Related papers: Operator Analysis of MACD
Functional data analysis in a mixed-effects model framework is done using operator calculus. In this approach the functional parameters are treated as serially correlated effects giving an alternative to the penalized likelihood approach,…
A large class of non-smooth practical optimization problems can be written as minimization of a sum of smooth and partly smooth functions. We examine such structured problems which also depend on a parameter vector and study the problem of…
In this paper, we explore a novel approach to 3D anomaly detection (AD) that goes beyond merely identifying anomalies based on structural characteristics. Our primary perspective is that most anomalies arise from unpredictable defective…
Agentic artificial intelligence (AI) -- multi-agent systems that combine large language models with external tools and autonomous planning -- are rapidly transitioning from research laboratories into high-stakes domains. Our earlier "Basic"…
We address a practical scenario of anomaly detection for industrial sound data, where the sound of a target machine is corrupted by background noise and interference from neighboring machines. Overcoming this challenge is difficult since…
Dynamic mode decomposition (DMD) is an efficient tool for decomposing spatio-temporal data into a set of low-dimensional modes, yielding the oscillation frequencies and the growth rates of physically significant modes. In this paper, we…
We shall say that a densely defined closed operator $T$ on a Hilbert space is balanced if $\cD(T)=\cD(T^*)$. Balanced operators are described in terms of their phase operators abnd their moduli. Examples of balanced operators are developed.…
The superposition of arrival processes is a fundamental yet analytically intractable operation in queueing networks when inputs are general non-renewal streams. Classical methods either reduce merged flows to renewal surrogates, rely on…
The Dynamic Mode Decomposition (DMD)---a popular method for performing data-driven Koopman spectral analysis---has gained increased adoption as a technique for extracting dynamically meaningful spatio-temporal descriptions of fluid flows…
We have deluge of data in time series format for numerous phenomena. The number of snapshots, resolution and many other factors come into play as we look to identify the dynamics in a given problem. The pre-processing and post-processing…
We analyze sparse frame based regularization of inverse problems by means of a diagonal frame decomposition (DFD) for the forward operator, which generalizes the SVD. The DFD allows to define a non-iterative (direct) operator-adapted frame…
We propose a new method for computing Dynamic Mode Decomposition (DMD) evolution matrices, which we use to analyze dynamical systems. Unlike the majority of existing methods, our approach is based on a variational formulation consisting of…
The classical sampling theorem for bandlimited functions has recently been generalized to apply to so-called bandlimited operators, that is, to operators with band-limited Kohn-Nirenberg symbols. Here, we discuss operator sampling versions…
To improve the performance in identifying the faults under strong noise for rotating machinery, this paper presents a dynamic feature reconstruction signal graph method, which plays the key role of the proposed end-to-end fault diagnosis…
The Dirac operator provides a unified framework for processing signals defined over different order topological domains, such as node and edge signals. Its eigenmodes define a spectral representation that inherently captures cross-domain…
In this paper, we introduce Masked Anomaly Detection (MAD), a general self-supervised learning task for multivariate time series anomaly detection. With the increasing availability of sensor data from industrial systems, being able to…
In static analysis by abstract interpretation, one often uses widening operators in order to enforce convergence within finite time to an inductive invariant. Certain widening operators, including the classical one over finite polyhedra,…
Delay-coordinates dynamic mode decomposition (DC-DMD) is widely used to extract coherent spatiotemporal modes from high-dimensional time series. A central challenge is distinguishing dynamically meaningful modes from spurious modes induced…
The ability of Variational Autoencoders to learn disentangled representations has made them appealing for practical applications. However, their mean representations, which are generally used for downstream tasks, have recently been shown…
Existing anomaly detection (AD) methods often treat the modality and class as independent factors. Although this paradigm has enriched the development of AD research branches and produced many specialized models, it has also led to…