Related papers: A reproducing kernel Hilbert space framework for f…
Functional linear discriminant analysis offers a simple yet efficient method for classification, with the possibility of achieving a perfect classification. Several methods are proposed in the literature that mostly address the…
Improving the performance of classifiers is the realm of feature mapping, prototype selection, and kernel function transformations; these techniques aim for reducing the complexity, and also, improving the accuracy of models. In particular,…
The classification of multivariate functional data is an important task in scientific research. Unlike point-wise data, functional data are usually classified by their shapes rather than by their scales. We define an outlyingness matrix by…
Linear autoregressive models serve as basic representations of discrete time stochastic processes. Different attempts have been made to provide non-linear versions of the basic autoregressive process, including different versions based on…
Kernels are often developed and used as implicit mapping functions that show impressive predictive power due to their high-dimensional feature space representations. In this study, we gradually construct a series of simple feature maps that…
Representing images by compact codes has proven beneficial for many visual recognition tasks. Most existing techniques, however, perform this coding step directly in image feature space, where the distributions of the different classes are…
Kernel methods are one of the cornerstones of learning-based control, modern system identification, surrogate modelling, and related fields. A key advantage of this class of learning and function approximation methods is the availability of…
We present a systematic study of the family of positive definite (p.d.) kernels with the use of their associated feature maps and feature spaces. For a fixed set $X$, generalizing Loewner, we make precise the corresponding partially ordered…
In this paper, we propose a random gradient-free method for optimization in infinite dimensional Hilbert spaces, applicable to functional optimization in diverse settings. Though such problems are often solved through finite-dimensional…
This paper introduces a novel framework for dynamic classification in high dimensional spaces, addressing the evolving nature of class distributions over time or other index variables. Traditional discriminant analysis techniques are…
The reproducing kernel Hilbert space (RKHS) embedding method is a recently introduced estimation approach that seeks to identify the unknown or uncertain function in the governing equations of a nonlinear set of ordinary differential…
Class imbalance is a common problem in the case of real-world object detection and classification tasks. Data of some classes is abundant making them an over-represented majority, and data of other classes is scarce, making them an…
This paper derives a new class of vector-valued reproducing kernel Hilbert spaces (vRKHS) defined in terms of operator-valued kernels for the representation of functional uncertainty arising in nonparametric adaptive control methods. These…
Dimensionality reduction is one of the key issues in the design of effective machine learning methods for automatic induction. In this work, we introduce recursive maxima hunting (RMH) for variable selection in classification problems with…
We propose a novel online learning paradigm for nonlinear-function estimation tasks based on the iterative projections in the L2 space with probability measure reflecting the stochastic property of input signals. The proposed learning…
The problem of supervised classification (or discrimination) with functional data is considered, with a special interest on the popular k-nearest neighbors (k-NN) classifier. First, relying on a recent result by Cerou and Guyader (2006), we…
We consider the problems of classification and intrinsic dimension estimation on image data. A new subspace based classifier is proposed for supervised classification or intrinsic dimension estimation. The distribution of the data in each…
We present a methodology for integrating functional data into deep densely connected feed-forward neural networks. The model is defined for scalar responses with multiple functional and scalar covariates. A by-product of the method is a set…
We propose a new class of generative diffusion models, called functional diffusion. In contrast to previous work, functional diffusion works on samples that are represented by functions with a continuous domain. Functional diffusion can be…
Data depth is a powerful nonparametric tool originally proposed to rank multivariate data from center outward. In this context, one of the most archetypical depth notions is Tukey's halfspace depth. In the last few decades notions of depth…