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					                      g                 g
           Parallel Algorithms for Mining 
                  Large‐
                  Large‐Scale Data


                       Edward Chang
                       Ed   d Ch
                Director, Google Research, Beijing
              http://infolab.stanford.edu/ echang/
              http://infolab stanford edu/~echang/



Ed Chang                   EMMDS 2009                1
Ed Chang   EMMDS 2009   2
Ed Chang   EMMDS 2009   3
                 Story of the Photos
                 Story of the Photos
   •   The photos on the first pages are statues of two
       “bookkeepers” displayed at the British Museum. One
       bookkeeper keeps a list of good people, and the other a list of
       bad. (Who is who, can you tell ? ☺)
   •   When I first visited the museum in 1998, I did not take a
       photo of them to conserve films. During this trip (June 2009),
       capacity is no longer a concern or constraint. In fact, one can
           kids,      d       ll taking h t     lot f h t
       see kid grandmas all t ki photos, a l t of photos. T    Ten
       years apart, data volume explodes.
   •   Data complexity also grows.
   •   So, can these ancient “bookkeepers” still classify good from
       bad? Is their capacity scalable to the data dimension and
       data quantity ?

Ed Chang                        EMMDS 2009                               4
Ed Chang   EMMDS 2009   5
                              Outline
  • Motivating Applications 
      – Q&A System
      – Social Ads
  • Key Subroutines
      –    Frequent Itemset Mining [ACM RS 08]
      –    L      Di i hl All      i
           Latent Dirichlet Allocation  [WWW 09, AAIM 09]
      –    Clustering [ECML 08]
      –    UserRank [Google TR 09]
           UserRank [Google TR 09]
      –    Support Vector Machines [NIPS 07]
    Distributed Computing Perspectives
  • Distributed Computing Perspectives
Ed Chang                       EMMDS 2009                   6
Query: What are must‐see attractions at Yellowstone




 Ed Chang               EMMDS 2009                    7
Query: What are must‐see attractions at Yellowstone




 Ed Chang               EMMDS 2009                    8
Query: Must‐see attractions at Yosemite




 Ed Chang               EMMDS 2009        9
Query: Must‐see attractions at Copenhagen




 Ed Chang              EMMDS 2009           10
Query: Must‐see attractions at Beijing



                Hotel ads




   Ed Chang               EMMDS 2009     11
           Who is Yao Ming




Ed Chang             EMMDS 2009   12
 Q&A Yao Ming
 Q&A Yao Ming




Ed Chang        EMMDS 2009   13
           Who is Yao Ming            Yao Ming Related Q&As
                                      Y Mi     R l t d Q&A




Ed Chang                 EMMDS 2009                           14
     Application: Google Q&A (Confucius)
               launched in China, Thailand, and Russia
               launched in China Thailand and Russia
                              Differentiated Content


                                      DC
           U

                    S                                     C
                 Search                                            U
                                                       Community

                                   CCS/Q&A

                                 Discussion/Question


       Trigger a discussion/question session during search
       Provide labels to a Q (semi-automatically)
       Given a Q, find similar Qs and their As (automatically)
       Evaluate quality of an answer, relevance and originality
       Evaluate          d ti l in topic         iti
       E l t user credentials i a t i sensitive way
       Route questions to experts
       Provide most relevant, high-quality content for Search to index


Ed Chang                         EMMDS 2009                              15
           Q&A Uses Machine Learning



                        Label suggestion
                        using ML algorithms.




                       • Real Time topic-to-
                         topic (T2T)
                         recommendation
                         using ML algorithms.

                       • Gi        t l t d high
                         Gives out related hi h
                         quality links to
                         previous questions
                         before human answer
                         appear.



