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Kernel methods are an extremely popular set of techniques used for many important machine learning and data analysis applications. In addition to having good practical performances, these methods are supported by a well-developed theory.…
Kernel methods are an incredibly popular technique for extending linear models to non-linear problems via a mapping to an implicit, high-dimensional feature space. While kernel methods are computationally cheaper than an explicit feature…
The problem of estimating the kernel mean in a reproducing kernel Hilbert space (RKHS) is central to kernel methods in that it is used by classical approaches (e.g., when centering a kernel PCA matrix), and it also forms the core inference…
For open vocabulary recognition of ingredients in food images, segmenting the ingredients is a crucial step. This paper proposes a novel approach that explores PCA-based feature representations of image pixels using a convolutional neural…
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…
Principal component analysis (PCA) is a dimensionality reduction method in data analysis that involves diagonalizing the covariance matrix of the dataset. Recently, quantum algorithms have been formulated for PCA based on diagonalizing a…
Spectral clustering is one of the most important algorithms in data mining and machine intelligence; however, its computational complexity limits its application to truly large scale data analysis. The computational bottleneck in spectral…
In this paper, we propose PCKID, a novel, robust, kernel function for spectral clustering, specifically designed to handle incomplete data. By combining posterior distributions of Gaussian Mixture Models for incomplete data on different…
Spectral clustering is a popular method for effectively clustering nonlinearly separable data. However, computational limitations, memory requirements, and the inability to perform incremental learning challenge its widespread application.…
Recently the use of neural networks has been introduced in the context of the signed particle formulation of quantum mechanics to rapidly and reliably compute the Wigner kernel of any provided potential. This new technique has introduced…
We present a new algorithm for spectral clustering based on a column-pivoted QR factorization that may be directly used for cluster assignment or to provide an initial guess for k-means. Our algorithm is simple to implement, direct, and…
Many statistical estimation techniques for high-dimensional or functional data are based on a preliminary dimension reduction step, which consists in projecting the sample $\bX_1, \hdots, \bX_n$ onto the first $D$ eigenvectors of the…
Although numerous clustering algorithms have been developed, many existing methods still leverage k-means technique to detect clusters of data points. However, the performance of k-means heavily depends on the estimation of centers of…
We present a principled spectral approach to the well-studied constrained clustering problem. It reduces clustering to a generalized eigenvalue problem on Laplacians. The method works in nearly-linear time and provides concrete guarantees…
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.…
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…
The Robust Perron Cluster Analysis (PCCA+) has become a popular spectral clustering algorithm for coarse-graining transition matrices of nearly decomposable Markov chains with transition states. Originally developed for reversible Markov…
We describe how cross-kernel matrices, that is, kernel matrices between the data and a custom chosen set of `feature spanning points' can be used for learning. The main potential of cross-kernels lies in the fact that (a) only one side of…
Clustering samples according to an effective metric and/or vector space representation is a challenging unsupervised learning task with a wide spectrum of applications. Among several clustering algorithms, k-means and its kernelized version…
When using Markov chain Monte Carlo (MCMC) algorithms to perform inference for Bayesian clustering models, such as mixture models, the output is typically a sample of clusterings (partitions) drawn from the posterior distribution. In…