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A hierarchical approach to ARTlike Clustering Algorithm Author : Mu-Chun Su Yi-Chun Liu Graduate : Chien-Ming Hsiao Outline Motivation Objective Introduction The proposed ART-like clustering algorithm Conclusion Personal Opinion Motivation Two crucial problems for most of clustering algorithm 1. 2. The determining of the optimal number of clusters The determining of the similarity measure base on which patterns are assigned to corresponding clusters Objective Propose a hierarchical approach to ART-like clustering algorithm which is able to deal with data consisting of arbitrarily geometrical-shaped clusters Feasible solution to the two problems of determining the number of clusters and clustering Introduction (1/2) Cluster validity problem The estimation of the number of clusters in the data set To solving the cluster validity problem usually involves (1) increasing the number of clusters (2) merging the existing cluster computing some certain cluster validity measures in each run, until partition into optimal number of clusters is obtain Introduction (2/2) It is easy to consider the idea of a data cluster on a rather informal basis It is very difficult to give a formal and universal definition of a cluster. Most of the conventional clustering methods assume that patterns having similar locations or constant density create a single cluster Different similarity measures will result in different clustering results The proposed ART-like clustering algorithm The adaptive resonance theory (ART) networks are able to cluster data without pre-specifying the number of clusters. The vigilance parameter to some extent implicitly prespecifies How much confidence do we have on the clustering results created by ART networks ? The proposed ART-like clustering algorithm Hierarchical clustering method Agglomerative Divisive To use the advantage provided by a dendrogram to increase our confidence on selecting a more trustable clustering results created by ART-like clustering algorithm The proposed ART-like clustering algorithm Fig.1 The idea of using of a set of ellipses to approximate an arbitrarily-shaped cluster The proposed ART-like clustering algorithm Adopt the neurons with quadratic neuron-type junctions To cluster data into hyperellipsoids The output of a quadratic neuron indicates the similarity between the present input and the prototype of the hyperellipsoid embedded in the synaptic weights of the neurons The proposed ART-like clustering algorithm The output of a quadratic neuron is computed by using the following equations : n y jk x w jki xi i 1 net j x y jk x b jk n 2 k 1 Out j x e s j 2 net j x where b jk , s j , and w jki are adjustable weights, x x1 ,, xn is an input pattern, T y j y j1 ,, y jn is the transform ed version of the input pattern x, and Out j x T is the output function of neuron j The proposed ART-like clustering algorithm Stage one : generate a single-layer neural network Step 1.1 : specify the initial value of the vigilance parameter and corresponding parameters Step 1.2 : if the present input pattern is the first pattern then generate a quadratic neuron whose weights are initialized b1 0 x 1 if k i w1ki 0 0 o.w Step 1.3 find the wining neuron j among the neurons generated in the network, using the following criterion: * j * j arg min Out j x j 1,, J The proposed ART-like clustering algorithm Step1.4 : if the output of the winning neuron is larger than the threshold. Then adjust the synaptic weights of the winning neurons b jk new b jk old b 2s 2j Out j x y jk x b jk w jki new w jki old w 2s 2j Out j x y jk x b jk xi otherwise, a new quadratic neuron is generated and initialized as follows: b1 0 x 1 if k i w1ki 0 0 o.w Step 1.5 : present next data pattern into the network and repeat steps 1.3-1.4 until all data patterns are processed. The proposed ART-like clustering algorithm Stage two : generate a dendrogram for the generated neural network Step 2.1: set the cycle number k to be 0, determine the value of a real-valued constantαwhose value is in the range (0,1), and initialize an N * J matrix E to be a zero matrix. Step 2.2: fill out the elements in the matrix E k+1 k+1 1 if Out j x i k 1 eij 0 o.w. for 1 i N ,1 j J Step 2.3: find so-called equivalent sets by examining the matrix E Step 2.4: Increase the value of k by one and repeat steps 2.22.3 until the number of cycles reaches a pre-specified limit or the number of equivalent sets, N , becomes just one. k+1 K 1 e The proposed ART-like clustering algorithm The proposed ART-like clustering algorithm Conclusion Utilize the dendrogram to help us to visually select believable clusters and clustering. Any clustering result must be viewed with extreme suspicion since the performance of most of the clustering algorithms more or less depends on some parameters. Personal Opinion No clustering algorithm can claim it works perfectly for any application.