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Clustering Search Results Using PLSA. 洪春涛. Outlines. Motivation Introduction to document clustering and PLSA algorithm Working progress and testing results. Motivation. Current Internet search engines are giving us too much information
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Outlines • Motivation • Introduction to document clustering and PLSA algorithm • Working progress and testing results
Motivation • Current Internet search engines are giving us too much information • Clustering the search results may help find the desired information quickly
The writer Truman Capote The film Truman Capote A demo of the searching result from Google.
Document clustering • Put the ‘similar’ documents together => How do we define ‘similar’?
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.
Cosine as Distance Between Documents The distance between doc1 and doc2 is then defined as
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’
Probabilistic Latent Semantic Analysis Graphical model of PLSA: D2 D1 D: document Z: latent class W: word D2 0.3 0.1 0.7 0.8 0.9 0.2 Z1 Z1 W1 W1 W1 These can also be written as:
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)
Our approach • Get the P(d|z) matrix by PLSA, and • Use k-means clustering algorithm on the matrix
Problems with this approach • PLSA takes too much time solution: optimization & parallelization
Algorithm Outline Expectation Maximization(EM) Algorithm: E-step: M-step: Tempered EM:
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 array Z n_d_w: sparse integer matrix N
Lemur Implementation • In-need calculation of p_z_d_w • Computational complexity: O(W*D*Z2) • For the new3 dataset containing 9558 documents, 83487 unique terms, it takes days to finish a TEM iteration
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<numDocs;d++){ for(int w=0;w<numTermsInThisDoc;w++){ for(int z=0;z<numZ;z++){ …. } } }
Parallelization: Access Pattern Data Race solution: divide the co-occurrence table into blocks
Block Dividing Algorithm cranmed
Speedup HPC134 Tulsa
Test Results Table 1. F-score of PLSA and VSM
Table 2. Time used in one EM iteration (in second) Uses the k1b dataset (2340 docs, 21247 unique terms, 530374 terms)
