Related papers: Rough Statistical Convergence of Double Sequences …

Sparse coding is a crucial subroutine in algorithms for various signal processing, deep learning, and other machine learning applications. The central goal is to learn an overcomplete dictionary that can sparsely represent a given input…

A time series is a sequence of data items; typical examples are videos, stock ticker data, or streams of temperature measurements. Quite some research has been devoted to comparing and indexing simple time series, i.e., time series where…

A measure of distance between two clusterings has important applications, including clustering validation and ensemble clustering. Generally, such distance measure provides navigation through the space of possible clusterings. Mostly used…

We investigate the convergence of series of random variables with second exponential moments. We give sufficient conditions for the convergence of these series with respect to an exponential Orlicz norm and almost surely. Applying this…

This paper introduces statistical order convergence and its pointwise variant for sequences of order bounded operators between Riesz spaces. We establish fundamental properties: uniqueness of the limit, stability under lattice operations,…

Lognormal random variables appear naturally in many engineering disciplines, including wireless communications, reliability theory, and finance. So, too, does the sum of (correlated) lognormal random variables. Unfortunately, no closed form…

Clustering is a fundamental data mining tool that aims to divide data into groups of similar items. Generally, intuition about clustering reflects the ideal case -- exact data sets endowed with flawless dissimilarity between individual…

We consider a system of weak* closed sets of finite-dimensional distributions. We show that a corresponding system of random variables can be defined on a probability space with a probability measure determined up to some set of measures,…

Deep clustering is a deep neural network-based speech separation algorithm that first trains the mixed component of signals with high-dimensional embeddings, and then uses a clustering algorithm to separate each mixture of sources. In this…

We study randomized variants of two classical algorithms: coordinate descent for systems of linear equations and iterated projections for systems of linear inequalities. Expanding on a recent randomized iterated projection algorithm of…

As one of the most important types of (weaker) supervised information in machine learning and pattern recognition, pairwise constraint, which specifies whether a pair of data points occur together, has recently received significant…

In this paper, we study the strong consistency of the sparse K-means clustering for high dimensional data. We prove the consistency in both risk and clustering for the Euclidean distance. We discuss the characterization of the limit of the…

Following the work of [Dikranjan et al., Fund. Math. 249:185-209, 2020] for arithmetic sequences, very recently in [Das et al., Expo. Math. 43(3):125653, 2025], statistically characterized subgroups have been investigated for certain types…

In this paper, we establish an almost sure central limit theorem for a general random sequence under a strong approximation condition. Additionally, we derive the law of the iterated logarithm for the center of mass corresponding to a…

We introduce and study deferred N\"{o}rlund statistical convergence in probability, mean of order $r,$ distribution, and study the interrelation among them. Based upon the proposed method to illustrate the findings, we present new Korovkin…

Two time scale stochastic approximation is analyzed when the iterates on either or both time scales do not necessarily converge.

The paper is concerned with stochastic approximation procedures having three main characteristics: truncations with random moving bounds, a matrix valued random step-size sequence, and a dynamically changing random regression function. We…

The subject of features normalization plays an important central role in data representation, characterization, visualization, analysis, comparison, classification, and modeling, as it can substantially influence and be influenced by all of…

We present a convex approach to probabilistic segmentation and modeling of time series data. Our approach builds upon recent advances in multivariate total variation regularization, and seeks to learn a separate set of parameters for the…

We study supervised learning problems using clustering constraints to impose structure on either features or samples, seeking to help both prediction and interpretation. The problem of clustering features arises naturally in text…