On Perfect Clustering of High Dimension, Low Sample Size Data
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Non-convex constrained optimization problems have become a powerful framework for modeling a wide range of machine learning problems, with applications in k-means clustering, large- scale semidefinite programs (SDPs), and various other tasks. As the perfor ...
Unsupervised graph representation learning aims to learn low-dimensional node embeddings without supervision while preserving graph topological structures and node attributive features. Previous Graph Neural Networks (GNN) require a large number of labeled ...
New York2023
In this thesis we present and analyze approximation algorithms for three different clustering problems. The formulations of these problems are motivated by fairness and explainability considerations, two issues that have recently received attention in the ...
In this paper, the recommended implementation of the post-quantum key exchange SIKE for Cortex-M4 is attacked through power analysis with a single trace by clustering with the k-means algorithm the power samples of all the invocations of the elliptic curve ...
A simple model to study subspace clustering is the high-dimensional k -Gaussian mixture model where the cluster means are sparse vectors. Here we provide an exact asymptotic characterization of the statistically optimal reconstruction error in this model i ...
Dynamical Systems (DS) are fundamental to the modeling and understanding time evolving phenomena, and have application in physics, biology and control. As determining an analytical description of the dynamics is often difficult, data-driven approaches are ...
MICROTOME PUBL2022
This thesis focuses on designing spectral tools for graph clustering in sublinear time. With the emergence of big data, many traditional polynomial time, and even linear time algorithms have become prohibitively expensive. Processing modern datasets requir ...
In high dimension, low sample size (HDLSS) settings, classifiers based on Euclidean distances like the nearest neighbor classifier and the average distance classifier perform quite poorly if differences between locations of the underlying populations get m ...
In Paralympic cross-country sit skiing, athlete classification is performed by an expert panel, so it may be affected by subjectivity. An evidence-based classification is required, in which objective measures of impairment must be identified. The purposes ...
Clustering in education, particularly in large-scale online environments like MOOCs, is essential for understanding and adapting to diverse student needs. However, the effectiveness of clustering depends on its interpretability, which becomes challenging w ...
