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A Self-Organizing Map with Expanding Force for Data Clustering and Visualization Advisor:Dr. Hsu Graduate:You-Cheng Chen Author:Wing-Ho Shum Hui-Dong Jin Kwong-Sak Leung Outline Motivation Objective Introduction Expanding SOM Experimental Results Example Conclusions Personal Opinion Review Motivation SOM maps high-dimensional data items onto a lowdimensional gird of neurons. The neighborhood preservation cannot always lead to perfect topology preservation. Objective We establish an Expanding SOM(ESOM) to detect and preserve better topology correspondence. Introduction Expanding SOM In order to detect and preserve topology relationship, we can figure out the distance between data and their center. And we introduce a new learning rule to liner ordering relationship. the expanding coefficient cj(t), which is used to push neurons away from the center of all data items during the learning process. Expanding SOM The ESOM algorithm 1. Linearly transform the coordinates ' xi x1' i , x2' i ,, xDi' (i 1, N) Let the center of all data items be xC ' 1 N N x ' i i ' ' R The input neurons xi ( xi xC ) for all i Dmax N is the number of data items D is the dimensionality of the data set Dmax is the maximum distance of data from the data center Expanding SOM The ESOM algorithm 2. The initialize weight vectors w j (0) (j 1,, M) with random value within the above sphere SR where M is the number of output neurons. 3. Select a data item at random , say feed it to the input neurons. xk (t ) x1k , x2k ,, xDk Expanding SOM The ESOM algorithm 4. Find the winning output neuron, say m(t) m(t ) min xk (t ) w j (t ) j 5. Train neuron m(t) and its neighbors by using the following w j (t 1) c j (t ) w j (t ) j (t ) xk (t ) w j (t ) Expanding SOM The ESOM algorithm c j (t ) 1 2 j (t )(1 j (t )) k j (t ) 1 2 where kj(t) is specified by 2 2 k j (t ) 1 xk (t ), w j (t ) (1 xk (t ) )(1 w j (t ) ) Expanding SOM The ESOM algorithm 6. Update α(t) . If the learning loop does not reach a predetermined number, go to Step 3 with t=t+1 Expanding SOM Expanding SOM We employ both the quantization error EQ and the topological error ET to evaluate the mapping obtained by our ESOM. 1 EQ N N k 1 xk (t ) wm (t ) Expanding SOM Theoretical analysis Theorem 1 w j (t ) SR then w j (t ) R for j {1,2, , M} 1 c j (t ) 1 1- R2 c j (t ) increases with x k (t ) when x k (t ) w j (t ) Expanding SOM Theoretical analysis Proof c j (t ) 1 2 j (t )(1 j (t )) k j (t ) 1 2 Expanding SOM Theoretical analysis says that cj(t) is always larger than or equal to 1.0 In other words, it always pushes neurons away from the origin. But it will never push the output neurons to infinite locations. points out that the larger the distance between a data item and the center of all data items is, the stronger the cj(t) will be associated output neuron. Experiment results Experiment results Experiment results Experiment results Experiment results Conclusions ESOM constructs better visualization results than the classic SOM in terms of both the topological and quantization errors. Personal Opinion We can apply this idea to improve the Extended SOM implemented by our lab. Review The key point of Expanding SOM ' ' R The input neurons xi ( xi xC ) for all i Dmax c j (t ) 1 2 j (t )(1 j (t )) k j (t ) 1 2