t) =    t.
                                                   W.-L. Hung et al. / Artificial Intelligence in Medicine 52 (2011) 33–43                                  37

Table 2
Values of MSE, NI and CPU time for the S-FSLVQ algorithm.
                        √
  Test           f (t) = t                                             f(t) = t                                             f(t) = t2

                 MSE              NI              CPU time             MSE                NI               CPU time         MSE          NI        CPU time

 A1              0.2944           9.41            0.797                0.2868             5.53             0.484            0.3078       5.00      0.469
 A2              0.3860           9.58            0.813                0.3771             5.54             0.468            0.3906       4.82      0.453
 A3              0.5258           9.79            0.828                0.5232             5.62             0.485            0.5182       4.82      0.437
 B1              0.2080           9.47            0.813                0.2029             5.64             0.484            0.2123       5.08      0.469
 B2              0.1448           9.64            0.813                0.1408             5.73             0.484            0.1490       5.17      0.469
 B3              0.1142           9.50            0.813                0.1105             5.72             0.484            0.1152       5.10      0.453
 C1              0.1927           9.59            0.828                0.1939             5.67             0.485            0.1950       5.15      0.484
 C2              0.1074           9.42            0.797                0.1082             5.40             0.468            0.1087       4.69      0.437
 C3              0.0690           9.33            0.797                0.0688             5.34             0.453            0.0685       4.57      0.422


Table 3
Values of MSE, NI and CPU time for the FSLVQ algorithm.
                       √
  Test          f (t) = t                                              f(t) = t                                             f(t) = t2

                MSE               NI              CPU time             MSE                NI                CPU time        MSE          NI        CPU time

 A1             0.2729            28.66           1.281                0.2931             18.99             0.860           0.3058       9.21      0.484
 A2             0.3700            30.16           1.328                0.3774             19.81             0.891           0.3852       9.11      0.469
 A3             0.5181            32.21           1.422                0.4976             21.10             0.937           0.4957       9.44      0.484
 B1             0.1836            28.91           1.297                0.2049             19.43             0.875           0.2115       9.26      0.485
 B2             0.1267            31.31           1.375                0.1417             20.78             0.922           0.1465       9.48      0.484
 B3             0.1011            32.38           1.422                0.1073             21.80             0.969           0.1099       9.57      0.500
 C1             0.1692            30.42           1.344                0.1938             20.11             0.907           0.1986       9.36      0.500
 C2             0.0907            30.70           1.375                0.1105             21.19             0.953           0.1121       9.34      0.484
 C3             0.0560            31.02           1.453                0.0690             21.62             0.953           0.0699       9.18      0.469


Table 4
Ratio values of MSE, NI and CPU time for the S-FSLVQ algorithm.
                        √
  Test           f (t) = t                                             f(t) = t                                             f(t) = t2

                r(MSE)            r(NI)             r(time)            r(MSE)             r(NI)              r(time)        r(MSE)       r(NI)       r(time)

 A1             1.0788            0.3283            0.6222             0.9785             0.2912             0.5628         1.0065       0.5429      0.9690
 A2             1.0432            0.3176            0.6122             0.9992             0.2797             0.5253         1.0140       0.5291      0.9659
 A3             1.0149            0.3039            0.5823             1.0514             0.2664             0.5176         1.0454       0.5106      0.9029
 B1             1.1329            0.3276            0.6268             0.9902             0.2903             0.5531         1.0038       0.5486      0.9670
 B2             1.1429            0.3079            0.5913             0.9936             0.2757             0.5249         1.0171       0.5454      0.9690
 B3             1.1296            0.2934            0.5717             1.0298             0.2624             0.4995         1.0482       0.5329      0.9060
 C1             1.1389            0.3153            0.6161             1.0005             0.2819             0.5347         0.9819       0.5502      0.9680
 C2             1.1841            0.3068            0.5796             0.9792             0.2548             0.4911         0.9697       0.5021      0.9029
 C3             1.2321            0.3008            0.5485             0.9971             0.2470             0.4753         0.9800       0.4978      0.8998


Table 5
Values of MSE, NI and CPU time for the ALVQ, GLVQ and RGLVQ algorithms.

