Related papers: Efficient solutions for weight-balanced partitioni…
Clustering may be the most fundamental problem in unsupervised learning which is still active in machine learning research because its importance in many applications. Popular methods like K-means, may suffer from instability as they are…
Many important combinatorial problems can be modeled as constraint satisfaction problems. Hence identifying polynomial-time solvable classes of constraint satisfaction problems has received a lot of attention. In this paper, we are…
We revisit the problem of large-scale assortment optimization under the multinomial logit choice model without any assumptions on the structure of the feasible assortments. Scalable real-time assortment optimization has become essential in…
The problem of interpreting or aggregating multiple rankings is common to many real-world applications. Perhaps the simplest and most common approach is a weighted rank aggregation, wherein a (convex) weight is applied to each input ranking…
We consider a variant of bin packing called multiple-choice vector bin packing. In this problem we are given a set of items, where each item can be selected in one of several $D$-dimensional incarnations. We are also given $T$ bin types,…
Given $n$ weighted points (positive or negative) in $d$ dimensions, what is the axis-aligned box which maximizes the total weight of the points it contains? The best known algorithm for this problem is based on a reduction to a related…
We study convex optimization problems where disjoint blocks of variables are controlled by binary indicator variables that are also subject to conditions, e.g., cardinality. Several classes of important examples can be formulated in such a…
One of the most widely used techniques for data clustering is agglomerative clustering. Such algorithms have been long used across many different fields ranging from computational biology to social sciences to computer vision in part…
The problem of organizing data that evolves over time into clusters is encountered in a number of practical settings. We introduce evolutionary subspace clustering, a method whose objective is to cluster a collection of evolving data points…
Convex clustering is a modern clustering framework that guarantees globally optimal solutions and performs comparably to other advanced clustering methods. However, obtaining a complete dendrogram (clusterpath) for large-scale datasets…
In many high-dimensional problems, like sparse-PCA, planted clique, or clustering, the best known algorithms with polynomial time complexity fail to reach the statistical performance provably achievable by algorithms free of computational…
In this paper, we solve a maximization problem where the objective function is quadratic and convex or concave and the constraints set is the reachable value set of a convergent discrete-time affine system. Moreover, we assume that the…
We consider the bin packing problem with d different item sizes s_i and item multiplicities a_i, where all numbers are given in binary encoding. This problem formulation is also known as the 1-dimensional cutting stock problem. In this…
We study a multi-factor block model for variable clustering and connect it to regularized subspace clustering through a distributionally robust version of nodewise regression. To solve the latter problem, we derive a convex relaxation,…
This paper studies an open question in the warehouse problem where a merchant trading a commodity tries to find an optimal inventory-trading policy to decide on purchase and sale quantities during a fixed time horizon in order to maximize…
Recently increasing penetration of renewable energy generation brings challenges for power system operators to perform efficient power generation daily scheduling, due to the intermittent nature of the renewable generation and discrete…
We continue the investigation of problems concerning correlation clustering or clustering with qualitative information, which is a clustering formulation that has been studied recently. The basic setup here is that we are given as input a…
Convex clustering is a convex relaxation of the $k$-means and hierarchical clustering. It involves solving a convex optimization problem with the objective function being a squared error loss plus a fusion penalty that encourages the…
Clustering is a fundamental task in data science that aims to group data based on their similarities. However, defining similarity is often ambiguous, making it challenging to determine the most appropriate objective function for a given…
We study the problem of efficient exact partitioning of the hypergraphs generated by high-order planted models. A high-order planted model assumes some underlying cluster structures, and simulates high-order interactions by placing…