Ed Chang            EMMDS 2009                    16
                Collaborative Filtering
                                                  Books/Photos
                                              1 1 1
                                          1       1 1       1       1       1
Based on membership so far,                             1       1           1
 and memberships of others                1       1     1 1
                                              1


                              Users
                                                            1 1
Predict further membership                        1                 1
                                      1 1
                                          1                             1
                                      1                                     1
                                          1 1 1 1 1

 Ed Chang                     EMMDS 2009                                    17
                      Collaborative Filtering
                                                                Books/Photos
        Based on partially                      ?       1 1 1           ?
        observed matrix                             1 ? 1 1             1       1       1
                                                                    1 ? 1               1
                                                    1       1 ? 1 1
  Predict unobserved entries
                                                        1                   ?


                                        Users
                                                    ?                   1 1

                                        U
                                                            1                   1 ?
I. Will user i enjoy photo j?                   1 1             ?
                                                    1               ?               1
II. Will user i be interesting to user j?
                                                1                               ?       1
III. Will photo i be related to photo j?            1 1 1 1 1 ?

    Ed Chang                           EMMDS 2009                                       18
           FIM based Recommendation
           FIM‐based Recommendation




Ed Chang            EMMDS 2009        19
                   FIM Preliminaries
• Observation 1: If an item A is not frequent, any pattern contains 
   A won’t be frequent [R. Agrawal]
                                        q
      use a threshold to eliminate infrequent items 
  {A}   {A,B}
• Observation 2: Patterns containing A are subsets of (or found 
   from) transactions containing A [J. Han]
   from) transactions containing A [J. Han]
      divide‐and‐conquer: select transactions containing A to form a 
   conditional database (CDB), and find patterns containing A from 
   that conditional database
  {A, B}, {A, C}, {A}   CDB A
  {A, B}, {B, C}  CDB B
   Observation 3: To prevent the same pattern from being found in 
• Observation 3: To prevent the same pattern from being found in
   multiple CDBs, all itemsets are sorted by the same manner (e.g., 
   by descending support)

 Ed Chang                    EMMDS 2009                          20
            Preprocessing
                                      • According to 
            f: 4
                                        Observation 1, we 
            c: 4
                                                h
                                        count the support of f
            a: 3
facdgimp    b: 3                fcamp   each item by 
            m: 3                        scanning the 
abcflmo     p: 3                fcabm   database, and 
                                        database and
                                        eliminate those 
bfhjo       o: 2                fb      infrequent items 
            d: 1                        from the
                                        from the 
bcksp       e: 1                cbp     transactions.
            g: 1
                                      • According to 
afcelpmn    h: 1                fcamp
            i: 1
                                        Observation 3, we 
                                        Observation 3, we
            k: 1                        sort items in each 
            l:1                         transaction by the 
            n: 1                        order of descending g
                                        support value.
 Ed Chang          EMMDS 2009                             21
                     Parallel Projection
• According to Observation 2, we construct CDB of item 
  A; then from this CDB, we find those patterns 
   ;                   ,               p
  containing A
• How to construct the CDB of A? 
      If a transaction contains A, this transaction should appear in 
    – If t        ti      t i A thi t          ti    h ld         i
      the CDB of A
    – Given a transaction {B, A, C}, it should appear in the CDB of 
      A, the CDB of B, and the CDB of C
      A the CDB of B and the CDB of C
• Dedup solution: using the order of items:
    –   sort {B,A,C} by the order of items    <A,B,C>
    –   Put <> into the CDB of A
    –   Put <A> into the CDB of B
    –   Put <A,B> into the CDB of C
        Put <A B> into the CDB of C
 Ed Chang                       EMMDS 2009                         22
                Example of Projection
           fcamp                 p: { f c a m / f c a m / c b }

           fcabm                 m: { f c a / f c a / f c a b }

           fb                    b: { f c a / f / c }

           cbp                   a: { f c / f c / f c }

           fcamp                 c: { f / f / f }

            Example of Projection of a database into CDBs.
            Left: sorted transactions in order of f, c, a, b, m, p
            Right: conditional databases of frequent items


