Related papers: SoS Degree Reduction with Applications to Clusteri…
This paper proposes a new generalized two dimensional learning approach for particle swarm based feature selection. The core idea of the proposed approach is to include the information about the subset cardinality into the learning…
Graph clustering and community detection are central problems in modern data mining. The increasing need for analyzing billion-scale data calls for faster and more scalable algorithms for these problems. There are certain trade-offs between…
We give a dimensionality reduction procedure to approximate the sum of distances of a given set of $n$ points in $R^d$ to any "shape" that lies in a $k$-dimensional subspace. Here, by "shape" we mean any set of points in $R^d$. Our…
High-order tensor methods that employ Taylor-based local models (of degree $p\ge 3$) within adaptive regularization frameworks have been recently proposed for both convex and nonconvex optimization problems. They have been shown to have…
We consider estimation models of the form $Y=X^*+N$, where $X^*$ is some $m$-dimensional signal we wish to recover, and $N$ is symmetrically distributed noise that may be unbounded in all but a small $\alpha$ fraction of the entries. We…
Advances in sensing technologies and the growth of the internet have resulted in an explosion in the size of modern datasets, while storage and processing power continue to lag behind. This motivates the need for algorithms that are…
In this paper we study the problem of convergence and generalization error bound of stochastic momentum for deep learning from the perspective of regularization. To do so, we first interpret momentum as solving an $\ell_2$-regularized…
Clustering of data points is a fundamental tool in data analysis. We consider points $X$ in a relaxed metric space, where the triangle inequality holds within a constant factor. The {\em cost} of clustering $X$ by $Q$ is $V(Q)=\sum_{x\in X}…
The $k$-$\mathtt{means}$++ seeding algorithm (Arthur & Vassilvitskii, 2007) is widely used in practice for the $k$-means clustering problem where the goal is to cluster a dataset $\mathcal{X} \subset \mathbb{R} ^d$ into $k$ clusters. The…
When solving real-world problems, practitioners often hesitate to implement solutions obtained from mathematical models, especially for important decisions. This hesitation stems from practitioners' lack of trust in optimization models and…
We study optimization problems in a metric space $(\mathcal{X},d)$ where we can compute distances in two ways: via a ''strong'' oracle that returns exact distances $d(x,y)$, and a ''weak'' oracle that returns distances $\tilde{d}(x,y)$…
Inferring cluster structure in microarray datasets is a fundamental task for the -omic sciences. A fundamental question in Statistics, Data Analysis and Classification, is the prediction of the number of clusters in a dataset, usually…
We present a framework that provides deterministic consistency algorithms for given memory models. Such an algorithm checks whether the executions of a shared-memory concurrent program are consistent under the axioms defined by a model. For…
In many real world applications, data cannot be accurately represented by vectors. In those situations, one possible solution is to rely on dissimilarity measures that enable sensible comparison between observations. Kohonen's…
We study a generalized framework for structured sparsity. It extends the well-known methods of Lasso and Group Lasso by incorporating additional constraints on the variables as part of a convex optimization problem. This framework provides…
Symbolic Data Analysis is based on special descriptions of data - symbolic objects (SO). Such descriptions preserve more detailed information about units and their clusters than the usual representations with mean values. A special kind of…
We introduce a method for proving Sum-of-Squares (SoS)/ Lasserre hierarchy lower bounds when the initial problem formulation exhibits a high degree of symmetry. Our main technical theorem allows us to reduce the study of the positive…
The area of constrained clustering has been extensively explored by researchers and used by practitioners. Constrained clustering formulations exist for popular algorithms such as k-means, mixture models, and spectral clustering but have…
Ensemble pruning, selecting a subset of individual learners from an original ensemble, alleviates the deficiencies of ensemble learning on the cost of time and space. Accuracy and diversity serve as two crucial factors while they usually…
We study the problem of estimating the covariance matrix of a high-dimensional distribution when a small constant fraction of the samples can be arbitrarily corrupted. Recent work gave the first polynomial time algorithms for this problem…