Noisy-free Length Discriminant Analysis with cosine hyperbolic framework for dimensionality reduction.

NRPS will remove noisy patterns with the help of a generalized threshold.NLDA models discrimination in terms of average length differences of the patterns.Cosine-hyperbolic framework formulates NLDAs objective.This framework makes the length differences between samples more significant.NLDA is efficient in handling multimodal data. Dimensionality Reduction (DR) is very useful and popular in many application areas of expert and intelligent systems, such as machine learning, finance, data and text mining, multimedia mining, image processing, anomaly detection, defense applications, bioinformatics and natural language processing. DR is widely applied for better data visualization and improving learning in all the above fields. In this manuscript, we propose a novel DR approach namely, Noisy-free Length Discriminant Analysis (NLDA) by developing Noisy-free Relevant Pattern Selection (NRPS). Traditional pattern selection methods discriminate boundary and non-boundary patterns with the help of class information and nearest neighbors. And these methods completely ignore noisy patterns which may degrade the performance of subsequent subspace learning. To overcome this, we develop Noisy-free Relevant Pattern Selection (NRPS), in which data instances are partitioned into boundary, non-boundary and noisy patterns. With the help of noisy-free boundary and non-boundary patterns, Noisy-free Length Discriminant Analysis (NLDA) has been proposed by developing new within and between-class scatters. These scatters model discriminations between lengths (L2-norms) of different class instances by considering only boundary and non-boundary patterns, while ignoring noisy patterns. A cosine hyperbolic frame work has been developed to formulate the objective of NLDA. Moreover, NLDA can also model the discrimination of multimodal data as different class data may consist of different lengths. Experimental study conducted on the synthesized data, UCI, and leeds butterfly databases. Moreover, an experimental study over human and computer interaction, i.e., face recognition (one of the application areas of expert and intelligent systems), has been performed. And, these studies prove that the proposed method can produce better discriminated subspace compare to the state-of-the-art methods.