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This paper develops a novel mathematical framework for collaborative learning by means of geometrically inspired kernel machines which includes statements on the bounds of generalisation and approximation errors, and sample complexity. For…
The parameters of support vector machines (SVMs) such as the penalty parameter and the kernel parameters have a great impact on the classification accuracy and the complexity of the SVM model. Therefore, the model selection in SVM involves…
Supervised learning in reproducing kernel Hilbert space (RKHS) and vector-valued RKHS (vvRKHS) has been investigated for more than 30 years. In this paper, we provide a new twist to this rich literature by generalizing supervised learning…
Despite the effectiveness of Convolutional Neural Networks (CNNs) for image classification, our understanding of the relationship between shape of convolution kernels and learned representations is limited. In this work, we explore and…
The support vector machines (SVM) is one of the most widely used and practical optimization based classification models in machine learning because of its interpretability and flexibility to produce high quality results. However, the big…
We introduce the anti-profile Support Vector Machine (apSVM) as a novel algorithm to address the anomaly classification problem, an extension of anomaly detection where the goal is to distinguish data samples from a number of anomalous and…
In this paper, we develop a generalized theory of convolutional signal processing and neural networks for Reproducing Kernel Hilbert Spaces (RKHS). Leveraging the theory of algebraic signal processing (ASP), we show that any RKHS allows the…
Substring kernels are classical tools for representing biological sequences or text. However, when large amounts of annotated data are available, models that allow end-to-end training such as neural networks are often preferred. Links…
This article proposes a performance analysis of kernel least squares support vector machines (LS-SVMs) based on a random matrix approach, in the regime where both the dimension of data $p$ and their number $n$ grow large at the same rate.…
Support Vector Machine (SVM) is powerful classification technique based on the idea of structural risk minimization. Use of kernel function enables curse of dimensionality to be addressed. However, proper kernel function for certain problem…
Support Vector Machines (SVMs) are a cornerstone of supervised learning, widely used for data classification. A central component of their success lies in kernel functions, which enable efficient computation of inner products in…
The convolution operator at the core of many modern neural architectures can effectively be seen as performing a dot product between an input matrix and a filter. While this is readily applicable to data such as images, which can be…
In supervised learning with distributional inputs in the two-stage sampling setup, relevant to applications like learning-based medical screening or causal learning, the inputs (which are probability distributions) are not accessible in the…
Kernel methods have been among the most popular techniques in machine learning, where learning tasks are solved using the property of reproducing kernel Hilbert space (RKHS). In this paper, we propose a novel data analysis framework with…
The support vector machine (SVM) and deep learning (e.g., convolutional neural networks (CNNs)) are the two most famous algorithms in small and big data, respectively. Nonetheless, smaller datasets may be very important, costly, and not…
Features play a crucial role in computer vision. Initially designed to detect salient elements by means of handcrafted algorithms, features are now often learned by different layers in Convolutional Neural Networks (CNNs). This paper…
It is shown that bootstrap approximations of support vector machines (SVMs) based on a general convex and smooth loss function and on a general kernel are consistent. This result is useful to approximate the unknown finite sample…
The support vector machines (SVM) algorithm is a popular classification technique in data mining and machine learning. In this paper, we propose a distributed SVM algorithm and demonstrate its use in a number of applications. The algorithm…
This paper presents a novel and uniform algorithm for edge detection based on SVM (support vector machine) with Three-dimensional Gaussian radial basis function with kernel. Because of disadvantages in traditional edge detection such as…
In this article, a large dimensional performance analysis of kernel least squares support vector machines (LS-SVMs) is provided under the assumption of a two-class Gaussian mixture model for the input data. Building upon recent advances in…