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In 1980 and 1981, two pioneering papers laid the foundation for what became known as nonlinear time-series analysis: the analysis of observed data---typically univariate---via dynamical systems theory. Based on the concept of state-space…

This survey is written in summer, 2016. The purpose of this survey is to briefly introduce nonlinear dimensionality reduction (NLDR) in data reduction. The first two NLDR were respectively published in Science in 2000 in which they solve…

This is a tutorial and survey paper for nonlinear dimensionality and feature extraction methods which are based on the Laplacian of graph of data. We first introduce adjacency matrix, definition of Laplacian matrix, and the interpretation…

Dimensionality reduction is a crucial step for pattern recognition and data mining tasks to overcome the curse of dimensionality. Principal component analysis (PCA) is a traditional technique for unsupervised dimensionality reduction, which…

Time series analysis by state-space models is widely used in forecasting and extracting unobservable components like level, slope, and seasonality, along with explanatory variables. However, their reliance on traditional Kalman filtering…

In this paper, we introduce a new extension of the Singular Spectrum Analysis (SSA) called functional SSA to analyze functional time series. The new methodology is developed by integrating ideas from functional data analysis and univariate…

Classifying hyperspectral images (HSIs) is a complex task in remote sensing due to the high-dimensional nature and volume of data involved. To address these challenges, we propose the Spectral-Spatial non-Linear Model, a novel framework…

Anomaly detection of multivariate time series is meaningful for system behavior monitoring. This paper proposes an anomaly detection method based on unsupervised Short- and Long-term Mask Representation learning (SLMR). The main idea is to…

Efficient spectrum management in massive-scale wireless networks is increasingly challenged by explosive action spaces and the computational intractability of traditional optimization. This study proposes a Large-Scale LLM-Driven Spectrum…

Hyper-spectral data can be analyzed to recover physical properties at large planetary scales. This involves resolving inverse problems which can be addressed within machine learning, with the advantage that, once a relationship between…

Neural recordings are nonstationary time series, i.e. their properties typically change over time. Identifying specific changes, e.g. those induced by a learning task, can shed light on the underlying neural processes. However, such changes…

This paper addresses classification problems with matrix-valued data, which commonly arise in applications such as neuroimaging and signal processing. Building on the assumption that the data from each class follows a matrix normal…

Anomalies are samples that significantly deviate from the rest of the data and their detection plays a major role in building machine learning models that can be reliably used in applications such as data-driven design and novelty…

We propose a kernel-spectral embedding algorithm for learning low-dimensional nonlinear structures from high-dimensional and noisy observations, where the datasets are assumed to be sampled from an intrinsically low-dimensional manifold and…

The recent development of more sophisticated spectroscopic methods allows acqui- sition of high dimensional datasets from which valuable information may be extracted using multivariate statistical analyses, such as dimensionality reduction…

The Laplacian eigenvalues of a network play an important role in the analysis of many structural and dynamical network problems. In this paper, we study the relationship between the eigenvalue spectrum of the normalized Laplacian matrix and…

Understanding the temporal characteristics of data from low frequency radio telescopes is of importance in devising suitable calibration strategies. Application of time series analysis techniques to data from radio telescopes can reveal a…

A new array signal reconstruction and signal-channel DOA estimation method based on TMLA by nonuniform period modulation are proposed. By using non-uniform period modulation, the harmonic component produced by different elements could be…

This paper is a study of continuous time Singular Spectrum Analysis (SSA). We show that the principal eigenfunctions are solutions to a set of linear ODEs with constant coefficients. We also introduce a natural generalization of SSA,…

Spectral methods have been the mainstay in several domains such as machine learning and scientific computing. They involve finding a certain kind of spectral decomposition to obtain basis functions that can capture important structures for…