Related papers: Kernel Methods on Approximate Infinite-Dimensional…

Machine-learning algorithms offer immense possibilities in the development of several cognitive applications. In fact, large scale machine-learning classifiers now represent the state-of-the-art in a wide range of object…

The present phase of Machine Learning is characterized by supervised learning algorithms relying on large sets of labeled examples ($n \to \infty$). The next phase is likely to focus on algorithms capable of learning from very few labeled…

Machine learning models can represent climate processes that are nonlocal in horizontal space, height, and time, often by combining information across these dimensions in highly nonlinear ways. While this can improve predictive skill, it…

Classification is a central task in deep learning algorithms. Usually, images are first captured and then processed by a sequence of operations, of which the artificial neuron represents one of the fundamental units. This paradigm requires…

In this work, we consider the problem of learning nonlinear operators that correspond to discrete-time nonlinear dynamical systems with inputs. Given an initial state and a finite input trajectory, such operators yield a finite output…

Data-driven approximations of the infinite-dimensional Koopman operator rely on finite-dimensional projections, where the predictive accuracy of the resulting models hinges heavily on the invariance of the chosen subspace. Subspace pruning…

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…

This paper generalizes recent advances on quadratic manifold (QM) dimensionality reduction by developing kernel methods-based nonlinear-augmentation dimensionality reduction. QMs, and more generally feature map-based nonlinear corrections,…

A popular way to approximate the Koopman operator's action on a finite-dimensional subspace of functions is via orthogonal projections. The quality of the projected model directly depends on the selected subspace, specifically on how close…

In this paper, we propose a neural network architecture for scale-invariant semantic segmentation using RGB-D images. We utilize depth information as an additional modality apart from color images only. Especially in an outdoor scene which…

Segmentation-based methods have achieved great success for arbitrary shape text detection. However, separating neighboring text instances is still one of the most challenging problems due to the complexity of texts in scene images. In this…

Neural operators have achieved significant success in modern scientific computing due to their flexibility and strong generalization capabilities. Existing models, however, primarily rely on first-order kernel integral approximations, which…

Super resolution (SR) methods typically assume that the low-resolution (LR) image was downscaled from the unknown high-resolution (HR) image by a fixed 'ideal' downscaling kernel (e.g. Bicubic downscaling). However, this is rarely the case…

Retinal image of surrounding objects varies tremendously due to the changes in position, size, pose, illumination condition, background context, occlusion, noise, and nonrigid deformations. But despite these huge variations, our visual…

Low-rank approximation of kernels is a fundamental mathematical problem with widespread algorithmic applications. Often the kernel is restricted to an algebraic variety, e.g., in problems involving sparse or low-rank data. We show that…

Unsupervised semantic segmentation aims to discover groupings within and across images that capture object and view-invariance of a category without external supervision. Grouping naturally has levels of granularity, creating ambiguity in…

Operator learning is the approximation of operators between infinite dimensional Banach spaces using machine learning approaches. While most progress in this area has been driven by variants of deep neural networks such as the Deep Operator…

Human vision possesses strong invariance in image recognition. The cognitive capability of deep convolutional neural network (DCNN) is close to the human visual level because of hierarchical coding directly from raw image. Owing to its…

In this draft, fault diagnosis in nonlinear dynamic systems is addressed. The objective of this work is to establish a framework, in which not only model-based but also data-driven and machine learning based fault diagnosis strategies can…

Kernel transfer operators, which can be regarded as approximations of transfer operators such as the Perron-Frobenius or Koopman operator in reproducing kernel Hilbert spaces, are defined in terms of covariance and cross-covariance…