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Clustering Search Results Using PLSA 洪春涛

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Outlines Motivation Introduction to document clustering and PLSA algorithm Working progress and testing results

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Motivation Current Internet search engines are giving us too much information Clustering the search results may help find the desired information quickly

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The writer Truman Capote The film Truman Capote A demo of the searching result from Google.

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Document clustering Put the ‘similar’ documents together => How do we define ‘similar’?

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Vector Space Model of documents The Vector Space Model (VSM) sees a document as a vector of terms: Doc1: I see a bright future. Doc2:I see nothing. Iseeabrightfuturenothing doc doc

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The distance between doc1 and doc2 is then defined as Cosine as Distance Between Documents

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Problems with cosine similarity Synonymy: different words may have the same meaning –Car manufacturer=automobile maker Polysemy: a word may have several different meanings - ‘Truman Capote’ may mean the writer or the film => We need a model that reflects the ‘meaning’

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Probabilistic Latent Semantic Analysis Graphical model of PLSA: D1 Z1 W1 D: document Z: latent class W: word These can also be written as: D2 Z1 W D

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Through Maximization Likelihood, one gets the estimated parameters: P(d|z) This is what we want – a document-topic matrix that reflects meanings of the documents. P(w|z) P(z)

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Our approach 1.Get the P(d|z) matrix by PLSA, and 2.Use k-means clustering algorithm on the matrix

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Problems with this approach PLSA takes too much time solution: optimization & parallelization

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Algorithm Outline Expectation Maximization(EM) Algorithm: Tempered EM: E-step: M-step:

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Basic Data Structures p_w_z_current, p_w_z_prev: dense double matrix W*Z p_d_z_current, p_d_z_prev: dense double matrix D*Z p_z_current, p_z_prev: double arrayZ n_d_w: sparse integer matrixN

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Lemur Implementation In-need calculation of p_z_d_w Computational complexity: O(W*D*Z 2 ) For the new3 dataset containing 9558 documents, unique terms, it takes days to finish a TEM iteration

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Optimization of the Algorithm Reduce complexity –calculate p_z_d_w just once in an iteration –complexity reduced to O(N*Z) Reduce cache miss by reverting loops for(int d=1;d

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Parallelization: Access Pattern Data Race solution: divide the co-occurrence table into blocks

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Block Dispatching Algorithm

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Block Dividing Algorithm cranmed

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Experiment Setup

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Speedup HPC134Tulsa

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Memory Bandwidth Usage

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Memory Related Pipeline Stalls

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Available Memory Bandwidth of the Two Machines

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END

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Backup slides

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Test Results PLSAVSM Tr K1b sports Table 1. F-score of PLSA and VSM

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sizeZ Lemur Optimized Table 2. Time used in one EM iteration (in second) Uses the k1b dataset (2340 docs, unique terms, terms)

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Thanks!

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