Nir Geffen Yotam Margolin Supervisor Professor Zeev Volkovich 1 ORT BRAUDE COLLEGE – SE DEPT

Our goal is to study the results of different clustering ensemble techniques and to present the distinction between the cluster ensemble and clustering aggregation approaches via self learning methodology – implemented for image segmentation. /24 2

 Introduction  What Does It Do?  Clustering  Spectral Clustering  Cluster Ensembles.  Consensus  HGPA  MCLA  Volkovich-Yahalom  Main Algorithm  SE Documents 2/24

What does it do? /24 4 Comparison VYCAA MCLA HGPA Preprocess

 Clustering is a method of the unsupervised learning aimed at partitioning a given data set into subsets named clusters, so that items belonging to the same cluster are similar to each other while items belonging to different clusters are not similar. /24 5

 What is wrong with classic clustering?  Spectral Clustering  Eigenvectors and eigenvalues  Noise removed /24 6 Clustered by K-MeansClustered by Spectral

 As no clustering algorithm is agreed to be superior for any data set, a common practice is to construct several cluster solutions and to aggregate them.  We use the Consensus function approach to combine the resulting partitions into a new one, in order t increase the robustness of the clustering process. /24 7

 Algorithms that solve the Cluster Ensemble problem, are also known as Consensus functions, most of which rely on Graph theory. /24 8

 Cluster-based Similarity Partitioning Algorithm (CSPA)  Simple.  Considered the brute-force.  Hyper Graph Partitioning Algorithm (HGPA),  Balanced.  Not always optimal.  Meta-CLustering Algorithm (MCLA)  high-end solution.  yields robust results. /24 9

 A criteria by which to choose any specific consensus function is ANMI. ANMI (or Average Normalized Mutual Information) is defined as the average of the NMI which the final Clustering shares with the solutions.  Mutual Information I(X,Y )≤min(H(X),H(Y )). /24 10

/ Create hyper-graph (hyper-edges are clusters from all clusterings). 2. Repeat K -1 times:  Obtain sub-set (Cluster) by min-cutting the hyper-graph while maintaining a vertex imbalance of at most 5%.

/ Create hyper-graph G. 2. Expand hyper edges. (Create meta-graph from G). 3. Collapse meta-graph (Cluster meta graph to K clusters). 4. Compete for Objects

 Use various partitions of the same data set in order to define a new metric on the data set.  Using the new metric as an enhanced input for a clustering algorithm will produce better and more robust partitions.  This process can be utilized repeatedly, where in each step the metric is updated using the original data as well as the new cluster partition. /24 13

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 Produce r individual spectral partitions  Use MCLA to obtain Sc MCLA(x);  Use HGPA to obtain Sc HGPA(x);  Use Volkovich-Yahalom to obtain SC VYCAA(x);  By ANMI criterion, get the final decision Sc*(x) from Sc MCLA(x) and Sc HGPA(x) and Sc VYCAA (x). /24 15

GUI – Main window 16

GUI – Results window 17

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 Unit test is our first line in the test plan (Test Driven Development)  Coding conventions.  Lint the code for errors such as dead-code or uninitialized pointers.  Usage and code coverage Test. /24 21

References [1]Z. Volkovich, O. Yahalom, "Clustering aggregation via the self-learning approach", work in preparation [2]A. Strehl, J Ghosh, "Cluster Ensembles – a knowledge Reuse Framework for Combining Multiple Partitions", Journal of machine Learning Research 3 (2002) [3]Y. Ng, M, Jordan, Y Weish, "On spectral clustering: analysis and an algorithm", 2002, Advances in neural information processing systems 14: proceedings of the 2002 conference, Sec.2, 849. [4]X. Ma, W. Wan, L. Jiao, “Spectral Clustering Ensemble for Image Segmentation”, 2009 GEC '09 Proceedings of the first ACM/SIGEVO Summit on Genetic and Evolutionary Computation. [5]I.S. Dhilon, Y. Guan, B. Kulis, “Kernel k-means, Spectral Clustering and Normalized Cuts”, [6]E. David, “Spectral Clustering”, 2008 Image Processing Seminar. /24 22

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