RETRACTED CHAPTER: A Computer Vision-Based Approach for Subspace Clustering and Lagrange Multiplier Optimization in High-Dimensional Data

Abstract

In this work, we discuss the issues raised due to the high-dimensionality data in real-life scenario and present a novel approach to overcome the high-dimensionality issue. Principal component analysis (PCA)-based dimension reduction and clustering are considered as promising techniques in this field. Due to computational complexities, PCA fails to achieve the desired performance for high-dimensional data, whereas subspace clustering has gained huge attraction from research community due to its nature of handling the high-dimensional data. Here, we present a new approach for subspace clustering for computer vision-based applications. According to the proposed approach, first all subspace clustering problem is formulated which is later converted into an optimization problem. This optimization problem is resolved using a diagonal optimization. Further, we present a Lagrange multiplier-based optimization strategy to reduce the error during reconstruction of low-level data from high-dimensional input data. Proposed approach is validated through experiments where face clustering and motion segmentation experiments are conducted using MATLAB simulation tool. A comparative analysis is presented which shows that the proposed approach achieves better performance when compared with the existing subspace clustering techniques.