 Algorithm             ALVQ                                                GLVQ                                                 RGLVQ

 Test                  MSE             NI             CPU time             MSE                 NI               CPU time        MSE        NI        CPU time

 A1                    0.4569          26.97          39.141                41.5391            50.00            29.734          0.5867     50.00     34.766
 A2                    0.5888          26.47          38.047               183.0225            50.00            29.579          0.4553     50.00     34.703
 A3                    0.7765          27.58          39.844                58.3944            50.00            29.359          0.9353     50.00     34.750
 B1                    0.4031          24.18          35.156               218.8366            50.00            29.547          0.2415     50.00     34.703
 B2                    0.3988          28.86          41.406                38.2463            50.00            29.547          0.1670     50.00     35.157
 B3                    0.4505          30.44          44.703                 5.8623            50.00            29.813          0.3793     50.00     35.094
 C1                    0.2620          24.05          34.797                82.7799            49.99            29.391          0.2627     50.00     34.594
 C2                    0.2353          27.45          39.734                93.2109            50.00            29.500          0.2360     50.00     34.829
 C3                    0.2431          30.57          44.344                 6.1174            50.00            29.578          0.2438     50.00     34.687


Table 6
Ratio values of MSE, NI and CPU time for the S-FSLVQ algorithm.

 Test           ALVQ                                                   GLVQ                                                 RGLVQ

                r(MSE)            r(NI)             r(time)            r(MSE)             r(NI)              r(time)        r(MSE)       r(NI)       r(time)

 A1             0.6634            0.2050            0.0124             0.0073             0.1106             0.0163         0.8580       0.1106      0.0139
 A2             0.6596            0.2093            0.0123             0.0021             0.1108             0.0158         0.8531       0.1108      0.0135
 A3             0.6738            0.2038            0.0122             0.0090             0.1124             0.0165         0.5594       0.1124      0.0140
 B1             0.5220            0.2333            0.0138             0.0010             0.1128             0.0164         0.8712       0.1128      0.0139
 B2             0.3694            0.1985            0.0117             0.0039             0.1146             0.0164         0.8820       0.1146      0.0138
 B3             0.2542            0.1879            0.0108             0.0195             0.1144             0.0162         0.3019       0.1144      0.0138
 C1             0.7401            0.2358            0.0139             0.0023             0.1134             0.0165         0.7381       0.1134      0.0140
 C2             0.4598            0.1967            0.0118             0.0012             0.1080             0.0159         0.4585       0.1080      0.0134
 C3             0.2830            0.1747            0.0102             0.0112             0.1068             0.0153         0.2822       0.1068      0.0131
38                                                   W.-L. Hung et al. / Artificial Intelligence in Medicine 52 (2011) 33–43


