Application of Approximate Equality for Reduction of Feature Vector Dimension

Reduction of feature vector dimension is a problem of selecting the most informative features from an information system. Using rough set theory (RST) we can reduce the feature vector dimension when all the attribute values are crisp or discrete. For any information system or decision system, if attributes contain real-valued data, RST cannot be applied directly. Fuzzy-rough set techniques may be applied on this kind of system to reduce the dimension. But, Fuzzy-rough set uses the concept of fuzzy-equivalence relation, which is not suitable to model approximate equality. In this paper we propose a new alternative method to reduce the dimension of feature vectors of a decision system where the attribute values may be discrete or real or even mixed in nature. To model approximate equality we first consider the intuitive relationship between distance measure and equality. Subsequently we fuzzify the distance measures to establish the degree of equality (or closeness) among feature vectors (objects or points). Finally we use the concept of a cut to obtain equivalence relation based on which dimension of feature vectors can be reduced. We also compare the performance of the present method to reduce the feature vector dimension with those of principle component analysis (PCA), Kernel Principal Component Analysis (KPCA) and independent component analysis (ICA). In most of the cases the present method performs same or even better than the other methods.