Related papers: Higher order multi-dimension reduction methods via…
Large models and enormous data are essential driving forces of the unprecedented successes achieved by modern algorithms, especially in scientific computing and machine learning. Nevertheless, the growing dimensionality and model…
Based on the theory of reproducing kernel Hilbert space (RKHS) and semiparametric method, we propose a new approach to nonlinear dimension reduction. The method extends the semiparametric method into a more generalized domain where both the…
The Einstein-Hilbert action with a cosmological constant is the most general local four-dimensional action leading to second-order derivative equations of motion that are symmetric and divergence free. In higher dimensions, additional terms…
We present a forward sufficient dimension reduction method for categorical or ordinal responses by extending the outer product of gradients and minimum average variance estimator to multinomial generalized linear model. Previous work in…
With the advances in data acquisition technology, tensor objects are collected in a variety of applications including multimedia, medical and hyperspectral imaging. As the dimensionality of tensor objects is usually very high,…
First-order methods such as stochastic gradient descent (SGD) are currently the standard algorithm for training deep neural networks. Second-order methods, despite their better convergence rate, are rarely used in practice due to the…
The covariate shift is a challenging problem in supervised learning that results from the discrepancy between the training and test distributions. An effective approach which recently drew a considerable attention in the research community…
Data-driven problem solving in many real-world applications involves analysis of time-dependent multivariate data, for which dimensionality reduction (DR) methods are often used to uncover the intrinsic structure and features of the data.…
We discuss various aspects of dimensional reduction of gravity with the Einstein-Hilbert action supplemented by a lowest order deformation formed as the Riemann tensor raised to powers two, three or four. In the case of R^2 we give an…
When performing classification tasks, raw high dimensional features often contain redundant information, and lead to increased computational complexity and overfitting. In this paper, we assume the data samples lie on a single underlying…
We address the problem of class incremental learning, which is a core step towards achieving adaptive vision intelligence. In particular, we consider the task setting of incremental learning with limited memory and aim to achieve better…
We develop a novel deep learning technique, termed Deep Orthogonal Decomposition (DOD), for dimensionality reduction and reduced order modeling of parameter dependent partial differential equations. The approach consists in the construction…
This paper proposes a generalized framework with joint normalization which learns lower-dimensional subspaces with maximum discriminative power by making use of the Riemannian geometry. In particular, we model the similarity/dissimilarity…
First-order methods like stochastic gradient descent(SGD) are recently the popular optimization method to train deep neural networks (DNNs), but second-order methods are scarcely used because of the overpriced computing cost in getting the…
Several regularization methods have been considered over the last decade for sparse high-dimensional linear regression models, but the most common ones use the least square (quadratic) or likelihood loss and hence are not robust against…
We introduce a finite element method for numerical upscaling of second order elliptic equations with highly heterogeneous coefficients. The method is based on a mixed formulation of the problem and the concepts of the domain decomposition…
It is well known that multigrid methods are optimally efficient for solution of elliptic equations (O(N)), which means that effort is proportional to the number of points at which the solution is evaluated). Thus this is an ideal method to…
High dynamic range (HDR) image is widely-used in graphics and photography due to the rich information it contains. Recently the community has started using deep neural network (DNN) to reconstruct standard dynamic range (SDR) images into…
During the past decade, deep neural networks have led to fast-paced progress and significant achievements in computer vision problems, for both academia and industry. Yet despite their success, state-of-the-art image classification…
Aiming at better representing multivariate relationships, this paper investigates a motif dimensional framework for higher-order graph learning. The graph learning effectiveness can be improved through OFFER. The proposed framework mainly…