Intelligent Database Systems Lab Advisor ： Dr. Hsu Graduate ： Yu Cheng Chen Author ： Yongqiang Cao Jianhong Wu 國立雲林科技大學 National Yunlin University of Science and Technology Projective ART for clustering data sets in high dimensional spaces Neural Networks, Proceedings Elsevier Science Ltd

Intelligent Database Systems Lab Outline Motivation Objective Introduction Projective adaptive resonance theory Algorithms Simulation and comparisons Conclusions Personal Opinion Review N.Y.U.S.T. I.M.

Intelligent Database Systems Lab Motivation Most clustering algorithms do not work efficiently for data sets in high dimensional spaces because of the inherent sparsity of data. Consequently, a clustering algorithms is often preceded by feature selection, but a feature selection procedure can lead to a significant loss of information. N.Y.U.S.T. I.M.

Intelligent Database Systems Lab Objective PART and the resulting algorithms are proposed to find projected clusters for data sets in high dimensional spaces. N.Y.U.S.T. I.M.

Intelligent Database Systems Lab Introduction Projected Clustering The goal of Projected clustering is to find projected clustering, each of which consists of a subset C of data points together with a subset D of dimensions such that the points in C are closely correlated in the subspace of dimensions D. N.Y.U.S.T. I.M.

Intelligent Database Systems Lab Introduction ART1 architecture N.Y.U.S.T. I.M.

Intelligent Database Systems Lab PART architecture N.Y.U.S.T. I.M. Introduction

Intelligent Database Systems Lab Introduction The principal difference between PART and ART is selectively sends signals in F 1 layer to nodes in the F 2 layer. In other words, a node in the F 1 layer can be active relative to some F 2 nodes, but inactive relative to other F 2 nodes. An F 1 node is active is determined by a similarity test between the corresponding top-down weight and the signal generated in the F 1 node. N.Y.U.S.T. I.M.

Intelligent Database Systems Lab We define the selective output signal of node v i to node v j by N.Y.U.S.T. I.M. Projective adaptive resonance We say that v i is active to v j if h ij =1,and inactive to v j if h ij =0

Intelligent Database Systems Lab STM equations N.Y.U.S.T. I.M. Projective adaptive resonance

Intelligent Database Systems Lab STM equations N.Y.U.S.T. I.M. Projective adaptive resonance F2 layer makes a choice by winner-take –all paradigm

Intelligent Database Systems Lab LTM equations N.Y.U.S.T. I.M. Projective adaptive resonance

Intelligent Database Systems Lab LTM equations N.Y.U.S.T. I.M. Projective adaptive resonance

Intelligent Database Systems Lab Vigilance and reset and we reset the winner v j if and only if N.Y.U.S.T. I.M. Projective adaptive resonance

Intelligent Database Systems Lab The extension of PART architecture: PART tree N.Y.U.S.T. I.M. Projective adaptive resonance

Intelligent Database Systems Lab Algorithms F 1 activation and computation of h ij Here, we take f 1 (x i )=x i, and by Eq. (4), x i =I i N.Y.U.S.T. I.M.

Intelligent Database Systems Lab F 2 activation and selection of winner We compute the input T j to the committed F 2 node v j by Eq. (8), and then select the winner. N.Y.U.S.T. I.M. Algorithms

Intelligent Database Systems Lab Vigilance and reset We use the vigilance and reset mechanism show in Eqs. (16) and (17). Namely winner v j is reset if and only if N.Y.U.S.T. I.M. Algorithms

Intelligent Database Systems Lab Learning For the committed winning F 2 node v j which has passed the vigilance test, we have N.Y.U.S.T. I.M. Algorithms

Intelligent Database Systems Lab Learning For the committed winning F 2 node v j which has passed the vigilance test, we have N.Y.U.S.T. I.M. Algorithms

Intelligent Database Systems Lab Learning For a noncommitted winner v j, and for every F 1 node v i we have N.Y.U.S.T. I.M. Algorithms

Intelligent Database Systems Lab PART tree algorithm N.Y.U.S.T. I.M. Algorithms

Intelligent Database Systems Lab N.Y.U.S.T. I.M. Simulations and comparisons

Intelligent Database Systems Lab Simulations and comparisons N.Y.U.S.T. I.M.

Intelligent Database Systems Lab Simulations and comparisons N.Y.U.S.T. I.M.

Intelligent Database Systems Lab Simulations and comparisons Data set 1 with 10,000 data points and number of clusters k=5 N.Y.U.S.T. I.M.

Intelligent Database Systems Lab Simulations and comparisons N.Y.U.S.T. I.M.

Intelligent Database Systems Lab Simulations and comparisons N.Y.U.S.T. I.M.

Intelligent Database Systems Lab Simulations and comparisons N.Y.U.S.T. I.M.

Intelligent Database Systems Lab Simulations and comparisons N.Y.U.S.T. I.M.

Intelligent Database Systems Lab Conclusions PART provides a solution to the feasibility-reliability dilemma in clustering data sets in high dimensional spaces. N.Y.U.S.T. I.M.

Intelligent Database Systems Lab Personal Opinion N.Y.U.S.T. I.M.

Intelligent Database Systems Lab Review N.Y.U.S.T. I.M.