                                                                                           Although GLVQ (Fig. 7(5)) can distinguish the tumor, its perfor-
                                                                                           mance is not good, and RGLVQ (Fig. 7(6)) cannot distinguish the
                                                                                           tumor from the healthy tissue.
                                                                                               MRI medical imaging uncertainty is widely present in the col-
                                                                                           lected data because of noise in the partial volume effects originating
                                                                                           from the low resolution of the sensors. Another factor causing
                                                                                           uncertainty is the fact that the eyeball moves during the imaging
                                                                                           and it is difficult to control this movement, especially in younger
                                                                                           patients. A distorted MR image, shown in Fig. 8, is used here to
                                                                                           illustrate how an algorithm can detect tumorous tissue, despite
                                                                                           uncertainty of the image. Using the AFCM with m = 2 (Fig. 8(1)),
                                                                                           S-FSLVQ (Fig. 8(2)), FSLVQ (Fig. 8(3)) and ALVQ (Fig. 8(4)), we can
                                                                                           still detect the tumorous tissue. But GLVQ (Fig. 8(5)) and RGLVQ
                                                                                           (Fig. 8(6)) fail.
     Fig. 6. Values of CPU time for S-FLVQ and FLVQ algorithms with f(t) = t2 .
                                                                                               Fig. 9 in the second MRI data set was processed at 283 × 292
                                                                                           pixels. From this picture, one lesion was clearly seen in the MR
efficiency and is more accurate than the FSLVQ algorithm when                               image. However, some fuzzy shadows of lesions were suspected
f(t) = t.                                                                                  to be tumor invasion though these suspected abnormalities cannot
    Next, we compare the performance of the S-FSLVQ algorithm                              easily be ascertained as tumorous. To detect these abnormal tis-
(f(t) = t) with the ALVQ, GLVQ and RGLVQ algorithms according the                          sues, a window of the area around the chiasma was selected from
ratios of MSE, NI and the CPU time. The results of Table 6 indicate                        the original MR images as shown in Fig. 9. First, we applied AFCM,
that the S-FSLVQ algorithm has better computational efficiency and                          S-FSLVQ and FSLVQ to the window selection as illustrated in Fig.
is more accurate than the ALVQ, GLVQ and RGLVQ algorithms.                                 9(1)–(3). We can see that occult lesions (red circles) were clearly
    As supported by the above experiments, the S-FSLVQ algorithm                           enhanced with AFCM (m = 2) in Fig. 9(1) and S-FSLVQ in Fig. 9(2).
has better computational efficiency and is more accurate than the                           The results shown in Fig. 9(3) show FLVQ can indicate these occult
FSLVQ, ALVQ, GLVQ and RGLVQ algorithms when f(t) = t. In the next                          lesions. Next, we use the ALVQ, GLVQ and RGLVQ algorithms to
section, we will apply these algorithms to an MRI segmentation.                            segment this image and the segmentation results, respectively, as
                                                                                           depicted in Fig. 9(4)–(6). With ALVQ Fig. 9(4) does not clearly indi-
5. Application to ophthalmological MRI segmentation                                        cate the occult lesions on the right upper corner; with GLVQ Fig. 9(5)
                                                                                           shows poor segmentation performance; while Fig. 9(6) shows that
    Segmentation of medical images obtained from MRI is a pri-                             RGLVQ can indicate these occult lesions.
mary step in most applications of computer vision for medical                                  In order to examine and compare the performance of S-FSLVQ,
