Minimum Spanning Trees Displaying Semantic Similarity Włodzisław Duch & Paweł Matykiewicz Department of Informatics, UMK Toruń School of Computer Engineering, NTU Singapore Cincinnati Children’s Hospital Research Foundation, OH, USA Google: Duch

The Problem Finding people who share some of our interests in large organizations or worldwide is difficult. Analyzing people’s homepages and their lists of publications is a good way to find groups and individuals sharing common scientific interest. Maps should display individuals and groups. The structure of graphical representations depends strongly on the selection of keywords or dimensionality reduction.

The Data Reuters datasets, with 5 categories and 1 – 176 elements per category. 124 Personal Web Pages of the School of Electrical and Electronic Engineering (EEE) of the Nanyang Technological University (NTU) in Singapore, with 5 categories (control, microelectronics, information, circuit, power), and 14 – 41 documents per category.

Document-word matrix Document1: word1 word2 word3. word4 word3 word5. Document2: word1 word3 word5. word1 word3 word6. The matrix: documents x word frequencies

Methods used Inverse document frequency and term weighting. Simple selection of relevant terms. Latent Semantic Analysis (LSA) for dimensionality reduction. Minimum Spanning Trees for visual representation. TouchGraph XML visualization of MST trees.

Data Preparation Normalize columns of F dividing by highest word frequencies: Among n documents, term j occurs d j times; inverse document frequency idf j measures uniqueness of term j: tf x idf term weights:

Simple selection Simple selection: take w ij weights above certain threshold, binarize and remove zero rows: Calculate similarity using cosine measure:

Dimensionality reduction Latent Semantic Analysis (LSA): use Singular Value Decomposition on weight matrix W with U = eigenvectors of WW T and V of W T W. Remove small eigenvalues, recreate reduced W and calculate similarity:

Kruskal’s Algorithm and Top - Down Clusterization

Modified Kruskal’s Algorithm and Bottom - Up Clusterization

Reuters results Method topics clusters accuracy No dim red % LSA dim red. 0.8 (476) % LSA dim red. 0.6 (357) % Simple Selection % W rank in SVD = 595

Results for EEE NTU Web pages Method topics clusters accuracy No dim red % LSA dim red. 0.8 (467) % LSA dim red. 0.6 (350) % Simple Selection %

Examples TouchGraph LinkBrowser

Results for Summary Discharges New experiments on medical texts. 10 classes and 10 documents per class: Plain Doc-Word matrix ≈ 23% Stop-List, TW-IDF, S.S. ≈ 64% Concept Space ≈ 64% Transformation ≈ 93%

Simple Word-Doc Vector Space

Meta-Map Concept Vector Space

Concept Vector Space after transformation

Summary In real application knowledge-based approach is needed to select only useful words and to parse their web pages. Other visualization methods (like MDS) may be explored. People have many interests and thus may belong to several topic groups. Could be a very useful tool to create new shared interest groups in the Internet.