Ed Chang                       EMMDS 2009                            23
                    p         j
                Example of Projection
           fcamp              p: { f c a m / f c a m / c b }

           fcabm              m: { f c a / f c a / f c a b }

           fb                 b: { f c a / f / c }

           cbp                a: { f c / f c / f c }

           fcamp              c: { f / f / f }

            Example of Projection of a database into CDBs.
            Left: sorted transactions;
            Right: conditional databases of frequent items


Ed Chang                     EMMDS 2009                        24
                Example of Projection
                Example of Projection
           fcamp              p: { f c a m / f c a m / c b }

           fcabm              m: { f c a / f c a / f c a b }

           fb                 b: { f c a / f / c }

           cbp                a: { f c / f c / f c }

           fcamp              c: { f / f / f }

            Example of Projection of a database into CDBs.
            Left: sorted transactions;
            Right: conditional databases of frequent items


Ed Chang                     EMMDS 2009                        25
       Recursive Projections [H. Li, et al. ACM RS 08]
       Recursive Projections [H Li et al ACM RS 08]
    MapReduce       MapReduce MapReduce
                                                • Recursive projection form 
    Iteration 1     Iteration 2 Iteration 3
                                                  a search tree
                                                  a search tree
                                                • Each node is a CDB
                        b   D|ab     c    D|abc
                                                • Using the order of items to 
        a     D|a
                                                          t d li t d CDB
                                                  prevent duplicated CDBs.
                        c   D|ac                • Each level of breath‐first 
                                                  search of the tree can be 
D                       c
                            D|bc
                                                  done by a MapReduce 
                                                  done by a MapReduce
        b     D|b                                 iteration.
                                                • Once a CDB is small 
                                                  enough to fit in memory, 
                                                  enough to fit in memory
        c     D|c                                 we can invoke FP‐growth 
                                                  to mine this CDB, and no 
                                                  more growth of the sub‐
                                                  more growth of the sub
                                                  tree.
Ed Chang                                 EMMDS 2009                       26
                    Projection using MapReduce
   Map inputs       Sorted transactions   Map outputs                  Reduce inputs                     Reduce outputs
   (transactions)   (with infrequent      (conditional transactions)   (conditional databases)           (patterns and supports)
key="": value        items eliminated)    key: value                   key: value                         key: value

   facdgimp            fcamp               p:
                                           m:
                                                fcam
                                                fca           p:{fcam/fcam/cb} p:3, pc:3
                                                                    p: { f c a m / f c a m / c b }
                                                                                                   p:3
                                                                                                   pc:3
                                           a:   fc
                                           c:   f                                                          mf:3
                                                                                                           mc:3
   abcflmo             fcabm               m: f c a b                                                      ma:3
                                           b: f c a                     m: { f c a / f c a / f c a b }     mfc:3
                                           a: f c                                                          mfa:3
                                           c: f                                                            mca:3
   bfhjo               fb                  b: f                                                            mfca:3

   bcksp               cbp                 p: c b                       b:   {fca/f/c}                     b:3
   afcelpmn            fcamp               b:   c                       a:   {fc/fc/fc}                    a:3
                                           p:   fcam                                                       af:3
                                           m:   fca                                                        ac:3
                                           a:   fc                                                         afc:3
                                           c:   f
                                                                                                           c:3
                                                                        c:   {f/f/f}                       cf:3


     Ed Chang                                             EMMDS 2009                                                      27
                Collaborative Filtering
                                                            Indicators/Diseases
                                                    1 1 1
                                                1       1 1         1       1       1
Based on membership so far,                                     1       1           1




                                      als
 and memberships of others                      1       1       1 1




                              Individua
                                                    1
                                                                    1 1
Predict further membership                              1                   1
                                            1 1
                                                1                               1
                                            1                                       1
                                                1 1 1 1 1

 Ed Chang                     EMMDS 2009                                            28
                              Latent Semantic Analysis
•    Search                                                                                       Users/Music/Ads/Question

      – Construct a latent layer for better 
         for semantic matching




                                                                                      ers
                                                                          sic/Ads/Answe
•    Example:
      – iPhone crack
      – Apple pie