image analysis. Yang et al. [20] applied an alternative fuzzy c-means                      the following two criteria are used: the number of iterations (NI)
(AFCM) algorithm, proposed by Wu and Yang [23], in a real case                             and the CPU time until convergence as an indication of the needed
study of MRI segmentation to differentiate normal and abnormal                             computing time. Table 7 shows the computational performance of
tissue in ophthalmology. The MRI data sets were from a 2-year-                             these algorithms. From Table 7, we find that (i) in Fig. 7, the pro-
old female patient. She was diagnosed with retinoblastoma of her                           posed S-FLVQ algorithm reduces the CPU time by 345.2, 7682.3,
left eye, an inborn malignant neoplasm of the retina with frequent                         10779.1, 12557%, compared with FSLVQ, ALVQ, GLVQ and RCLVQ
metastasis beyond the lacrimal cribrosa. The MRI images showed an                          algorithms, respectively; (ii) in Fig. 8, the proposed S-FLVQ algo-
intra-muscle cone tumor mass with high T1-weight signal images                             rithm reduces the CPU time by 334.7, 7659.1, 10901.2, 12612.9%,
and low T2-weight signal images in the left eyeball. The tumor                             compared with FSLVQ, ALVQ, GLVQ and RCLVQ algorithms, respec-
measured 20 mm in diameter and occupied nearly the entire vit-                             tively; and (iii) in Fig. 9, the proposed S-FLVQ algorithm reduces
reous cavity. There was a shady signal abnormality all along the                           the CPU time by 870.4, 26638.7, 24460.2, 27975.3%, compared with
optic nerve reaching as far as the optic chiasma near the brain. In                        FSLVQ, ALVQ, GLVQ and RCLVQ algorithms, respectively. These
this current study we use S-FSLVQ, FSLVQ, ALVQ, GLVQ and RGLVQ                             results show the superiority of the proposed S-FLVQ algorithm over
algorithms with max NI = 500 to analyze these MRI data sets. The                           the other algorithms.
first MRI data set is illustrated in Figs. 7 and 8 and the second MRI                           On the other hand, to evaluate detection of abnormal tissue,
data set is shown in Fig. 9. We first attempt to cluster the full size                      it is necessary to make a quantitative comparison of the image,
images (Figs. 7 and 8) into the same five clusters used by Yang et al.                      segmented by each algorithm, with a reference image. Because
[20]: muscle tissue, connective tissue, nerve tissue, the lens, and                        the segmentation results with AFCM (m = 2) in Figs. 7–9 can suc-
tumor tissue. According to Yang et al. [20], a window as shown in                          cessfully differentiate the tumor from the normal tissues [20],
Fig. 9 can be used to enhance areas of the tumor to better detect                          Figs. 7(1), 8(1) and 9(1) are considered as reference images. The
small tumors. We also apply the above algorithms to segmenting                             comparison score S [16,24] for each algorithm is defined as
the image shown in Fig. 9. The lens and muscle tissue are excluded
from the window so that the original five categories are reduced
to three; connective tissue, nervous tissue and tumor tissue. A gray                            |A ∩ Aref |
                                                                                           S=
scale histogram comparison shows that there are actually three                                  |A ∪ Aref |
peaks appearing for the image.
    The two pictures (Figs. 7 and 8) were processed at 400 × 286
pixels. The sample size of these two pictures is 114,400 and the                           where A represents the set of pixels belonging to the tumor tissue
data take values on the gray levels from 0 to 255. From the red                            found by a algorithm and Aref represents the set of pixels belonging
circle on the full-sized two-dimensional MRI in Fig. 7, we can                             to the tumor tissue in the reference segmented image. The value
clearly detect white tumor tissue at the chiasma. The segmenta-                            of S (0 ≤ S ≤ 1) describes the degree of similarity between A and
tion results by AFCM with m = 2 (Fig. 7(1)), S-FSLVQ with f(t) = t                         Aref , where the greater the value of S, the higher the segmentation’s
(Fig. 7(2)), FSLVQ with f(t) = t (Fig. 7(3)), ALVQ (Fig. 7(4)) can dis-                    quality. Moreover, adopting the similar idea of false negative and
tinguish the tumor from the healthy tissue using five clusters.                             false positive from Fernández-García et al. [25], we may also define
                                                       W.-L. Hung et al. / Artificial Intelligence in Medicine 52 (2011) 33–43                                                     39




