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Radial Basis Function (RBF), or Gaussian, kernels are among the most widely used parametric kernels in machine learning, particularly in methods such as Support Vector Machines (SVM) and kernel-based subspace approaches. The kernel…

Recent work in metric learning has significantly improved the state-of-the-art in k-nearest neighbor classification. Support vector machines (SVM), particularly with RBF kernels, are amongst the most popular classification algorithms that…

Support Vector Machines (SVMs) with various kernels have played dominant role in machine learning for many years, finding numerous applications. Although they have many attractive features interpretation of their solutions is quite…

An increasing number of systems are being designed by gathering significant amounts of data and then optimizing the system parameters directly using the obtained data. Often this is done without analyzing the dataset structure. As task…

The kernel matrix used in kernel methods encodes all the information required for solving complex nonlinear problems defined on data representations in the input space using simple, but implicitly defined, solutions. Spectral analysis on…

Recent research shows that the dynamics of an infinitely wide neural network (NN) trained by gradient descent can be characterized by Neural Tangent Kernel (NTK) \citep{jacot2018neural}. Under the squared loss, the infinite-width NN trained…

This work concerns a comparison of SVM kernel methods in text categorization tasks. In particular I define a kernel function that estimates the similarity between two objects computing by their compressed lengths. In fact, compression…

In the context of deep learning with kernel machines, the deep Restricted Kernel Machine (DRKM) framework allows multiple levels of kernel PCA (KPCA) and Least-Squares Support Vector Machines (LSSVM) to be combined into a deep architecture…

Plant breeders and agricultural researchers can increase crop productivity by identifying desirable features, disease resistance, and nutritional content by analysing the Dry Bean dataset. This study analyses and compares different Support…

Quantum kernel methods are a promising branch of quantum machine learning, yet their effectiveness on diverse, high-dimensional, real-world data remains unverified. Current research has largely been limited to low-dimensional or synthetic…

Support Vector Machines (SVMs) rely heavily on the choice of the kernel function to map data into high-dimensional feature spaces. While the Gaussian Radial Basis Function (RBF) is the industry standard, its exponential decay makes it…

Deep kernel learning aims at designing nonlinear combinations of multiple standard elementary kernels by training deep networks. This scheme has proven to be effective, but intractable when handling large-scale datasets especially when the…

An increasing amount of collected data are high-dimensional multi-way arrays (tensors), and it is crucial for efficient learning algorithms to exploit this tensorial structure as much as possible. The ever-present curse of dimensionality…

Many interesting machine learning problems are best posed by considering instances that are distributions, or sample sets drawn from distributions. Previous work devoted to machine learning tasks with distributional inputs has done so…

Kernel-based approaches for sequence classification have been successfully applied to a variety of domains, including the text categorization, image classification, speech analysis, biological sequence analysis, time series and music…

We present a Gaussian kernel loss function and training algorithm for convolutional neural networks that can be directly applied to both distance metric learning and image classification problems. Our method treats all training features…

Radial basis function (RBF) networks are expanded to incorporate quantum kernel functions enabling a new type of hybrid quantum-classical machine learning algorithm. Using this approach, synthetic examples are introduced which allow for…

Kernel functions in support vector machines (SVM) are needed to assess the similarity of input samples in order to classify these samples, for instance. Besides standard kernels such as Gaussian (i.e., radial basis function, RBF) or…

Learning a distance metric from the given training samples plays a crucial role in many machine learning tasks, and various models and optimization algorithms have been proposed in the past decade. In this paper, we generalize several…

We propose a novel algorithm for the task of supervised discriminative distance learning by nonlinearly embedding vectors into a low dimensional Euclidean space. We work in the challenging setting where supervision is with constraints on…