Related papers: A Linear Approximation to the chi^2 Kernel with Ge…
We provide guarantees for approximate Gaussian Process (GP) regression resulting from two common low-rank kernel approximations: based on random Fourier features, and based on truncating the kernel's Mercer expansion. In particular, we…
We provide guarantees for approximate Gaussian Process (GP) regression resulting from two common low-rank kernel approximations: based on random Fourier features, and based on truncating the kernel's Mercer expansion. In particular, we…
Approximating non-linear kernels using feature maps has gained a lot of interest in recent years due to applications in reducing training and testing times of SVM classifiers and other kernel based learning algorithms. We extend this line…
We propose a novel adaptive kernel based regression method for complex-valued signals: the generalized complex-valued kernel least-mean-square (gCKLMS). We borrow from the new results on widely linear reproducing kernel Hilbert space…
Fisher's linear discriminant analysis is a classical method for classification, yet it is limited to capturing linear features only. Kernel discriminant analysis as an extension is known to successfully alleviate the limitation through a…
Large kernel systems are prone to be ill-conditioned. Pivoted Cholesky decomposition (PCD) render a stable and efficient solution to the systems without a perturbation of regularization. This paper proposes a new PCD algorithm by tuning…
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.…
Positive-definite kernel functions are fundamental elements of kernel methods and Gaussian processes. A well-known construction of such functions comes from Bochner's characterization, which connects a positive-definite function with a…
We propose a method for the approximation of high- or even infinite-dimensional feature vectors, which play an important role in supervised learning. The goal is to reduce the size of the training data, resulting in lower storage…
Straightforward methods for adapting the familiar chi^2 statistic to histograms of discrete events and other Poisson distributed data generally yield biased estimates of the parameters of a model. The bias can be important even when the…
This work studies low-rank approximation of a positive semidefinite matrix from partial entries via nonconvex optimization. We characterized how well local-minimum based low-rank factorization approximates a fixed positive semidefinite…
The principal component analysis (PCA) is widely used for data decorrelation and dimensionality reduction. However, the use of PCA may be impractical in real-time applications, or in situations were energy and computing constraints are…
The empirical success of deep convolutional networks on tasks involving high-dimensional data such as images or audio suggests that they can efficiently approximate certain functions that are well-suited for such tasks. In this paper, we…
We prove and apply an optimal low-rank approximation of the Cauchy kernel over separated real domains. A skeleton decomposition is the minimum over real-valued functions of the maximum relative pointwise error. We present an algorithm to…
Despite advances in feature representation, leveraging geometric relations is crucial for establishing reliable visual correspondences under large variations of images. In this work we introduce a Hough transform perspective on…
We present in this work a new methodology to design kernels on data which is structured with smaller components, such as text, images or sequences. This methodology is a template procedure which can be applied on most kernels on measures…
Despite the rapid development of computational hardware, the treatment of large and high dimensional data sets is still a challenging problem. This paper provides a twofold contribution to the topic. First, we propose a Gaussian Mixture…
Random Fourier Features (RFF) demonstrate wellappreciated performance in kernel approximation for largescale situations but restrict kernels to be stationary and positive definite. And for non-stationary kernels, the corresponding RFF could…
In this paper we analyze approximate methods for undertaking a principal components analysis (PCA) on large data sets. PCA is a classical dimension reduction method that involves the projection of the data onto the subspace spanned by the…
This paper studies kernel PCA in a decentralized setting, where data are distributively observed with full features in local nodes and a fusion center is prohibited. Compared with linear PCA, the use of kernel brings challenges to the…