Fig. 7. Original MR image. (1) Segmentation result of AFCM (S = 1, FN = 0, FP = 0). (2) Segmentation result of S-FSLVQ (S = 0.9091, FN = 0.0909, FP = 0). (3) Segmentation result
of FSLVQ (S = 0.9091, FN = 0.0909, FP = 0). (4) Segmentation result of ALVQ (S = 0.9091, FN = 0.0909, FP = 0). (5) Segmentation result of GLVQ (S = 0.6667, FN = 0, FP = 0.0067). (6)
Segmentation result of RGLVQ (S = 0.0133, FN = 0, FP = 1).


the following two error types based on A and Aref :                                          the proposed S-FSLVQ algorithm can detect tumorous tissue more
                                                                                             accurately than the others.
                              |Aref ∩ Ac |                                   |Ac ∩ A|
                                                                               ref
False Negative (FN) =                        ,   False Positive (FP) =
                                 |Aref |                                       |Ac |
                                                                                 ref         6. Discussion

where Aref    ∩ Ac
                represents that the set of pixels in Aref has not been
                                                                                                 Combining the concept of suppression [5] and machine learn-
detected as tumor tissue by a algorithm, and Ac ∩ A represents
                                                    ref                                      ing [6], we propose using the S-FSLVQ algorithm to speed up the
that the set of pixels in Ac has been detected as tumor tissue
                            ref                                                              LVQ calculations. First, we reviewed the related LVQ algorithms,
by a algorithm, and Ac and Ac represent the complements of A
                                ref                                                          which include ALVQ, GLVQ and RGLVQ algorithms. Furthermore,
and Aref , respectively. The values of S, FN and FP corresponding                            the technical details of the FSLVQ algorithm are described in Section
to these algorithms are shown in Table 6. The results show that                              3. These algorithms were implemented on a variety of 2-mixture
40                                                    W.-L. Hung et al. / Artificial Intelligence in Medicine 52 (2011) 33–43




Fig. 8. Distorted MR image. (1) Segmentation result of AFCM (S = 1, FN = 0, FP = 0). (2) Segmentation result of S-FSLVQ (S = 07374, FN = 0.2626, FP = 0). (3) Segmentation result
of FSLVQ (S = 0.6403, FN = 0.3597, FP = 0). (4) Segmentation result of ALVQ (S = 0.7374, FN = 0.2626, FP = 0). (5) Segmentation result of GLVQ (S = 0.1679, FN = 0, FP = 1). (6)
Segmentation result of RGLVQ (S = 0.1679, FN = 0, FP = 1)



normal data sets. The proposed S-FSLVQ algorithm based on the                               the segmented images. Table 6 shows that the proposed algorithm
criteria of accuracy and computation time outperformed others.                              is more accurate than other algorithms for detecting tumorous tis-
    To evaluate how well these algorithms worked for large data                             sue.
sets, we applied them to a real case study of MRI segmentation to                               Furthermore, Alzheimer’s disease (AD) and vascular dementia
differentiate normal and abnormal tissue in ophthalmology. Details                          are the two most common diseases causing dementia. A change
of the data set are given in Section 5. The key issue in the present                        in hippocampal volume is found by brain MRI in individuals with
analysis was whether the proposed algorithm could improve the                               mild cognitive impairment (MCI). Although these MCI individuals
computation time. As depicted in Table 7, the proposed algorithm                            did not have stroke nor neurological deficits, about two-thirds of
provided a significant improvement in computational efficiency, as                            them had at least one subcortical lacunar infarct. The proposed
measured by the NI and CPU time. To analyze how far these seg-                              risk factors for converting MCI to AD include apolipoprotein E4,
mentation results of the different algorithms are from the reference                        delayed recall, smaller hippocampal volume and decreased blood
segmented image, the values of S, FN and FP were computed over                              flow on brain HMPAO-SPECT, but there is no universal agreement.
                                                     W.-L. Hung et al. / Artificial Intelligence in Medicine 52 (2011) 33–43                                                 41

Table 7
The execution time and a quantitative comparison of the algorithms S-FSLVQ, FSLVQ, ALVQ, GLVQ and RGLVQ for Figs. 1–3.

  Criterion                     Figures                  S-FSLVQ                    FSLVQ                    ALVQ                      GLVQ                        RGLVQ

  NI                            Fig. 1                  28                       163                         188                       500                         500
                                Fig. 2                  28                       159                         187                       500                         500
                                Fig. 3                  16                       246                         274                       500                         500

  CPU time(s)                   Fig. 1                  22.062                     98.219                    1716.937                  2400.140                    2792.391
                                Fig. 2                  22.063                     95.906                    1711.891                  2427.203                    2804.844
                                Fig. 3                   5.969                     57.922                    1596.031                  1466.000                    1675.812

