Non‐negative matrix factorisation based on fuzzy K nearest neighbour graph and its applications

Abstract

Non-negative matrix factorisation (NMF) has been widely used in pattern recognition problems. For the tasks of classification, however, most of the existing variants of NMF ignore both the discriminative information and the local geometry of data into the factorisation. The actual conditions of the problems will be affected by the change of the environmental factors to affect the recognition accuracy. In order to overcome these drawbacks, the authors regularised NMF by intra-class and inter-class fuzzy K nearest neighbour graphs, leading to NMF-FK-NN in this study. By introducing two novel fuzzy K nearest neighbour graphs, NMF-FK-NN can contract the intra-class neighbourhoods and expand the inter-class neighbourhoods in the decomposition. This method not only exploits the discriminative information and uses the geometric structure in the data effectively, but also reduces the influence of the external factors to improve recognition effect. In the factorisation, the authors minimised the approximation error whilst contracting intra-class fuzzy neighbourhoods and expanding inter-class fuzzy neighbourhoods. The authors develop simple multiplicative updates for NMF-FK-NN and present monotonic convergence results. Experiments of the text clustering on the CLUTO toolkit and face recognition on ORL and YALE datasets show the effectiveness of our proposed method.

Fuzzy local discriminant embedding for image feature extraction

“…Since the distances between the samples in local k-nearest neighborhood might also vary in a big range, the graph constructed in this way might have potential disadvantages that the weights are not in accordance with the natural relations of samples in actual applications. To better describe the relations in the samples, some fuzzy pattern recognition methods [18][19][20][21][22][23][24][25] are proposed in recent years. Kwak et al [18] proposed a fuzzy fisher classifier based on fuzzy k-nearest neighbor (FKNN) [25] and the recognition rate is improved on different face databases.…”

“…Zhao et al [21] introduced fuzzy gradual graphs to reflect the relationship between samples and achieve impressive pattern matching results. Ye et al [23] designed a non-negative matrix factorization algorithm based on fuzzy k nearest neighbor graph and achieved reliable recognition performance for classification. Li et al [24] presented a fuzzy maximum scatter difference (FMSD) algorithm by incorporating fuzzy theory into traditional MSD [9] algorithm and obtained promising result for face recognition.…”