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The present paper is devoted to clustering geometric graphs. While the standard spectral clustering is often not effective for geometric graphs, we present an effective generalization, which we call higher-order spectral clustering. It…

Subsethood, which is to measure the degree of set inclusion relation, is predominant in fuzzy set theory. This paper introduces some basic concepts of spatial granules, coarse-fine relation, and operations like meet, join, quotient meet and…

We study the set of all pseudoline arrangements with contact points which cover a given support. We define a natural notion of flip between these arrangements and study the graph of these flips. In particular, we provide an enumeration…

Convolutional networks are at the center of best-in-class computer vision applications for a wide assortment of undertakings. Since 2014, a profound amount of work began to make better convolutional architectures, yielding generous…

In clustering problems, a central decision-maker is given a complete metric graph over vertices and must provide a clustering of vertices that minimizes some objective function. In fair clustering problems, vertices are endowed with a color…

The goal of data clustering is to partition data points into groups to minimize a given objective function. While most existing clustering algorithms treat each data point as vector, in many applications each datum is not a vector but a…

Granular convergence is a property of a granular pack as it is repeatedly sheared in a cyclic, quasistatic fashion, as the packing configuration changes via discrete events. Under suitable conditions the set of microscopic configurations…

Representation learning aims to extract meaningful lower-dimensional embeddings from data, known as representations. Despite its widespread application, there is no established definition of a ``good'' representation. Typically, the…

Over the last three decades, researchers have intensively explored various clustering tools for categorical data analysis. Despite the proposal of various clustering algorithms, the classical k-modes algorithm remains a popular choice for…

Clustering is considered a non-supervised learning setting, in which the goal is to partition a collection of data points into disjoint clusters. Often a bound $k$ on the number of clusters is given or assumed by the practitioner. Many…

We introduce a novel end-to-end approach for learning to cluster in the absence of labeled examples. Our clustering objective is based on optimizing normalized cuts, a criterion which measures both intra-cluster similarity as well as…

Mixture model-based frameworks are very popular for statistical inference in clustering. While convenient for producing probabilistic estimates of cluster assignments and uncertainty, they are prone to misspecification, which can lead to…

Training machine learning models in a meaningful order, from the easy samples to the hard ones, using curriculum learning can provide performance improvements over the standard training approach based on random data shuffling, without any…

There is a growing interest in characterizing circular data found in biological systems. Such data are wide ranging and varied, from signal phase in neural recordings to nucleotide sequences in round genomes. Traditional clustering…

Deep clustering as an important branch of unsupervised representation learning focuses on embedding semantically similar samples into the identical feature space. This core demand inspires the exploration of contrastive learning and…

Coreset, which is a summary of the original dataset in the form of a small weighted set in the same sample space, provides a promising approach to enable machine learning over distributed data. Although viewed as a proxy of the original…

Recent studies have revealed that neural networks learn interpretable algorithms for many simple problems. However, little is known about how these algorithms emerge during training. In this article, I study the training dynamics of a small…

Distributional text clustering delivers semantically informative representations and captures the relevance between each word and semantic clustering centroids. We extend the neural text clustering approach to text classification tasks by…

A clustering algorithm partitions a set of data points into smaller sets (clusters) such that each subset is more tightly packed than the whole. Many approaches to clustering translate the vector data into a graph with edges reflecting a…

Neural networks have achieved success in a wide array of perceptual tasks but often fail at tasks involving both perception and higher-level reasoning. On these more challenging tasks, bespoke approaches (such as modular symbolic…