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 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. Iseeabrightfuturenothing doc doc

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

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: D1 Z1 W1 D: document Z: latent class W: word These can also be written as: D2 Z1 W D

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 1.Get the P(d|z) matrix by PLSA, and 2.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: Tempered EM: E-step: M-step:

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

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

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 Dispatching Algorithm

Block Dividing Algorithm cranmed

Experiment Setup

Speedup HPC134Tulsa

Memory Bandwidth Usage

Memory Related Pipeline Stalls

Available Memory Bandwidth of the Two Machines

END

Backup slides

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

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

Thanks!