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

In this work, we discuss about the issues raised due to the high-dimensional 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 Low-level data from high-dimension 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 shows that the proposed approach achieves better performance when compared with the existing subspace clustering techniques.