Related papers: Deep Learning for Subspace Regression
In this paper, we propose a novel subspace learning framework for one-class classification. The proposed framework presents the problem in the form of graph embedding. It includes the previously proposed subspace one-class techniques as its…
This work investigates the ways in which deep learning methods can benefit from random projection (RP), a classic linear dimensionality reduction method. We focus on two areas where, as we have found, employing RP techniques can improve…
The rapid growth of earth observation systems calls for a scalable approach to interpolate remote-sensing observations. These methods in principle, should acquire more information about the observed field as data grows. Gaussian processes…
We present a dynamic subspace approach for efficiently approximating large-scale systems by learning time-continuous trajectories on the Grassmannian manifold. By parameterizing a low-dimensional basis as a geodesic path, the method allows…
Majority of the current dimensionality reduction or retrieval techniques rely on embedding the learned feature representations onto a computable metric space. Once the learned features are mapped, a distance metric aids the bridging of gaps…
Gradient descent typically converges to a single minimum of the training loss without mechanisms to explore alternative minima that may generalize better. Searching for diverse minima directly in high-dimensional parameter space is…
Datasets such as images, text, or movies are embedded in high-dimensional spaces. However, in important cases such as images of objects, the statistical structure in the data constrains samples to a manifold of dramatically lower…
The joint optimization of the reconstruction and classification error is a hard non convex problem, especially when a non linear mapping is utilized. In order to overcome this obstacle, a novel optimization strategy is proposed, in which a…
Deep Learning (DL) models can be used to tackle time series analysis tasks with great success. However, the performance of DL models can degenerate rapidly if the data are not appropriately normalized. This issue is even more apparent when…
Spectral dimensionality reduction algorithms are widely used in numerous domains, including for recognition, segmentation, tracking and visualization. However, despite their popularity, these algorithms suffer from a major limitation known…
The Grassmann manifold of linear subspaces is important for the mathematical modelling of a multitude of applications, ranging from problems in machine learning, computer vision and image processing to low-rank matrix optimization problems,…
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 present a subspace method based on neural networks (SNN) for solving the partial differential equation with high accuracy. The basic idea of our method is to use some functions based on neural networks as base functions to span a…
We present a novel method for learning reduced-order models of dynamical systems using nonlinear manifolds. First, we learn the manifold by identifying nonlinear structure in the data through a general representation learning problem. The…
We consider the problem of learning a linear subspace from data corrupted by outliers. Classical approaches are typically designed for the case in which the subspace dimension is small relative to the ambient dimension. Our approach works…
Bayesian inference for neural networks, or Bayesian deep learning, has the potential to provide well-calibrated predictions with quantified uncertainty and robustness. However, the main hurdle for Bayesian deep learning is its computational…
Spectral decomposition of the Koopman operator is attracting attention as a tool for the analysis of nonlinear dynamical systems. Dynamic mode decomposition is a popular numerical algorithm for Koopman spectral analysis; however, we often…
Machine-learned regression models represent a promising tool to implement accurate and computationally affordable energy-density functionals to solve quantum many-body problems via density functional theory. However, while they can easily…
This paper considers optimization problems over networks where agents have individual objectives to meet, or individual parameter vectors to estimate, subject to subspace constraints that require the objectives across the network to lie in…
The effectiveness of supervised learning techniques has made them ubiquitous in research and practice. In high-dimensional settings, supervised learning commonly relies on dimensionality reduction to improve performance and identify the…