Related papers: Path-Based Spectral Clustering: Guarantees, Robust…
Internal measures that are used to assess the quality of a clustering usually take into account intra-group and/or inter-group criteria. There are many papers in the literature that propose algorithms with provable approximation guarantees…
Graph clustering involves the task of dividing nodes into clusters, so that the edge density is higher within clusters as opposed to across clusters. A natural, classic and popular statistical setting for evaluating solutions to this…
Physical layer security (PLS) is a potential solution for secure and reliable transmissions in future Ultra-Reliable and Low-Latency Communications (URLLC). This work jointly optimizes redundant bits and blocklength allocation in practical…
Quantum Clustering is a powerful method to detect clusters in data with mixed density. However, it is very sensitive to a length parameter that is inherent to the Schr\"odinger equation. In addition, linking data points into clusters…
We benchmark the robustness of maximum likelihood based uncertainty estimation methods to outliers in training data for regression tasks. Outliers or noisy labels in training data results in degraded performances as well as incorrect…
Discovering and clustering subspaces in high-dimensional data is a fundamental problem of machine learning with a wide range of applications in data mining, computer vision, and pattern recognition. Earlier methods divided the problem into…
We study the problem of estimating the means of well-separated mixtures when an adversary may add arbitrary outliers. While strong guarantees are available when the outlier fraction is significantly smaller than the minimum mixing weight,…
Spectral clustering is a popular and effective algorithm designed to find $k$ clusters in a graph $G$. In the classical spectral clustering algorithm, the vertices of $G$ are embedded into $\mathbb{R}^k$ using $k$ eigenvectors of the graph…
Determining the appropriate number of clusters in unsupervised learning is a central problem in statistics and data science. Traditional validity indices such as Calinski-Harabasz, Silhouette, and Davies-Bouldin-depend on centroid-based…
We study the problem of clustering networks whose nodes have imputed or physical positions in a single dimension, for example prestige hierarchies or the similarity dimension of hyperbolic embeddings. Existing algorithms, such as the…
The consistency of the maximum likelihood estimator for mixtures of elliptically-symmetric distributions for estimating its population version is shown, where the underlying distribution $P$ is nonparametric and does not necessarily belong…
Local general depth ($LGD$) functions are used for describing the local geometric features and mode(s) in multivariate distributions. In this paper, we undertake a rigorous systematic study of $LGD$ and establish several analytical and…
Graph Laplacians computed from weighted adjacency matrices are widely used to identify geometric structure in data, and clusters in particular; their spectral properties play a central role in a number of unsupervised and semi-supervised…
The performance of spectral clustering can be considerably improved via regularization, as demonstrated empirically in Amini et. al (2012). Here, we provide an attempt at quantifying this improvement through theoretical analysis. Under the…
Recent spectral clustering methods are a propular and powerful technique for data clustering. These methods need to solve the eigenproblem whose computational complexity is $O(n^3)$, where $n$ is the number of data samples. In this paper, a…
Motivated by applications of large-scale graph clustering, we study random-walk-based LOCAL algorithms whose running times depend only on the size of the output cluster, rather than the entire graph. All previously known such algorithms…
For ultra-reliable, low-latency communications (URLLC) applications such as mission-critical industrial control and extended reality (XR), it is important to ensure the communication quality of individual packets. Prior studies have…
Graph clustering, or community detection, is the task of identifying groups of closely related objects in a large network. In this paper we introduce a new community-detection framework called LambdaCC that is based on a specially weighted…
The goal of clustering is to group similar objects into meaningful partitions. This process is well understood when an explicit similarity measure between the objects is given. However, far less is known when this information is not readily…
Clustering is a popular machine learning technique for data mining that can process and analyze datasets to automatically reveal sample distribution patterns. Since the ubiquitous categorical data naturally lack a well-defined metric space…