A Unified Tensor Framework for Clustering and Simultaneous Reconstruction of Incomplete Imaging Data

Abstract

Incomplete observations in the data are always troublesome to data clustering algorithms. In fact, most of the well-received techniques are not designed to encounter such imperative scenarios. Hence, clustering of images under incomplete samples is an inquisitive yet unaddressed area of research. Therefore, the aim of this article is to design a single-stage optimization procedure for clustering as well as simultaneous reconstruction of images without breaking the intrinsic spatial structure. The method employs the self-expressiveness property of submodules, and images are stacked as the lateral slices of a three-dimensional tensor. The proposed optimization method is designed to extract a sparse t -linear combination tensor with low multirank constraint, consisting of a unique set of linear coefficients in the form of mode-3 fibers and the spectral clustering is performed on these fibers. Simultaneously, the recovery of lost samples is accomplished by twisting the entire lateral slices of the data tensor and applying a low-rank approximation on each slice. The prominence of the proposed method lies in the simultaneous execution of data clustering and reconstruction of incomplete observations in a single step. Experimental results reveal the excellence of the proposed method over state-of-the-art clustering algorithms in the context of incomplete imaging data.

A Tensor-Based Submodule Clustering for 2D Images Using $$l_{\frac{1}{2}}$$-Induced Tensor Nuclear Norm Minimization

“…Further, in [9], Wu extended the work in [11] by incorporating a manifold regularization, exploiting the local structure of data. In another way, based on UoFS model, Francis et al proposed a combined framework for clustering of images and simultaneous reconstruction of missing samples in the images [3].…”

“…Tensors, matrices, vectors, and scalars are denoted in this work by calligraphic uppercase, bold uppercase, bold lowercase, and non bold letters. For a third order tensor X , X (:, l, m), X (l, :, m) and X (l, m, :) represent the (l, m)th mode-1, mode-2 and mode-3 tubes or ( f ibers), respectively [3,11]. Then, X (k, :, :), X (:, k, :), denotes the kth horizontal, lateral slices.…”

“…In recent years, a vast volume of data, such as videos, images, audio and text documents have been generated, stored, and transferred among various sources, all around the world [1][2][3]. However, the majority of them are unstructured, requiring proper grouping in order to obtain meaningful information [1,2].…”

“…In light of this, clustering is an unsupervised data grouping approach in which objects are classified based on similarity inherent in the data [6,7]. Clustering algorithms are now widely employed in domains such as computer vision, data mining, pattern recognition, and motion segmentation [1,3,8]. In recent years, a variety of algorithms have been presented for a number of purposes.…”

“…High-dimensional data is mostly composed up of data of several types, such as images, videos, text, and web documents [8]. Conventional clustering methods generally fail to address the clustering of large dimensional data due to its complicated and diversified nature, as well as its high dimensionality [3,8]. The concept of subspace clustering has been presented as a solution to this problem [6].…”