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The K-core of a graph is the maximal subgraph within which each vertex is connected to at least K other vertices. It is a fundamental network concept for understanding threshold cascading processes with a discontinuous percolation…
Error-Correcting Output Codes (ECOCs) offer a principled approach for combining simple binary classifiers into multiclass classifiers. In this paper, we investigate the problem of designing optimal ECOCs to achieve both nominal and…
In this paper we propose a new iterative algorithm to solve the fair PCA (FPCA) problem. We start with the max-min fair PCA formulation originally proposed in [1] and derive a simple and efficient iterative algorithm which is based on the…
A spanner of a graph is a subgraph that preserves lengths of shortest paths up to a multiplicative distortion. For every $k$, a spanner with size $O(n^{1+1/k})$ and stretch $(2k+1)$ can be constructed by a simple centralized greedy…
A $k$-defective clique is a relaxation of the traditional clique definition, allowing up to $k$ missing edges. This relaxation is crucial in various real-world applications such as link prediction, community detection, and social network…
The $k$-core decomposition is a widely studied summary statistic that describes a graph's global connectivity structure. In this paper, we move beyond using $k$-core decomposition as a tool to summarize a graph and propose using $k$-core…
This thesis aims to invent new approaches for making inferences with the k-means algorithm. k-means is an iterative clustering algorithm that randomly assigns k centroids, then assigns data points to the nearest centroid, and updates…
Are the embeddings of a graph's degenerate core stable? What happens to the embeddings of nodes in the degenerate core as we systematically remove periphery nodes (by repeated peeling off $k$-cores)? We discover three patterns w.r.t.…
The $k$-NN graph has played a central role in increasingly popular data-driven techniques for various learning and vision tasks; yet, finding an efficient and effective way to construct $k$-NN graphs remains a challenge, especially for…
Given a set of $n$ points in $d$ dimensions, the Euclidean $k$-means problem (resp. the Euclidean $k$-median problem) consists of finding $k$ centers such that the sum of squared distances (resp. sum of distances) from every point to its…
In the Euclidean $k$-center problem in sliding window model, input points are given in a data stream and the goal is to find the $k$ smallest congruent balls whose union covers the $N$ most recent points of the stream. In this model, input…
Spectral clustering has found extensive use in many areas. Most traditional spectral clustering algorithms work in three separate steps: similarity graph construction; continuous labels learning; discretizing the learned labels by k-means…
The U-curve optimization problem is characterized by a decomposable in U-shaped curves cost function over the chains of a Boolean lattice. This problem can be applied to model the classical feature selection problem in Machine Learning.…
Given a graph $G=(V, E)$ and a positive integer $k$, in Maximum $k$-Order Bounded Component Set (Max-$k$-OBCS), it is required to find a vertex set $S \subseteq V$ of maximum size such that each component in the induced graph $G[S]$ has at…
Key graph-based problems play a central role in understanding network topology and uncovering patterns of similarity in homogeneous and temporal data. Such patterns can be revealed by analyzing communities formed by nodes, which in turn can…
This paper develops an efficient algorithm for computing the Euclidean projection onto the top-k-sum constraint, a key operation in financial risk management and matrix optimization problems. Existing projection methods rely on sorting and…
This paper addresses the problem of finding the densest $k$-vertex subgraph in an arbitrary graph. This problem is NP-hard and has important applications in social network analysis, fraud detection, recommendation systems, and…
Core decomposition is a fundamental graph problem with a large number of applications. Most existing approaches for core decomposition assume that the graph is kept in memory of a machine. Nevertheless, many real-world graphs are big and…
A coreset is a point set containing information about geometric properties of a larger point set. A series of previous works show that in many machine learning problems, especially in clustering problems, coreset could be very useful to…
The Maximum Common Subgraph is a computationally challenging problem with countless practical applications. Even if it has been long proven NP-hard, its importance still motivates searching for exact solutions. This work starts by…