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Identifying a set of homogeneous clusters in a heterogeneous dataset is one of the most important classes of problems in statistical modeling. In the realm of unsupervised partitional clustering, k-means is a very important algorithm for…
Clustering categorical data is an integral part of data mining and has attracted much attention recently. In this paper, we present k-histogram, a new efficient algorithm for clustering categorical data. The k-histogram algorithm extends…
Centroid-based clustering algorithms, such as hard K-means (HKM) and fuzzy K-means (FKM), have suffered from learning bias towards large clusters. Their centroids tend to be crowded in large clusters, compromising performance when the true…
Deep learning models have become widely adopted in various domains, but their performance heavily relies on a vast amount of data. Datasets often contain a large number of irrelevant or redundant samples, which can lead to computational…
Although numerous clustering algorithms have been developed, many existing methods still leverage k-means technique to detect clusters of data points. However, the performance of k-means heavily depends on the estimation of centers of…
We investigate the efficiency of k-means in terms of both statistical and computational requirements. More precisely, we study a Nystr\"om approach to kernel k-means. We analyze the statistical properties of the proposed method and show…
This paper presents a novel method for efficient image retrieval, based on a simple and effective hashing of CNN features and the use of an indexing structure based on Bloom filters. These filters are used as gatekeepers for the database of…
Autoregressive language models rely on a Key-Value (KV) Cache, which avoids re-computing past hidden states during generation, making it faster. As model sizes and context lengths grow, the KV Cache becomes a significant memory bottleneck,…
The impressive capabilities of Large Language Models (LLMs) come at the cost of substantial computational resources during deployment. While KV Cache can significantly reduce recomputation during inference, it also introduces additional…
Reduced k-means clustering is a method for clustering objects in a low-dimensional subspace. The advantage of this method is that both clustering of objects and low-dimensional subspace reflecting the cluster structure are simultaneously…
Clustering is one of the most crucial problems in unsupervised learning, and the well-known $k$-means clustering algorithm has been shown to be implementable on a quantum computer with a significant speedup. However, many clustering…
K-Means algorithm is a popular clustering method. However, it has two limitations: 1) it gets stuck easily in spurious local minima, and 2) the number of clusters k has to be given a priori. To solve these two issues, a multi-prototypes…
Clustering is one of the most important tools for analysis of large datasets, and perhaps the most popular clustering algorithm is Lloyd's algorithm for $k$-means. This algorithm takes $n$ vectors $V=[v_1,\dots,v_n]\in\mathbb{R}^{d\times…
The quadratic complexity of the attention mechanism and the substantial memory footprint of the Key-Value (KV) cache present severe computational and memory challenges for Large Language Models (LLMs) processing long contexts. Existing…
The k-means clustering is one of the most popular clustering algorithms in data mining. Recently a lot of research has been concentrated on the algorithm when the dataset is divided into multiple parties or when the dataset is too large to…
High-throughput approximations of quantum mechanics calculations and combinatorial experiments have been traditionally used to reduce the search space of possible molecules, drugs and materials. However, the interplay of structural and…
In this study we introduce a novel energy functional for long-sequence memory, building upon the framework of dense Hopfield networks which achieves exponential storage capacity through higher-order interactions. Building upon earlier work…
The outlier detection problem in some cases is similar to the classification problem. For example, the main concern of clustering-based outlier detection algorithms is to find clusters and outliers, which are often regarded as noise that…
We propose a simple yet effective multiple kernel clustering algorithm, termed simple multiple kernel k-means (SimpleMKKM). It extends the widely used supervised kernel alignment criterion to multi-kernel clustering. Our criterion is given…
Factorial k-means (FKM) clustering is a method for clustering objects in a low-dimensional subspace. The advantage of this method is that the partition of objects and the low-dimensional subspace reflecting the cluster structure are…