Intelligent Database Systems Lab 國立雲林科技大學 National Yunlin University of Science and Technology O( ㏒ 2 M) Self-Organizing Map Algorithm Without Learning of Neighborhood Vectors Hiroki Kusumoto and Yoshiyasu Takefuji, IEEE Transaction on Neural Networks, Vol. 17, No. 6, 2006, pp Presenter : Wei-Shen Tai Advisor : Professor Chung-Chian Hsu 2007/3/1

N.Y.U.S.T. I. M. Intelligent Database Systems Lab Outline Introduction Algorithm  Initialization  Subdividing method  Binary search Simulation and results Discussion Conclusion Comments

N.Y.U.S.T. I. M. Intelligent Database Systems Lab Motivation BMU searching time  One input vector to search a winner vector by exhaustive search is equivalent to M 2.(M*M matrix) Similar input in different clusters  Two similar inputs that belong to the same cluster are mapped on the distant weight vectors. Neighborhood function  Time-consuming parameter tuning

N.Y.U.S.T. I. M. Intelligent Database Systems Lab Objective A new SOM algorithm with O(log 2 M)  Composed of the subdividing method and the binary search method.  Reduces the computational costs and eliminates the time-consuming parameter tuning in the neighborhood function.  Similar input vectors will be clustered in the same neuron.

N.Y.U.S.T. I. M. Intelligent Database Systems Lab Initialization A feature map  A 2-D layer of M*M nodes (M = 2m + 1, m = 1, 2, 3,...). Four initial nodes  On the coordinates (1, 1), (1,M), (M, 1), and (M, M) have k-dimensional weight vectors W(x, y).  They are trained by the basic SOM with total O(1) computation, respectively.

N.Y.U.S.T. I. M. Intelligent Database Systems Lab Subdividing Method Subdividing  Draws center lines between all neighboring, it subdivides an M ’* M ’ feature map into a (2M ’- 1) * (2M ’- 1) feature map. Weight of the new gray nodes  The average of the values of weight vectors of the closest nodes to the new node.

N.Y.U.S.T. I. M. Intelligent Database Systems Lab Binary Search and learning Step A. search space  x 1 ≦ x ≦ x 2 and y 1 ≦ y ≦ y 2  Closest vector to X(t) Step B. dividing search space  A winner vector is on a quarter space where the closest vector W(x c, y c ) exits. Learning

N.Y.U.S.T. I. M. Intelligent Database Systems Lab Simulations and results Computational cost Codon Frequencies of E. Coli K12 Genes

N.Y.U.S.T. I. M. Intelligent Database Systems Lab Discussion Problem in basic SOMs with a large feature map  The proposed algorithm does not search all weight vectors for the winner vectors.  It can avoid two similar input vectors that belong to the same cluster are mapped on the distant weight vectors. Subdividing method  The search space is reduced to a quarter that includes the temporary winner vector. Binary search method  Reduces the computational costs and can work only when it is combined with the subdividing method.  Eliminates the time-consuming parameter tuning in neighborhood function.

N.Y.U.S.T. I. M. Intelligent Database Systems Lab Transmissions of a learning effect Learning effect  Each square denotes a weight vector and L denotes the variation of W(M, M) by the training.  L/2 is transmitted to the just adjacent two vectors out of five new vectors and L/4 to the center vector and none to the other two far vectors, accordingly.

N.Y.U.S.T. I. M. Intelligent Database Systems Lab Conclusion A new SOM algorithm with computational cost O(log 2 M)  Eliminates the time-consuming parameter tuning in neighborhood function in SOM applications.

N.Y.U.S.T. I. M. Intelligent Database Systems Lab Comments Advantage  A novel idea for reducing the computational cost and parameter tuning in neighborhood function in SOM.  Subdividing method is applicable for reducing search space. Drawback  If the initial weighting of each neuron is arbitrary, it maybe causes some subdividing problems such as the spectrum of each neuron are extreme different. Application  SOM related applications.