Related papers: Learning in High-Dimensional Feature Spaces Using …
We study fast algorithms for computing fundamental properties of a positive semidefinite kernel matrix $K \in \mathbb{R}^{n \times n}$ corresponding to $n$ points $x_1,\ldots,x_n \in \mathbb{R}^d$. In particular, we consider estimating the…
Modern machine learning systems are increasingly trained on large amounts of data embedded in high-dimensional spaces. Often this is done without analyzing the structure of the dataset. In this work, we propose a framework to study the…
In this article, a novel approach to learning a complex function which can be written as the system of linear equations is introduced. This learning is grounded upon the observation that solving the system of linear equations by a…
We extend the diffusion-map formalism to data sets that are induced by asymmetric kernels. Analytical convergence results of the resulting expansion are proved, and an algorithm is proposed to perform the dimensional reduction. In this work…
The kernel trick concept, formulated as an inner product in a feature space, facilitates powerful extensions to many well-known algorithms. While the kernel matrix involves inner products in the feature space, the sample covariance matrix…
In this work, we introduce kernels with random Fourier features in the meta-learning framework to leverage their strong few-shot learning ability. We propose meta variational random features (MetaVRF) to learn adaptive kernels for the…
Nonnegative matrix factorization is a powerful technique to realize dimension reduction and pattern recognition through single-layer data representation learning. Deep learning, however, with its carefully designed hierarchical structure,…
We propose a new method for input variable selection in nonlinear regression. The method is embedded into a kernel regression machine that can model general nonlinear functions, not being a priori limited to additive models. This is the…
The field of quantum machine learning is a promising way to lead to a revolution in intelligent data processing methods. In this way, a hybrid learning method based on classic kernel methods is proposed. This proposal also requires the…
Hyperspectral imagery is rich in spatial and spectral information. Using 3D-CNN can simultaneously acquire features of spatial and spectral dimensions to facilitate classification of features, but hyperspectral image information spectral…
Domain specific (dis-)similarity or proximity measures used e.g. in alignment algorithms of sequence data, are popular to analyze complex data objects and to cover domain specific data properties. Without an underlying vector space these…
Nonnegative Matrix Factorization (NMF) has been continuously evolving in several areas like pattern recognition and information retrieval methods. It factorizes a matrix into a product of 2 low-rank non-negative matrices that will define…
Value approximation using deep neural networks is at the heart of off-policy deep reinforcement learning, and is often the primary module that provides learning signals to the rest of the algorithm. While multi-layer perceptron networks are…
ANOVA decomposition of function with random input variables provides ANOVA functionals (AFs), which contain information about the contributions of the input variables on the output variable(s). By embedding AFs into an appropriate…
In many applications, input data are sampled functions taking their values in infinite dimensional spaces rather than standard vectors. This fact has complex consequences on data analysis algorithms that motivate modifications of them. In…
Kernels are often developed and used as implicit mapping functions that show impressive predictive power due to their high-dimensional feature space representations. In this study, we gradually construct a series of simple feature maps that…
Risk prediction capitalizing on emerging human genome findings holds great promise for new prediction and prevention strategies. While the large amounts of genetic data generated from high-throughput technologies offer us a unique…
As the size and richness of available datasets grow larger, the opportunities for solving increasingly challenging problems with algorithms learning directly from data grow at the same pace. Consequently, the capability of learning…
Kernel-based methods are heavily used in machine learning. However, they suffer from $O(N^2)$ complexity in the number $N$ of considered data points. In this paper, we propose an approximation procedure, which reduces this complexity to…
We present a quantum kernel method for high-dimensional data analysis using Google's universal quantum processor, Sycamore. This method is successfully applied to the cosmological benchmark of supernova classification using real spectral…