                                                                  Users/Mus
               1 recipe pastry for a 9
Documents        inch double crust       How to install apps on
                  9 apples, 2/1 cup,     Apple mobile phones?
                     brown sugar


   Topic
Distribution



                                                                                            •   Other Collaborative Filtering Apps
                                                                                                Other Collaborative Filtering Apps
                                                                                                 –   Recommend Users  Users
   Topic
Distribution
                                                                                                 –   Recommend Music  Users
                                                                                                 –   Recommend Ads  Users
                                                                                                 –   Recommend Answers  Q
                                                                                                     R       dA
                 iPhone crack                Apple pie
User quries                                                                                 •   Predict the ? In the light‐blue cells
Ed Chang                                         EMMDS 2009                                                                        29
           Documents, Topics, Words
           Documents, Topics, Words
  A document consists of a number of topics
• A document consists of a number of topics
    – A document is a probabilistic mixture of topics
  Each topic generates a number of words
• Each topic generates a number of words
    – A topic is a distribution over words
    – The probability of the ith word in a document




Ed Chang                 EMMDS 2009                     30
    Latent Dirichlet Allocation [M. Jordan 04]
• α: uniform Dirichlet φ prior 
                                            α
  for per document d topic
  for per document d topic 
  distribution (corpus level 
  parameter)
                                            θ
• β: uniform Dirichlet φ prior 
          f          hl
  for per topic z word 
  distribution (corpus level 
  parameter)                                z
• θd is the topic distribution of 
          (
  doc d (document level)
• zdj the topic if the jth word in          w            φ            β
  d, wdj the specific word (word                Nm           K
       ) 
  level)
                                                     M
Ed Chang                       EMMDS 2009                        31
  LDA Gibbs Sampling: Inputs And Outputs
  LDA Gibbs Sampling: Inputs And Outputs
Inputs: 
1. training data: documents as bags              words    topics
   of words
               h     b    f
2. parameter: the number of topics      docs                   docs

Outputs: 
1. by‐product: a co‐occurrence 
1 by product: a co occurrence
   matrix of topics and documents.
                                        topics
2. model parameters: a co‐                        words
   occurrence matrix of topics and 
   words.



Ed Chang                         EMMDS 2009                    32
            Parallel Gibbs Sampling [aaim 09]
            Parallel Gibbs Sampling [aaim 09]
Inputs: 
1. training data: documents as bags              words    topics
   of words
               h     b    f
2. parameter: the number of topics      docs                   docs

Outputs: 
1. by‐product: a co‐occurrence 
1 by product: a co occurrence
   matrix of topics and documents.
                                        topics
2. model parameters: a co‐                        words
   occurrence matrix of topics and 
   words.



Ed Chang                         EMMDS 2009                    33
Ed Chang   EMMDS 2009   34
Ed Chang   EMMDS 2009   35
                              Outline
  • Motivating Applications 
      – Q&A System
      – Social Ads
  • Key Subroutines
      –    Frequent Itemset Mining [ACM RS 08]
      –    L      Di i hl All      i
           Latent Dirichlet Allocation  [WWW 09, AAIM 09]
      –    Clustering [ECML 08]
      –    UserRank [Google TR 09]
           UserRank [Google TR 09]
      –    Support Vector Machines [NIPS 07]
    Distributed Computing Perspectives
  • Distributed Computing Perspectives
Ed Chang                       EMMDS 2009                   36
Ed Chang   EMMDS 2009   37
Ed Chang   EMMDS 2009   38
                           Open Social APIs
                           Open Social APIs
                             1


                                 Profiles (who I am)



                                                                                      2


     Stuff (what I have)             Open Social              Friends (who I know)

4




                                 Activities (what I do)


                                                          3




Ed Chang                              EMMDS 2009                                     39
                    Activities




                                 Recommendations




Applications

  Ed Chang     EMMDS 2009                          40
Ed Chang   EMMDS 2009   41
Ed Chang   EMMDS 2009   42
Ed Chang   EMMDS 2009   43
Ed Chang   EMMDS 2009   44
       Task: Targeting Ads at SNS Users
       Task: Targeting Ads at SNS Users
 Users




   Ads




Ed Chang            EMMDS 2009            45
   Mining Profiles, Friends & Activities 
             for Relevance
             for Relevance




Ed Chang          EMMDS 2009                46
           Consider also User Influence
• Advertisers consider 
         h
  users who are
    – Relevant
    – Influential
• SNS Influence Analysis
    –   Centrality
    –   Credential
    –   Activeness
    –   etc.


