8 accepted papers
This paper focuses on the Matrix Factorization based Clustering (MFC) method which is one of the few closed-form algorithms for the subspace clustering algorithm. Despite being simple, closed-form, and computation-efficient, MFC can outperform the other sophisticated subspace clustering methods in…
The idea of Innovation Search, initially proposed for data clustering, was recently used for outlier detection where the directions of innovation were utilized to measure the innovation of the data points. We study the Innovation Values computed by the Innovation Search algorithm under a quadratic c…
Several recent papers have discussed a modification of linear regression in which the correspondence between input variables and labels is missing or erroneous, referred to as "Linear Regression with Unknown Permutation", or "Linear Regression with Shuffled Data". Prior studies of this setup have s…
This paper presents a provable and strong algorithm, termed Innovation Search (iSearch), to robust Principal Component Analysis (PCA) and outlier detection. An outlier by definition is a data point which does not participate in forming a low dimensional structure with a large number of data point…
This paper presents a remarkably simple, yet powerful, algorithm for robust Principal Component Analysis (PCA). In the proposed approach, an outlier is set apart from an inlier by comparing their coherence with the rest of the data points. As inliers lie on a low dimensional subspace, they are likel…
This paper focuses on the low rank plus sparse matrix decomposition problem in big data settings. Conventional algorithms solve high-dimensional optimization problems that scale with the data dimension, which limits their scalability. In addition, existing randomized approaches mostly rely on blind…
This paper presents a new scalable approach, termed Innovation Pursuit (iPursuit), to the problem of subspace clustering. iPursuit rests on a new geometrical idea whereby each subspace is identified based on its novelty with respect to the other subspaces. The subspaces are identified consecutively…
This paper presents a new randomized approach to high-dimensional low rank (LR) plus sparse matrix decomposition. For a data matrix D ∈R^N_1 \times N_2, the complexity of conventional decomposition methods is O(N_1 N_2 r), which limits their usefulness in big data settings (r is the rank of the LR c…