Evaluation of Clustering Techniques on DMOZ Data Alper Rifat Uluçınar Rıfat Özcan Mustafa Canım

Outline What is DMOZ and why do we use it? What is our aim? Conclusion Evaluation of partitioning clustering algorithms Evaluation of hierarchical clustering algorithms Conclusion

What is DMOZ and why do we use it? www.dmoz.org Another name for ODP, Open Directory Project The largest human edited directory on the Internet 5,300,000 sites 72,000 editors 590,000 categories

What is our aim? Evaluating cluster algorithms is not easy We will use DMOZ as reference point (ideal cluster structure) Run our own cluster algorithms on same data Finally compare results.

? Applying Clustering Algorithms such as C3M, K Means etc. All DMOZ documents (websites) Applying Clustering Algorithms such as C3M, K Means etc. Human Evaluation ? DMOZ Clusters ??

A) Evaluation of Partitioning Clustering Algorithms 20,000 documents from DMOZ flat partitioned data (214 folders) We applied html parsing, stemming, stop word list elimination We will apply two clustering algorithms : C3M K-Means

Before applying html parsing, stemming, stop word list elimination

After applying html parsing, stemming, stop word list elimination

Applying C3M Human Evaluation 214 Clusters 642 Clusters 20,000 DMOZ documents Applying C3M Human Evaluation 214 Clusters 642 Clusters

How to compare DMOZ Clusters and C3M clusters ? Answer: Corrected Rand

Validation of Partitioning Clustering Comparison of two clustering structures N documents Clustering structure 1: R clusters Clustering structure 2: C clusters Metrics [1]: Rand Index Jaccard Coefficient Corrected Rand Coefficient

Validation of Partitioning Clustering ….. ….. ….. d1,d2 d2 d1 Type II, Frequency: b d1,d2 d1,d2 Type I, Frequency: a ….. d2 d1 d1,d2 Type III, Frequency: c ….. d2 d1 Type IV, Frequency: d

Validation of Partitioning Clustering Rand Index = (a+d) / (a+b+c+d) Jaccard Coefficient = a / (a+b+c) Corrected Rand Coefficient Accounts for randomness Normalize rand index so that 0 when the partitions are selected by chance and 1 when a perfect match achieved. CR = (R – E(R)) / (1 – E(R))

Validation of Partitioning Clustering Example: Docs: d1 , d2 , d3 , d4 , d5 , d6 Clustering Structure 1: C1: d1 , d2 , d3 C2: d4 , d5 , d6 Clustering Structure 2: D1: d1 , d2 D2: d3 , d4 D3: d5 , d6

Validation of Partitioning Clustering Contingency Table: a : (d1, d2), (d5, d6) b : (d1, d3), (d2, d3), (d4, d5), (d4, d6) c : (d3, d4) d : remaining 8 pairs (15-7) Rand Index = (2+8)/15 = 0.66 Jaccard Coeff. = 2/(2+4+1) = 0.29 Corrected Rand = 0.24 D1 D2 D3 C1 2 1 3 C2 6

Results Results: Possible Reasons: Low corrected rand and jaccard values ~=0.01 Rand index ~= 0.77 Possible Reasons: Noise in the data Ex: 300 Document Not Found pages. Problem is difficult: Ex: Homepages category.

B) Evaluation of Hierarchical Clustering Algorithms Obtain a partitioning of DMOZ Determine a depth (experiment?) Collect documents of higher (or equal) depth at that level Documents of lower depths? Ignore them…

Hierarchical Clustering: Steps Obtain the hierarchical clusters using: Single Linkage Average Linkage Complete Linkage Obtain a partitioning on the hierarchical cluster…

Hierarchical Clustering: Steps One way, treat DMOZ clusters as “queries”: For each selected cluster of DMOZ Find the number of “target clusters” on computerized partitioning Take the average See if Nt < Ntr If not, either choice of partitioning or hierarchical clustering did not perform well…

Hierarchical Clustering: Steps Another way: Compare the two partitions using an index, i.e. C-RAND…

Choice of Partition: Outline Obtain the dendrogram Single linkage Complete linkage Group average linkage Ward’s methods

Choice of Partition: Outline How to convert a hierarchical cluster structure into a partition? Visually inspect the dendrogram? Use tools from statistics?

Choice of Partition: Inconsistency Coefficient At each fusion level: Calculate the “inconsistency coefficient” Utilize statistics from the previous fusion levels Choose the fusion level for which inconsistency coefficient is at maximum.

Choice of Partition: Inconsistency Coefficient Inconsistency coefficient (I.C.) at fusion level i:

Choice of Partition: I.C. Hands on, Objects Plot of the objects Distance measure: Euclidean Distance

Choice of Partition: I.C. Hands on, Single Linkage

Choice of Partition: I.C. Single Linkage Results Level 1  0 Level 2  0 Level 3  0 Level 4  0 Level 5  0 Level 6  1.1323 Level 7  0.6434 => Cut the dendrogram at a height between level 5 & 6

Choice of Partition: I.C. Single Linkage Results

Choice of Partition: I.C. Hands on, Average Linkage

Choice of Partition: I.C. Average Linkage Results Level 1  0 Level 2  0 Level 3  0.7071 Level 4  0 Level 5  0.7071 Level 6  1.0819 Level 7  0.9467 => Cut the dendrogram at a height between level 5 & 6

Choice of Partition: I.C. Hands on, Complete Linkage

Choice of Partition: I.C. Complete Linkage Results Level 1  0 Level 2  0 Level 3  0.7071 Level 4  0 Level 5  0.7071 Level 6  1.0340 Level 7  1.0116 => Cut the dendrogram at a height between level 5 & 6

Conclusion Our aim is to evaluate clustering techniques on DMOZ Data. Analysis on partitioning & hierarchical clustering algorithms. If the experiments are succesfull we will apply same experiments on larger DMOZ data after we download it. Else We will try other methodologies to improve our experiment results.

References www.dmoz.org [1] A. K. Jain and R. C. Dubes. Algorithms for Clustering Data. Prentice Hall, 1988. [2] Korenius T., Laurikkala J., Juhola M., Jarvelin K. Hierarchical clustering of a Finnish newspaper article collection with graded relevance assessments. Information Retrieval, 9(1). Kluwer Academic Publishers, 2006. www.dmoz.org