Related papers: Noisy Sparse Subspace Clustering
Attribute-efficient PAC learning of sparse halfspaces has been a fundamental problem in machine learning theory. In recent years, machine learning algorithms are faced with prevalent data corruptions or even malicious attacks. It is of…
This work studies the robust subspace tracking (ST) problem. Robust ST can be simply understood as a (slow) time-varying subspace extension of robust PCA. It assumes that the true data lies in a low-dimensional subspace that is either fixed…
We study the problem of identifying a small set $k\sim n^\theta$, $0<\theta<1$, of infected individuals within a large population of size $n$ by testing groups of individuals simultaneously. All tests are conducted concurrently. The goal is…
There are synergies of research interests and industrial efforts in modeling fairness and correcting algorithmic bias in machine learning. In this paper, we present a scalable algorithm for spectral clustering (SC) with group fairness…
Clustering is a ubiquitous problem in data science and signal processing. In many applications where we observe noisy signals, it is common practice to first denoise the data, perhaps using wavelet denoising, and then to apply a clustering…
Subspace clustering (SC) algorithms utilize the union of subspaces model to cluster data points according to the subspaces from which they are drawn. To better address separability of subspaces and robustness to noise we propose a wavelet…
Image classification systems recently made a giant leap with the advancement of deep neural networks. However, these systems require an excessive amount of labeled data to be adequately trained. Gathering a correctly annotated dataset is…
There has been a surge in the number of large and flat data sets - data sets containing a large number of features and a relatively small number of observations - due to the growing ability to collect and store information in medical…
We introduce a novel framework for clustering a collection of tall matrices based on their column spaces, a problem we term Subspace Clustering of Subspaces (SCoS). Unlike traditional subspace clustering methods that assume vectorized data,…
Dimension reduction is widely regarded as an effective way for decreasing the computation, storage and communication loads of data-driven intelligent systems, leading to a growing demand for statistical methods that allow analysis (e.g.,…
In this paper, we propose an efficient clustering technique to solve the problem of clustering in the presence of obstacles. The proposed algorithm divides the spatial area into rectangular cells. Each cell is associated with statistical…
This paper is concerned with computationally efficient learning of homogeneous sparse halfspaces in $\mathbb{R}^d$ under noise. Though recent works have established attribute-efficient learning algorithms under various types of label noise…
In this paper, we propose a simple algorithm to cluster nonnegative data lying in disjoint subspaces. We analyze its performance in relation to a certain measure of correlation between said subspaces. We use our clustering algorithm to…
Sparse coding is an unsupervised learning algorithm that learns a succinct high-level representation of the inputs given only unlabeled data; it represents each input as a sparse linear combination of a set of basis functions. Originally…
In this paper, we consider batch supervised learning where an adversary is allowed to corrupt instances with arbitrarily large noise. The adversary is allowed to corrupt any $l$ features in each instance and the adversary can change their…
Sparse subspace clustering (SSC) relies on sparse regression for accurate neighbor identification. Inspired by recent progress in compressive sensing, this paper proposes a new sparse regression scheme for SSC via two-step reweighted…
In this paper we initiate the study of whether or not sparse estimation tasks can be performed efficiently in high dimensions, in the robust setting where an $\eps$-fraction of samples are corrupted adversarially. We study the natural…
The problem of structured noise suppression is addressed by i)modelling the subspaces hosting the components of the signal conveying the information and ii)applying a non-extensive nonlinear technique for effecting the right separation.…
Semi-supervised clustering seeks to augment traditional clustering methods by incorporating side information provided via human expertise in order to increase the semantic meaningfulness of the resulting clusters. However, most current…
We develop an efficient and robust high-dimensional sparse Fourier algorithm for noisy samples. Earlier in the paper ``Multi-dimensional sublinear sparse Fourier algorithm" (2016), an efficient sparse Fourier algorithm with $\Theta(ds \log…