Related papers: Multi-view Kernel PCA for Time series Forecasting
Principal Component Analysis (PCA) is a commonly used tool for dimension reduction in analyzing high dimensional data; Multilinear Principal Component Analysis (MPCA) has the potential to serve the similar function for analyzing tensor…
This paper presents a time series forecasting framework which combines standard forecasting methods and a machine learning model. The inputs to the machine learning model are not lagged values or regular time series features, but instead…
Factor-based forecasting using Principal Component Analysis (PCA) is an effective machine learning tool for dimension reduction with many applications in statistics, economics, and finance. This paper introduces a Supervised Screening and…
Kernel methods serve as powerful tools to capture nonlinear patterns behind data in machine learning. The quantum kernel, integrating kernel theory with quantum computing, has attracted widespread attention. However, existing studies…
Principal component regression (PCR) is a popular technique for fixed-design error-in-variables regression, a generalization of the linear regression setting in which the observed covariates are corrupted with random noise. We provide the…
Revisiting PCA for Time Series Reduction in Temporal Dimension; Jiaxin Gao, Wenbo Hu, Yuntian Chen; Deep learning has significantly advanced time series analysis (TSA), enabling the extraction of complex patterns for tasks like…
In this paper we propose a new non-linear classifier based on a combination of locally linear classifiers. A well known optimization formulation is given as we cast the problem in a $\ell_1$ Multiple Kernel Learning (MKL) problem using many…
This paper presents a method for building a preconditioner for a kernel ridge regression problem, where the preconditioner is not only effective in its ability to reduce the condition number substantially, but also efficient in its…
Kernel matrices, as well as weighted graphs represented by them, are ubiquitous objects in machine learning, statistics and other related fields. The main drawback of using kernel methods (learning and inference using kernel matrices) is…
We propose a stable version of Principal Component Analysis (PCA) in the general framework of a separable Hilbert space. It consists in interpreting the projection on the first eigenvectors as a step function applied to the spectrum of the…
Forecasts of prospective criminal behavior have long been an important feature of many criminal justice decisions. There is now substantial evidence that machine learning procedures will classify and forecast at least as well, and typically…
We implement an all-optical setup demonstrating kernel-based quantum machine learning for two-dimensional classification problems. In this hybrid approach, kernel evaluations are outsourced to projective measurements on suitably designed…
Time series are an interesting frontier for kernel-based methods, for the simple reason that there is no kernel designed to represent them and their unique characteristics in full generality. Existing sequential kernels ignore the time…
In this paper, we propose the problem of optimizing multivariate performance measures from multi-view data, and an effective method to solve it. This problem has two features: the data points are presented by multiple views, and the target…
Approximations based on random Fourier features have recently emerged as an efficient and formally consistent methodology to design large-scale kernel machines. By expressing the kernel as a Fourier expansion, features are generated based…
Many studies of neural activity in behaving animals aim to discover interpretable low-dimensional structure in large-scale neural population recordings. One approach to this problem is demixed principal component analysis (dPCA), a…
Principal Component Analysis (PCA) is a well-known linear dimension-reduction technique designed for Euclidean data. In a wide spectrum of applied fields, however, it is common to observe multivariate circular data (also known as toroidal…
Factor modeling is a powerful statistical technique that permits to capture the common dynamics in a large panel of data with a few latent variables, or factors, thus alleviating the curse of dimensionality. Despite its popularity and…
Many scientific problems involve data exhibiting both temporal and cross-sectional dependencies. While linear dependencies have been extensively studied, the theoretical analysis of regression estimators under nonlinear dependencies remains…
We present a new straightforward principal component analysis (PCA) method based on the diagonalization of the weighted variance-covariance matrix through two spectral decomposition methods: power iteration and Rayleigh quotient iteration.…