Related papers: Efficient Algorithms for Sum-of-Minimum Optimizati…
We initiate the study of the following general clustering problem. We seek to partition a given set $P$ of data points into $k$ clusters by finding a set $X$ of $k$ centers and assigning each data point to one of the centers. The cost of a…
Mining clusters from data is an important endeavor in many applications. The $k$-means method is a popular, efficient, and distribution-free approach for clustering numerical-valued data, but does not apply for categorical-valued…
We present a general approach to rounding semidefinite programming relaxations obtained by the Sum-of-Squares method (Lasserre hierarchy). Our approach is based on using the connection between these relaxations and the Sum-of-Squares proof…
These notes focus on the minimization of convex functionals using first-order optimization methods, which are fundamental in many areas of applied mathematics and engineering. The primary goal of this document is to introduce and analyze…
Bayesian optimization is a sequential method for minimizing objective functions that are expensive to evaluate and about which few assumptions can be made. By using all gathered data to train a Gaussian process model for the function and…
Fast and high quality document clustering is an important task in organizing information, search engine results obtaining from user query, enhancing web crawling and information retrieval. With the large amount of data available and with a…
We survey old and new results about optimal algorithms for summation of finite sequences and for integration of functions from Hoelder or Sobolev spaces. First we discuss optimal deterministic and randomized algorithms. Then we add a new…
Data-driven algorithm selection is a powerful approach for choosing effective heuristics for computational problems. It operates by evaluating a set of candidate algorithms on a collection of representative training instances and selecting…
The objective of a two-stage submodular maximization problem is to reduce the ground set using provided training functions that are submodular, with the aim of ensuring that optimizing new objective functions over the reduced ground set…
In this paper we propose a variant of the random coordinate descent method for solving linearly constrained convex optimization problems with composite objective functions. If the smooth part of the objective function has Lipschitz…
The $k$-means algorithm is a prevalent clustering method due to its simplicity, effectiveness, and speed. However, its main disadvantage is its high sensitivity to the initial positions of the cluster centers. The global $k$-means is a…
In this brief paper, we present a naive aggregation algorithm for a typical learning problem with expert advice setting, in which the task of improving generalization, i.e., model validation, is embedded in the learning process as a…
Composite function minimization captures a wide spectrum of applications in both computer vision and machine learning. It includes bound constrained optimization and cardinality regularized optimization as special cases. This paper proposes…
In this paper, we study clustering with respect to the k-modes objective function, a natural formulation of clustering for categorical data. One of the main contributions of this paper is to establish the connection between k-modes and…
Stochastic optimization of continuous objectives is at the heart of modern machine learning. However, many important problems are of discrete nature and often involve submodular objectives. We seek to unleash the power of stochastic…
In this paper we describe a new algorithm called Fast Adaptive Sequencing Technique (FAST) for maximizing a monotone submodular function under a cardinality constraint $k$ whose approximation ratio is arbitrarily close to $1-1/e$, is…
Global polynomial optimization is an important tool across applied mathematics, with many applications in operations research, engineering, and physical sciences. In various settings, the polynomials depend on external parameters that may…
Optimization methods have been broadly applied to two classes of objects viz. (i) modeling and description of data and (ii) the determination of the stationary points of functions. Here, a theoretical basis is developed that optimizes an…
In this paper, we propose a new Fully Composite Formulation of convex optimization problems. It includes, as a particular case, the problems with functional constraints, max-type minimization problems, and problems of Composite…
Clustering stands as one of the most prominent challenges in unsupervised machine learning. Among centroid-based methods, the classic $k$-means algorithm, based on Lloyd's heuristic, is widely used. Nonetheless, it is a well-known fact that…