arXiv research

Eigen component analysis combines quantum mechanics with machine learning for efficient data analysis.

The paper introduces eigen-portfolios using PCA to improve portfolio construction in finance.

Paper addresses eigenvector perturbation in small eigen-gap scenarios.

A new kernel test reduces noise in MMD by focusing on leading eigen-directions.

This paper is a tutorial for eigenvalue and generalized eigenvalue problems. We first introduce eigenvalue problem, eigen-decomposition (spectral decomposition), and generalized eigenvalue problem. Then, we mention the optimization problems which yield to the eigenvalue and generalized eigenvalue problems. We also prov…

This paper compares three portfolio designs for Indian stocks.

This is a detailed tutorial paper which explains the Principal Component Analysis (PCA), Supervised PCA (SPCA), kernel PCA, and kernel SPCA. We start with projection, PCA with eigen-decomposition, PCA with one and multiple projection directions, properties of the projection matrix, reconstruction error minimization, an…

Principal Component Analysis is a novel way of of dimensionality reduction. This problem essentially boils down to finding the top k eigen vectors of the data covariance matrix. A considerable amount of literature is found on algorithms meant to do so such as an online method be Warmuth and Kuzmin, Matrix Stochastic Gr…

Neural networks solve eigen-problems in differential equations.

Principal component analysis (PCA) is largely adopted for chemical process monitoring and numerous PCA-based systems have been developed to solve various fault detection and diagnosis problems. Since PCA-based methods assume that the monitored process is linear, nonlinear PCA models, such as autoencoder models and kern…

We explore the effect of past market movements on the instantaneous correlations between assets within the futures market. Quantifying this effect is of interest to estimate and manage the risk associated to portfolios of futures in a non-stationary context. We apply and extend a previously reported method called the P…

EigenGAN discovers interpretable dimensions in GAN layers for semantic control.

Proposes an online method for high-dimensional streaming data.

A new classifier uses weighted orthogonal regression for robust classification with limited data.

A hierarchical approach improves classification accuracy in large datasets.

A new method for sparse PCA using orthogonal rotations and soft-thresholding.

This work addresses two main issues of the standard Kernel Entropy Component Analysis (KECA) algorithm: the optimization of the kernel decomposition and the optimization of the Gaussian kernel parameter. KECA roughly reduces to a sorting of the importance of kernel eigenvectors by entropy instead of by variance as in K…

Eigen-GNN enhances GNNs by preserving graph structures.

TOLD++ improves convergence of diffusion models by critically damping the forward transition matrix.

The study characterizes harmonic spaces and their radial eigen-functions and vector fields.

This paper aims to address two fundamental challenges arising in eigenvector estimation and inference for a low-rank matrix from noisy observations: (1) how to estimate an unknown eigenvector when the eigen-gap (i.e. the spacing between the associated eigenvalue and the rest of the spectrum) is particularly small; (2) …

EFiGP uses Fourier and eigen-decomposition for efficient ODE parameter estimation.

IKD uses eigen-decomposition for nonlinear dimensionality reduction.

We prove polynomial and exponential decay at infinity of eigen-vectors of partial differential operators related to radiation problems for time-harmonic generalized Maxwell systems in an exterior domain with non-smooth inhomogeneous, anisotropic coefficients converging near infinity with a certain rate towards the iden…

A new mathematical approach detects frequency-based alterations in brain networks.

The paper analyzes high-dimensional kernel regression, showing different risk curves based on data and regularization.

Generalized canonical correlation analysis (GCCA) aims at finding latent low-dimensional common structure from multiple views (feature vectors in different domains) of the same entities. Unlike principal component analysis (PCA) that handles a single view, (G)CCA is able to integrate information from different feature …

Improves MARS for nonparametric multivariate regression with dimension reduction.

In this paper, energy function is used to investigate the eigen-solutions of $-Δu+ Vu=λu$ on the Riemannian manifolds. We give a new way to prove the positivity of the initial energy of energy function, which leads to a simple way to obtain the growth of eigen-solutions.

SpGAT learns graph representations using spectral attention for efficiency.

This study compares two portfolio optimization methods on Indian stocks.

Stratified models depend in an arbitrary way on a selected categorical feature that takes $K$ values, and depend linearly on the other $n$ features. Laplacian regularization with respect to a graph on the feature values can greatly improve the performance of a stratified model, especially in the low-data regime. A sign…

This paper speeds up K-FAC for deep learning by focusing on only a few eigen-modes.

In this paper, we introduce an algorithm for performing spectral clustering efficiently. Spectral clustering is a powerful clustering algorithm that suffers from high computational complexity, due to eigen decomposition. In this work, we first build the adjacency matrix of the corresponding graph of the dataset. To bui…

Proposes $σ$-PCA to learn identifiable linear transformations without whitening.

A family of parsimonious Gaussian cluster-weighted models is presented. This family concerns a multivariate extension to cluster-weighted modelling that can account for correlations between multivariate responses. Parsimony is attained by constraining parts of an eigen-decomposition imposed on the component covariance …

Principal component analysis (PCA) is one of the most powerful tools in machine learning. The simplest method for PCA, the power iteration, requires $\mathcal O(1/Δ)$ full-data passes to recover the principal component of a matrix with eigen-gap $Δ$. Lanczos, a significantly more complex method, achieves an accelerated…

In this paper, we obtain some properties of biconservative Lorentz hypersurface $M_{1}^{n}$ in $E_{1}^{n+1}$ having shape operator with complex eigen values. We prove that every biconservative Lorentz hypersurface $M_{1}^{n}$ in $E_{1}^{n+1}$ whose shape operator has complex eigen values with at most five distinct prin…

ASGD outperforms SGD in overparameterized linear regression, especially in subspaces of small eigenvalues.

Study on KRR with power-law data, showing better sample complexity.

We study the stochastic Riemannian gradient algorithm for matrix eigen-decomposition. The state-of-the-art stochastic Riemannian algorithm requires the learning rate to decay to zero and thus suffers from slow convergence and sub-optimal solutions. In this paper, we address this issue by deploying the variance reductio…

This paper has been withdrawn by the author and it is published in AGAG

Development systems for deep learning (DL), such as Theano, Torch, TensorFlow, or MXNet, are easy-to-use tools for creating complex neural network models. Since gradient computations are automatically baked in, and execution is mapped to high performance hardware, these models can be trained end-to-end on large amounts…

Repeated application of machine-learning, eigen-centric methods to an evolving dataset reveals that eigenvectors calculated by well-established computer implementations are not stable along an evolving sequence. This is because the sign of any one eigenvector may point along either the positive or negative direction of…

We investigate various structures associated with the hyperbolic Markov and homological spectra of a pseudoAnosov map $φ$ on a surface. Each unstable eigenvalue of the action of $φ$ on first cohomolgy yields an eigen-cocycle that is transverse and holonomy invariant to the stable foliation $\mathcal{F}^s$ of $φ$. Each …

New spinorial functional connects Perelman's W- and F-functionals.

In this article we give a classification of three dimensional m-quasi Einstein manifolds with two distinct Ricci-eigen values. Our study provides explicit description of local and complete metrics and potential functions. We also describe the associated warped product Einstein manifolds in detail. For the proof we pres…

Study on gradient pseudo-Ricci solitons on real hypersurfaces.