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Pseudoentropy characterizations provide a quantitatively precise demonstration of the close relationship between computational hardness and computational randomness. We prove a unified pseudoentropy characterization that generalizes and…
In this research, a novel adaptive filtering algorithm is proposed for complex domain signal processing. The proposed algorithm is based on Wirtinger calculus and is called as q-Complex Least Mean Square (q-CLMS) algorithm. The proposed…
Many common clustering methods cannot be used for clustering multivariate longitudinal data in cases where variables exhibit high autocorrelations. In this article, a copula kernel mixture model (CKMM) is proposed for clustering data of…
Machine learning techniques have received growing attention as an alternative strategy for developing general-purpose density functional approximations, augmenting the historically successful approach of human designed functionals derived…
Random features (RFs) are a popular technique to scale up kernel methods in machine learning, replacing exact kernel evaluations with stochastic Monte Carlo estimates. They underpin models as diverse as efficient transformers (by…
This work describes how the formalization of complex network concepts in terms of discrete mathematics, especially mathematical morphology, allows a series of generalizations and important results ranging from new measurements of the…
Quantization can be used to form new vectors/matrices with shared values close to the original. In recent years, the popularity of scalar quantization for value-sharing applications has been soaring as it has been found huge utilities in…
Hyperspectral imaging is a powerful technology that is plagued by large dimensionality. Herein, we explore a way to combat that hindrance via non-contiguous and contiguous (simpler to realize sensor) band grouping for dimensionality…
Contrastive representation learning (CRL) underpins many modern foundation models. Despite recent theoretical progress, existing analyses suffer from several key limitations: (i) the statistical consistency of CRL remains poorly understood;…
Clustering is a fundamental task in unsupervised learning. The focus of this paper is the Correlation Clustering functional which combines positive and negative affinities between the data points. The contribution of this paper is two fold:…
The search for patterns in time series is a very common task when dealing with complex systems. This is usually accomplished by employing a complexity measure such as entropies and fractal dimensions. However, such measures usually only…
The quantum relative entropy is a fundamental quantity in quantum information science, characterizing the distinguishability between two quantum states. However, this quantity is not additive in general for correlated quantum states,…
Graph-based clustering has shown promising performance in many tasks. A key step of graph-based approach is the similarity graph construction. In general, learning graph in kernel space can enhance clustering accuracy due to the…
Clustering under pairwise constraints is an important knowledge discovery tool that enables the learning of appropriate kernels or distance metrics to improve clustering performance. These pairwise constraints, which come in the form of…
Although some information-theoretic measures of uncertainty or granularity have been proposed in rough set theory, these measures are only dependent on the underlying partition and the cardinality of the universe, independent of the lower…
The paper introduces a new kernel-based Maximum Mean Discrepancy (MMD) statistic for measuring the distance between two distributions given finitely-many multivariate samples. When the distributions are locally low-dimensional, the proposed…
Classical machine learning models struggle with learning and prediction tasks on data sets exhibiting long-range correlations. Previously, the existence of a long-range correlational structure known as contextuality was shown to inhibit…
Random features is one of the most popular techniques to speed up kernel methods in large-scale problems. Related works have been recognized by the NeurIPS Test-of-Time award in 2017 and the ICML Best Paper Finalist in 2019. The body of…
This paper defines the notion of class discrepancy for families of functions. It shows that low discrepancy classes admit small offline and streaming coresets. We provide general techniques for bounding the class discrepancy of machine…
The purpose of this note is to discuss some aspects of recently proposed fractional-order variants of complex least mean square (CLMS) and normalized least mean square (NLMS) algorithms in ``Design of Fractional-order Variants of Complex…