  S                             Fig. 1                   0.9091                     0.9091                   0.9091                    0.6667                      0.0133
                                Fig. 2                   0.7374                     0.6403                   0.7374                    0.1679                      0.1679
                                Fig. 3                   1                          0.9103                   0.8138                    0.3034                      0.7360

  FN                            Fig. 1                   0.0909                     0.0909                   0.0909                    0                           0
                                Fig. 2                   0.2626                     0.3597                   0.2626                    0                           0
                                Fig. 3                   0                          0.0897                   0.1862                    0.6966                      0

  FP                            Fig. 1                   0                          0                        0                         0.0067                      1
                                Fig. 2                   0                          0                        0                         1                           1
                                Fig. 3                   0                          0                        0                         0                           0.0122




Therefore, the accuracy of calculating the hippocampal volume in                            in the remedial temporal lobe. Thus, the segmentation efficiency
the remedial temporal lobe is a main concern for predicting the                             and accuracy are very important for the AD MRI data sets. In our
conversion of MCI to AD. Many MRI data sets which contain the hip-                          future work, we will apply the proposed S-FSLVQ algorithm to real
pocampus are added together to calculate the hippocampal volume                             AD MRI data sets and make more advanced analysis.




Fig. 9. Original MR image and its window selection. (1) Segmentation result of AFCM (S = 1, FN = 0, FP = 0). (2) Segmentation result of S-FSLVQ (S = 1, FN = 0, FP = 0). (3)
Segmentation result of FSLVQ (S = 0.9103, FN = 0.0897, FP = 0). (4) Segmentation result of ALVQ (S = 0.8138, FN = 0.1862, FP = 0). (5) Segmentation result of GLVQ (S = 0.3034,
FN = 0.6966, FP = 0). (6) Segmentation result of RGLVQ (S = 0.7360, FN = 0, FP = 0.0122).
42                                         W.-L. Hung et al. / Artificial Intelligence in Medicine 52 (2011) 33–43




                                                                   Fig. 9. (Continued).




7. Conclusions                                                                   References

   In this paper we modify the FSLVQ proposed by Wu and Yang                      [1] Lippmann RP. An introduction to computing with neural nets. IEEE ASSP Mag-
                                                                                      azine 1987:4–22.
[7] and then propose a suppressed version of FSLVQ algorithm. In                  [2] Kohonen T. The self-organizing map. Neurocomputing 2003;21:1–6.
the S-FSLVQ, we use a learning technique to search for the param-                 [3] Kohonen T. Self-organizing map. Berlin: Springer; 2001.
eter ˛. From the simulation results, we find that the advantages                   [4] Cheng Y. Convergence and ordering of Kohonen’s batch map. Neural Compu-
                                                                                      tation 1997;9:1667–76.
of S-FSLVQ algorithm are more accurate and reduce computation                     [5] Fan JL, Zhen WZ, Xie WX. Suppressed fuzzy c-means clustering algorithm. Pat-
time. Finally, the S-FSLVQ algorithm is applied in the segmenta-                      tern Recognition Letters 2003;24:1607–12.
tion of the MRI of an ophthalmic patient. The results show that the               [6] Hung WL, Yang MS, Chen DH. Parameter selection for suppressed fuzzy c-
                                                                                      means with an application to MRI segmentation. Pattern Recognition Letters
S-FSLVQ provides better detection of abnormal tissue than FSLVQ,                      2006;27:424–38.
ALVQ, GLVQ and RGLVQ. Furthermore, the S-FSLVQ can reduce the                     [7] Wu KL, Yang MS. A fuzzy-soft learning vector quantization. Neurocomputing
number of iterations and the CPU time. Therefore, the proposed                        2003;55:681–97.
                                                                                  [8] Pal NR, Bezdek JC, Tsao ECK. Generalized clustering networks and Kohonen’s
S-FSLVQ is a good algorithm for real applications and is highly rec-
                                                                                      self-organizing scheme. IEEE Transactions on Neural Networks 1993;4:549–57.
ommended for use in MRI segmentation as an aid for supportive                     [9] Karayiannis NB, Pai PI. Fuzzy algorithms for learning vector quantization. IEEE
diagnoses.                                                                            Transactions on Neural Networks 1996;7:1196–211.
                                                      W.-L. Hung et al. / Artificial Intelligence in Medicine 52 (2011) 33–43                                                  43


