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Support vector machine (SVM), is a popular kernel method for data classification that demonstrated its efficiency for a large range of practical applications. The method suffers, however, from some weaknesses including; time processing,…

A central challenge in Bayesian inference is efficiently approximating posterior distributions. Stein Variational Gradient Descent (SVGD) is a popular variational inference method which transports a set of particles to approximate a target…

The development of the manufacturing systems has made it increasingly necessary to monitor the data generated by multiple interconnected subsystems with rapid incoming of samples. Based on incremental Singular Value Decomposition (ISVD), we…

SVD serves as an exploratory tool in identifying the dominant features in the form of top rank-r singular factors corresponding to the largest singular values. For Big Data applications it is well known that Singular Value Decomposition…

Classical machine learning has proven remarkably useful in post-processing quantum data, yet typical learning algorithms often require prior training to be effective. In this work, we employ a tensorial kernel support vector machine…

Maximum mean discrepancies (MMDs) like the kernel Stein discrepancy (KSD) have grown central to a wide range of applications, including hypothesis testing, sampler selection, distribution approximation, and variational inference. In each…

Kernel-based multivariate statistical process control (K-MSPC) extends classical monitoring to nonlinear industrial processes. Its performance depends critically on kernel parameters such as lengthscales and variance terms. In current…

Tensor, a multi-dimensional data structure, has been exploited recently in the machine learning community. Traditional machine learning approaches are vector- or matrix-based, and cannot handle tensorial data directly. In this paper, we…

We address the problem of data-driven pattern identification and outlier detection in time series. To this end, we use singular value decomposition (SVD) which is a well-known technique to compute a low-rank approximation for an arbitrary…

Support vector machines (SVMs) are special kernel based methods and belong to the most successful learning methods since more than a decade. SVMs can informally be described as a kind of regularized M-estimators for functions and have…

Detecting and explaining anomalies is a challenging effort. This holds especially true when data exhibits strong dependencies and single measurements need to be assessed and analyzed in their respective context. In this work, we consider…

Quantum-inspired singular value decomposition (SVD) is a technique to perform SVD in logarithmic time with respect to the dimension of a matrix, given access to the matrix embedded in a segment-tree data structure. The speedup is possible…

Quantum one-class support vector machines leverage the advantage of quantum kernel methods for semi-supervised anomaly detection. However, their quadratic time complexity with respect to data size poses challenges when dealing with large…

Shewhart Control Charts (SCC)s are constructed under the assumption of normality and are widely recognized in statistical quality control by numerous researchers. Problems arise when the distribution of process data does not conform to a…

Support vector machine (SVM) is a particularly powerful and flexible supervised learning model that analyzes data for both classification and regression, whose usual algorithm complexity scales polynomially with the dimension of data space…

A new anomaly detection method called kernel outlier detection (KOD) is proposed. It is designed to address challenges of outlier detection in high-dimensional settings. The aim is to overcome limitations of existing methods, such as…

Data-driven techniques for analysis, modeling, and control of complex dynamical systems are on the uptake. Koopman theory provides the theoretical foundation for the popular kernel extended dynamic mode decomposition (kEDMD). In this work,…

A novel linear classification method that possesses the merits of both the Support Vector Machine (SVM) and the Distance-weighted Discrimination (DWD) is proposed in this article. The proposed Distance-weighted Support Vector Machine method…

We consider a streaming data model in which n sensors observe individual streams of data, presented in a turnstile model. Our goal is to analyze the singular value decomposition (SVD) of the matrix of data defined implicitly by the stream…

An unsolved issue in widely used methods such as Support Vector Data Description (SVDD) and Small Sphere and Large Margin SVM (SSLM) for anomaly detection is their nonconvexity, which hampers the analysis of optimal solutions in a manner…