Related papers: TrIK-SVM : an alternative decomposition for kernel…
We provide the first mathematically complete derivation of the Nystr\"om method for low-rank approximation of indefinite kernels and propose an efficient method for finding an approximate eigendecomposition of such kernel matrices. Building…
This is a survey on reproducing kernel Krein spaces and their interplay with operator valued Hermitian kernels. Existence and uniqueness properties are carefully reviewed. The approach we follow in this survey uses a more abstract but very…
A novel kernel-based support vector machine (SVM) for graph classification is proposed. The SVM feature space mapping consists of a sequence of graph convolutional layers, which generates a vector space representation for each vertex,…
Image convolution with complex kernels is a fundamental operation in photography, scientific imaging, and animation effects, yet direct dense convolution is computationally prohibitive on resource-limited devices. Existing approximations,…
Kernel approximation is widely used to scale up kernel SVM training and prediction. However, the memory and computation costs of kernel approximation models are still too high if we want to deploy them on memory-limited devices such as…
This work presents an approach for automating the discretization and approximation procedures in constructing digital representations of composites from Micro-CT images featuring intricate microstructures. The proposed method is guided by…
Support vector machine (SVM), is a popular kernel method for data classification that demonstrated its efficiency for a large range of practical applications. The method suffers, however, from some weaknesses including; time processing,…
Although support vector machines (SVMs) are theoretically well understood, their underlying optimization problem becomes very expensive, if, for example, hundreds of thousands of samples and a non-linear kernel are considered. Several…
Kernel methods are powerful tools in machine learning. Classical kernel methods are based on positive-definite kernels, which map data spaces into reproducing kernel Hilbert spaces (RKHS). For non-Euclidean data spaces, positive-definite…
Support Vector Machines (SVMs) are well-established Machine Learning (ML) algorithms. They rely on the fact that i) linear learning can be formalized as a well-posed optimization problem; ii) non-linear learning can be brought into linear…
Tensor, a multi-dimensional data structure, has been exploited recently in the machine learning community. Traditional machine learning approaches are vector- or matrix-based, and cannot handle tensorial data directly. In this paper, we…
In the last few years, various types of machine learning algorithms, such as Support Vector Machine (SVM), Support Vector Regression (SVR), and Non-negative Matrix Factorization (NMF) have been introduced. The kernel approach is an…
In many problems of supervised tensor learning (STL), real world data such as face images or MRI scans are naturally represented as matrices, which are also called as second order tensors. Most existing classifiers based on tensor…
The state-of-the-art dimensionality reduction approaches largely rely on complicated optimization procedures. On the other hand, closed-form approaches requiring merely eigen-decomposition do not have enough sophistication and nonlinearity.…
The training of Support Vector Machines may be a very difficult task when dealing with very large datasets. The memory requirement and the time consumption of the SVMs algorithms grow rapidly with the increase of the data. To overcome these…
Kernel-free quadratic surface support vector machines (QSVM) have recently gained traction due to their flexibility in modeling nonlinear decision boundaries without relying on kernel functions. However, the introduction of a full quadratic…
In this paper we study hermitian kernels invariant under the action of a semigroup with involution. We characterize those hermitian kernels which realize the given action by bounded operators on a Krein space. Applications to the GNS…
In this paper we propose a fast online Kernel SVM algorithm under tight budget constraints. We propose to split the input space using LVQ and train a Kernel SVM in each cluster. To allow for online training, we propose to limit the size of…
Support vector machine (SVM) is a particularly powerful and flexible supervised learning model that analyzes data for both classification and regression, whose usual algorithm complexity scales polynomially with the dimension of data space…
The kernel-independent fast multipole method (KIFMM) proposed in [1] is of almost linear complexity. In the original KIFMM the time-consuming M2L translations are accelerated by FFT. However, when more equivalent points are used to achieve…