Robust Subspace Clustering With Complex Noise

Abstract

Subspace clustering has important and wide applications in computer vision and pattern recognition. It is a challenging task to learn low-dimensional subspace structures due to complex noise existing in high-dimensional data. Complex noise has much more complex statistical structures, and is neither Gaussian nor Laplacian noise. Recent subspace clustering methods usually assume a sparse representation of the errors incurred by noise and correct these errors iteratively. However, large corruptions incurred by complex noise cannot be well addressed by these methods. A novel optimization model for robust subspace clustering is proposed in this paper. Its objective function mainly includes two parts. The first part aims to achieve a sparse representation of each high-dimensional data point with other data points. The second part aims to maximize the correntropy between a given data point and its low-dimensional representation with other points. Correntropy is a robust measure so that the influence of large corruptions on subspace clustering can be greatly suppressed. An extension of pairwise link constraints is also proposed as prior information to deal with complex noise. Half-quadratic minimization is provided as an efficient solution to the proposed robust subspace clustering formulations. Experimental results on three commonly used data sets show that our method outperforms state-of-the-art subspace clustering methods.

Adaptive Rank-One Matrix Completion Using Sum of Outer Products

“…In fact, nonconvex loss functions such as Welsch and Cauchy, are widely utilized to achieve robust performance [42]- [44], because the convex ℓ 1 -norm and Huber function are still sensitive to outliers with large magnitude. Among these nonconvex functions, Welsch function as an error measure has attained big success in robust principal component analysis (RPCA) [45], robust matrix completion (RMC) [19] and subspace clustering [46]. Nevertheless, Welsch function has two limitations: (i) The first issue is stated by comparing the Welsch function with its Huber counterpart.…”

Robust Subspace Clustering with Block Diagonal Representation for Noisy Image Datasets

“…They defined an energy function to measure a block in the projected space, and found the correct block with the maximal energy to lead clustering. He et al [38] proposed the subspace clustering algorithm via half-quadratic (SCHQ) to handle noisy data. SCHQ consisted of two parts, the first one adopted l 1 norm to obtain a sparse representation of data, and the second one maximized the correlation of low-dimensional representations among a given data point and other data points to reduce the damage of noisy data to coefficient representation.…”

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“…Subspace clustering initiates the task of finding a subspace belonging to the low-dimensional class in which the data from the individual groups can simultaneously accommodate its subspace structure. The classifications of subspace clustering methods are algebraic methodologies, iterative methods, spectral clustering derived methods and statistical technique of clustering [9]. An extension to the conventional method of clustering is the subspace clustering technique.…”