[10] Karayiannis NB. A methodology for constructing fuzzy algorithms for learning                  images of a hemorrhagic glioblastoma multiforme. Magnetic Resonance Imag-
     vector quantization. IEEE Transactions on Neural Network 1997;8:505–18.                       ing 1995;13:277–90.
[11] Karayiannis NB, Pai PI, Zervos N. Image compress based on fuzzy algorithms for         [19]   Suckling J, Sigmundsson T, Greenwood K, Bullmore ET. A modified fuzzy clus-
     learning vector quantization and wavelet image decomposition. IEEE Transac-                   tering algorithm for operator independent brain tissue classification of dual
     tions on Image Processing 1998;7:1223–30.                                                     echo MR images. Magnetic Resonance Imaging 1999;17:1065–76.
[12] Zhou SS, Wang WW, Zhou LH. A new technique for generalized learning vector             [20]   Yang MS, Hu YJ, Lin KCR, Lin CCL. Segmentation techniques for tissue differen-
     quantization algorithm. Image and Vision Computing 2006;24:649–55.                            tiation in MRI of ophthalmology using fuzzy clustering algorithms. Magnetic
[13] Yair E, Zeger K, Gersho A. Competitive learning and soft competition for vector               Resonance Imaging 2002;20:173–9.
     quantizer design. IEEE Transactions on Signal Processing 1992;40:294–309.              [21]   Lin KCR, Yang MS, Liu HC, Lirng JF. Generalized Kohonen’s competitive learning
[14] Wu KL, Yang MS. Alternative learning vector quantization. Pattern Recognition                 algorithms for ophthalmological MR image segmentation. Magnetic Resonance
     2006;39:351–62.                                                                               Imaging 2003;21:863–70.
[15] Ahmed MN, Yamany SM, Mohamed N, Farag AA, Moriarty T. A modified fuzzy                  [22]   Yang MS, Lin KCR, Liu HC, Lirng JF. Magnetic resonance imaging segmentation
     c-means algorithm for bias field estimation and segmentation of MRI data. IEEE                 techniques using batch-type learning vector quantization algorithms. Magnetic
     Transactions on Medical Imaging 2002;21:193–9.                                                Resonance Imaging 2007;25:265–77.
[16] Masulli F, Schenone A. A fuzzy clustering based segmentation system as                 [23]   Wu KL, Yang MS. Alternative c-means clustering algorithms. Pattern Recogni-
     support to diagnosis in medical imaging. Artificial Intelligence in Medicine                   tion 2002;35:2267–78.
     1999;16:129–47.                                                                        [24]   Zhang DQ, Chen SC. A novel kernelized fuzzy c-means algorithm with appli-
[17] Pham DL, Prince JL. Adaptive fuzzy segmentation of magnetic res-                              cation in medical image segmentation. Artificial Intelligence in Medicine
     onance images. IEEE Transactions on Medical Imaging 1999;18:                                  2004;32:37–50.
     737–52.                                                                                [25]   Fernández-García NL, Medina-Carnicer R, Carmona-Poyato A, Madrid-Cuevas
[18] Philips WE, Velthuizen RP, Phuphanich S, Hall LO, Clarke LP, Silbiger ML. Appli-              FJ, Prieto-Villegas M. Characterization of empirical discrepancy evaluation
     cation of fuzzy c-means segmentation technique for differentiation in MR                      measures. Pattern Recognition Letters 2004;25:35–47.

								
To top