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In this paper, we introduce a novel task termed unified anomaly detection and classification, which aims to simultaneously detect anomalous regions in images and identify their specific categories. Existing methods typically treat anomaly…
In this work, we develop a convergence framework for iterative algorithms whose updates can be described by a one-parameter family of nonexpansive operators. Within the framework, each step involving one of the main algorithmic operators is…
This paper studies the problem of parameter learning in probabilistic graphical models having latent variables, where the standard approach is the expectation maximization algorithm alternating expectation (E) and maximization (M) steps.…
Anomaly detection (AD) is a critical task across domains such as cybersecurity and healthcare. In the unsupervised setting, an effective and theoretically-grounded principle is to train classifiers to distinguish normal data from…
The analysis of nonlinear dynamical systems based on the Koopman operator is attracting attention in various applications. Dynamic mode decomposition (DMD) is a data-driven algorithm for Koopman spectral analysis, and several variants with…
We introduce a higher order phase averaging method for nonlinear oscillatory systems. Phase averaging is a technique to filter fast motions from the dynamics whilst still accounting for their effect on the slow dynamics. Phase averaging is…
Dynamic Mode Decomposition (DMD) is an unsupervised machine learning method that has attracted considerable attention in recent years owing to its equation-free structure, ability to easily identify coherent spatio-temporal structures in…
Anomaly detection aims to identify observations that deviate from the typical pattern of data. Anomalous observations may correspond to financial fraud, health risks, or incorrectly measured data in practice. We show detecting anomalies in…
In this paper, a modified method of anomaly detection using convolutional autoencoders is employed to predict phase transitions in several statistical mechanical models on a square lattice. We show that, when the autoencoder is trained with…
Graph signal processing is a framework to handle graph structured data. The fundamental concept is graph shift operator, giving rise to the graph Fourier transform. While the graph Fourier transform is a centralized procedure, distributed…
Tabular anomaly detection is often handled by single detectors or static ensembles, even though strong performance on tabular data typically comes from heterogeneous model families (e.g., tree ensembles, deep tabular networks, and tabular…
The state-of-the-art error correcting codes are based on large random constructions (random graphs, random permutations, ...) and are decoded by linear-time iterative algorithms. Because of these features, they are remarkable examples of…
Classical spectral theory provides powerful tools for analyzing linear operators, but does not extend naturally to nonlinear or compositional settings. In particular, there is no general way to transport spectral invariants in a functorial…
Deep functional map frameworks are widely employed for 3D shape matching. However, most existing deep functional map methods cannot adaptively capture important frequency information for functional map estimation in specific matching…
This paper presents a high-order differentiator for delayed measurement signal. The proposed differentiator not only can correct the delay in signal, but aslo can estimate the undelayed derivatives. The differentiator consists of two-step…
This paper studies dual-hop amplify-and-forward relaying system employing differential encoding and decoding over time-varying Rayleigh fading channels. First, the convectional "two-symbol" differential detection (CDD) is theoretically…
Dynamic sampling mechanisms in deep learning architectures have demonstrated utility across many computer vision models, though the theoretical analysis of these structures has not yet been unified. In this paper we connect the various…
The Koopman Mode Decomposition (KMD) is a data-analysis technique which is often used to extract the spatio-temporal patterns of complex flows. In this paper, we use KMD to study the dynamics of the lid-driven flow in a two-dimensional…
Multifractal analysis has become a powerful signal processing tool that characterizes signals or images via the fluctuations of their pointwise regularity, quantified theoretically by the so-called multifractal spectrum. The practical…
Monitoring is an important body of techniques in runtime verification of real-time, embedded, and cyber-physical systems. Mathematically, the monitoring problem can be formalized as a pattern matching problem against a pattern automaton.…