Ed Chang              EMMDS 2009          47
              p                g [ g,
             Spectral Clustering [A. Ng, M. Jordan]]
• Important subroutine in tasks of machine learning  
  and data mining
    – Exploit pairwise similarity of data instances
      More effective than traditional methods e.g., k‐means
    – More effective than traditional methods e g k means
• Key steps
      Construct pairwise similarity matrix
    – Construct pairwise similarity matrix
           • e.g., using Geodisc distance
    – Compute the Laplacian matrix
      Apply eigendecomposition
    – A l i d             iti
    – Perform k‐means


Ed Chang                            EMMDS 2009                48
                   Scalability Problem
                   Scalability Problem
• Quadratic computation of nxn matrix
• Approximation methods



                            Dense Matrix


       Sparsification          Nystrom               Others



t NN
t-NN   ξ neighborhood
       ξ-neighborhood   …    random      greedy ….

Ed Chang                      EMMDS 2009                      49
            p                    p g
           Sparsification vs. Sampling
• Construct the dense         • Randomly sample l
  similarity matrix S
  similarity matrix S           points, where l << n
                                points where l << n
• Sparsify S                  • Construct dense 
  Compute Laplacian 
• Compute Laplacian             similarity matrix [A B] 
                                similarity matrix [A B]
  matrix L                      between l and n points
                                Normalize A and B to be 
                              • Normalize A and B to be
                                in Laplacian form
• Apply ARPACLK on L             R = A + A‐1/2BBTA‐1/2 ;
                                 R  A + A              ;  
• Use k‐means to cluster         R = U∑UT
  rows of V into k groups
                              • k‐means
Ed Chang                 EMMDS 2009                          50
              Empirical Study [song, et al., ecml 08]
              Empirical Study [song et al ecml 08]
• Dataset: RCV1 (Reuters Corpus Volume I)
      A filtered collection of 193,944 d
    – A filt d ll ti                          t i 103
                             f 193 944 documents in 103
      categories
• Photo set: PicasaWeb
    – 637,137 photos
• Experiments
    – Clustering quality vs. computational time
           • Measure the similarity between CAT and CLS 
           • Normalized Mutual Information (NMI)



    – Scalability

Ed Chang                            EMMDS 2009             51
           NMI Comparison (on RCV1)
           NMI Comparison (on RCV1)




           Nystrom method
           N t       th d          S        ti         i ti
                                   Sparse matrix approximation
Ed Chang                    EMMDS 2009                           52
      Speedup Test on 637,137
      Speedup Test on 637,137 Photos
• K = 1000 clusters




  Achiever linear speedup when using 32 machines, after that, 
• A hi     li         d    h      i 32       hi    ft th t
  sub‐linear speedup because of increasing communication and 
  sync time

Ed Chang                  EMMDS 2009                        53
            p                    p g
           Sparsification vs. Sampling
                  Sparsification      Nystrom, random 
                                      sampling

Information       Full n x n
                  Full n x n          None
                  similarity scores
Pre processing
Pre‐processing    O(n2) worst case; O(nl) l << n
                       ) worst case;  O(nl), l << n
Complexity        easily parallizable
(bottleneck)
Effectiveness     Good                Not bad (Jitendra M., 
                                      PAMI)

