A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Nyström KPCA balances computational efficiency and statistical accuracy.
New bounds on KPCA efficiency reveal conditions for fast convergence.
Paper extends KPCA using dualization for faster, more robust algorithms.
Kernel methods are powerful learning methodologies that allow to perform non-linear data analysis. Despite their popularity, they suffer from poor scalability in big data scenarios. Various approximation methods, including random feature approximation, have been proposed to alleviate the problem. However, the statistic…
KPCA improves OoD detection by separating InD and OoD data.
KPCA-BO improves BO for high-dimensional optimization problems by learning a non-linear sub-manifold.
This paper presents a practical, and theoretically well-founded, approach to improve the speed of kernel manifold learning algorithms relying on spectral decomposition. Utilizing recent insights in kernel smoothing and learning with integral operators, we propose Reduced Set KPCA (RSKPCA), which also suggests an easy-t…
In this paper, we propose a new method to perform Sparse Kernel Principal Component Analysis (SKPCA) and also mathematically analyze the validity of SKPCA. We formulate SKPCA as a constrained optimization problem with elastic net regularization (Hastie et al.) in kernel feature space and solve it. We consider outlier d…
Kernel principal component analysis (KPCA) provides a concise set of basis vectors which capture non-linear structures within large data sets, and is a central tool in data analysis and learning. To allow for non-linear relations, typically a full kernel matrix is constructed over data points, but this…
Paper explores how unsupervised learning reduces financial crime risks.
This paper aims to develop new techniques to describe joint behavior of stocks, beyond regression and correlation. For example, we want to identify the clusters of the stocks that move together. Our work is based on applying Kernel Principal Component Analysis(KPCA) and Functional Principal Component Analysis(FPCA) to …
Sensor data analysis plays a key role in health assessment of critical equipment. Such data are multivariate and exhibit nonlinear relationships. This paper describes how one can exploit nonlinear dimension reduction techniques, such as the t-distributed stochastic neighbor embedding (t-SNE) and kernel principal compon…
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…
The main contribution of the paper is to show that Gaussian sketching of a kernel-Gram matrix yields an operator whose counterpart in an RKHS , is a \emph{random projection} operator---in the spirit of Johnson-Lindenstrauss (J-L) lemma. To be precise, given a random matrix with i.i.d. Ga…
In this paper we introduce the deep kernelized autoencoder, a neural network model that allows an explicit approximation of (i) the mapping from an input space to an arbitrary, user-specified kernel space and (ii) the back-projection from such a kernel space to input space. The proposed method is based on traditional a…
One of the major problems in natural language processing (NLP) is the word sense disambiguation (WSD) problem. It is the task of computationally identifying the right sense of a polysemous word based on its context. Resolving the WSD problem boosts the accuracy of many NLP focused algorithms such as text classification…
New asymmetric kernel methods improve feature learning.
ProbDR framework interprets DR algorithms as probabilistic inference.
Faced with the growing research towards crude oil price fluctuations influential factors following the accelerated development of Internet technology, accessible data such as Google search volume index are increasingly quantified and incorporated into forecasting approaches. In this paper, we apply multi-scale data tha…
Because of high dimensionality, correlation among covariates, and noise contained in data, dimension reduction (DR) techniques are often employed to the application of machine learning algorithms. Principal Component Analysis (PCA), Linear Discriminant Analysis (LDA), and their kernel variants (KPCA, KLDA) are among th…
Spofe bridges statistical rigor and interpretability in feature extraction from tabular data.