Clustering based on Generalized Inverse Transformation

Abstract

This paper presents a novel approach which incorporates dimension extension and generalized inverse transformation (DEGIT) to realize data clustering. Unlike k-means algorithm, DEGIT needs not pre-specify the number of clusters k, centroid locations are updated and redundant centroids eliminated automatically during iterative training process. The essence of DEGIT is that clustering is performed by generalized inverse transforming the input data such that each data point is represented by a linear combination of bases with extended dimension, with each basis corresponding to a centroid and its coefficient representing the closeness between the data point and the basis. Issue of clustering validation is also addressed in this paper. First, principal component analysis is applied to detect if there exists a dominated dimension, if so, the original input data will be rotated by a certain angle w.r.t. a defined center of mass, and the resulting data undergo another run of iterative training process. After plural runs of rotation and iterative process, the labeled results from various runs are compared, a data point labeled to a centroid more times than others will be labeled to the class indexed by that wining centroid.