Ed Chang               EMMDS 2009                        54
                              Outline
  • Motivating Applications 
      – Q&A System
      – Social Ads
  • Key Subroutines
      –    Frequent Itemset Mining [ACM RS 08]
      –    L      Di i hl All      i
           Latent Dirichlet Allocation  [WWW 09, AAIM 09]
      –    Clustering [ECML 08]
      –    UserRank [Google TR 09]
           UserRank [Google TR 09]
      –    Support Vector Machines [NIPS 07]
    Distributed Computing Perspectives
  • Distributed Computing Perspectives
Ed Chang                       EMMDS 2009                   55
      Matrix Factorization Alternatives
      Matrix Factorization Alternatives



   exact




           approximate

Ed Chang                 EMMDS 2009       56
            PSVM [E. Chang, et al, NIPS 07]
            PSVM [E Chang et al NIPS 07]
  Column based ICF
• Column‐based ICF
    – Slower than row‐based on single machine
      Parallelizable on multiple machines
    – Parallelizable on multiple machines
• Changing IPM computation order to achieve 
      ll li ti
  parallelization




Ed Chang               EMMDS 2009               57
           Speedup




Ed Chang    EMMDS 2009   58
           Overheads




Ed Chang     EMMDS 2009   59
           Comparison between Parallel 
                                k
             Computing Frameworks
                                   MapReduce        Project B        MPI
GFS/IO and task rescheduling       Yes              No               No
overhead between iterations                         +1               +1

Flexibility of computation model
          y       p                             y
                                   AllReduce only                y
                                                    AllReduce only   Flexible
                                   +0.5             +0.5             +1
Efficient AllReduce                Yes              Yes              Yes
                                   +1               +1               +1
Recover from faults between        Yes              Yes              Apps
iterations                         +1               +1
Recover from faults within each    Yes              Yes              Apps
iteration                          +1               +1
Final Score for scalable machine   3.5              4.5              5
       g
learning

Ed Chang                           EMMDS 2009                               60
                    Concluding Remarks
• Applications demand scalable solutions
• Have parallelized key subroutines for mining massive data sets
   –   Spectral Clustering [ECML 08]
   –   Frequent Itemset Mining [ACM RS 08]
   –   PLSA [KDD 08]
   –   LDA [WWW 09]
   –   UserRank 
   –   Support Vector Machines [NIPS 07]
• Relevant papers
   – http://infolab.stanford.edu/~echang/
  Open Source PSVM, PLDA
• Open Source PSVM PLDA
   – http://code.google.com/p/psvm/
   – http://code.google.com/p/plda/


 Ed Chang                         EMMDS 2009                   61
                   Collaborators
   •                      (   )
       Prof. Chih‐Jen Lin (NTU)
   •   Hongjie Bai (Google)
   •   Wen‐Yen Chen (UCSB)
   •            (
       Jon Chu (MIT))
   •   Haoyuan Li (PKU)
   •   Yangqiu Song (Tsinghua)
       Yangqiu Song (Tsinghua)
   •   Matt Stanton (CMU)
   •   Yi Wang (Google)
              g(     g )
   •   Dong Zhang (Google)
   •   Kaihua Zhu (Google)

Ed Chang                  EMMDS 2009   62
                                      References
[1] Alexa internet. http://www.alexa.com/.
[ ]                                                                     p
[2] D. M. Blei and M. I. Jordan. Variational methods for the dirichlet process. In Proc. of the 21st international
      conference on Machine learning, pages 373-380, 2004.
[3] D. M. Blei, A. Y. Ng, and M. I. Jordan. Latent dirichlet allocation. Journal of Machine Learning Research, 3:993-
      1022, 2003.
[4] D. Cohn and H. Chang. Learning to probabilistically identify authoritative documents. In Proc. of the Seventeenth
      International Conference on Machine Learning, pages 167-174, 2000.
[5] D. Cohn and T. Hofmann. The missing link - a probabilistic model of document content and hypertext connectivity. In
[ ]                                        g         p                                              yp                y
      Advances in Neural Information Processing Systems 13, pages 430-436, 2001.
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Ed Chang                                            EMMDS 2009                                                         65

				
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