Related papers: Learning nonlinear level sets for dimensionality r…
In recent years, deep metric learning has achieved promising results in learning high dimensional semantic feature embeddings where the spatial relationships of the feature vectors match the visual similarities of the images. Similarity…
Line segment detection is a fundamental low-level task in computer vision, and improvements in this task can impact more advanced methods that depend on it. Most new methods developed for line segment detection are based on Convolutional…
Training deep neural networks typically relies on backpropagating high dimensional error signals a computationally intensive process with little evidence supporting its implementation in the brain. However, since most tasks involve…
In human-level NLP tasks, such as predicting mental health, personality, or demographics, the number of observations is often smaller than the standard 768+ hidden state sizes of each layer within modern transformer-based language models,…
Dimension reduction (DR) aims to learn low-dimensional representations of high-dimensional data with the preservation of essential information. In the context of manifold learning, we define that the representation after…
Recognizing symmetries in data allows for significant boosts in neural network training, which is especially important where training data are limited. In many cases, however, the exact underlying symmetry is present only in an idealized…
The learning rate (LR) is one of the most important hyper-parameters in stochastic gradient descent (SGD) algorithm for training deep neural networks (DNN). However, current hand-designed LR schedules need to manually pre-specify a fixed…
Deep learning based methods hold state-of-the-art results in low-level image processing tasks, but remain difficult to interpret due to their black-box construction. Unrolled optimization networks present an interpretable alternative to…
This paper proposed a new explicit nonlinear dimensionality reduction using neural networks for image retrieval tasks. We first proposed a Quasi-curvature Locally Linear Embedding (QLLE) for training set. QLLE guarantees the linear…
We propose a novel framework for learning a low-dimensional representation of data based on nonlinear dynamical systems, which we call dynamical dimension reduction (DDR). In the DDR model, each point is evolved via a nonlinear flow towards…
On account of its many successes in inference tasks and denoising applications, Dictionary Learning (DL) and its related sparse optimization problems have garnered a lot of research interest. While most solutions have focused on single…
We propose Neural Gradient Learning (NGL), a deep learning approach to learn gradient vectors with consistent orientation from 3D point clouds for normal estimation. It has excellent gradient approximation properties for the underlying…
Dimensionality reduction can distort vector space properties such as orthogonality and linear independence, which are critical for tasks including cross-modal retrieval, clustering, and classification. We propose a Relationship Preserving…
In this work, we study distance metric learning (DML) for high dimensional data. A typical approach for DML with high dimensional data is to perform the dimensionality reduction first before learning the distance metric. The main…
In the signal processing and statistics literature, the minimum description length (MDL) principle is a popular tool for choosing model complexity. Successful examples include signal denoising and variable selection in linear regression,…
Machine learning methods are commonly used to solve inverse problems, wherein an unknown signal must be estimated from few indirect measurements generated via a known acquisition procedure. In particular, neural networks perform well…
Deep neural networks need a big amount of training data, while in the real world there is a scarcity of data available for training purposes. To resolve this issue unsupervised methods are used for training with limited data. In this…
Most of the existing methods for estimating the local intrinsic dimension of a data distribution do not scale well to high-dimensional data. Many of them rely on a non-parametric nearest neighbors approach which suffers from the curse of…
We adapt previous research on category theory and topological unsupervised learning to develop a functorial perspective on manifold learning, also known as nonlinear dimensionality reduction. We first characterize manifold learning…
Sparse representations has shown to be a very powerful model for real world signals, and has enabled the development of applications with notable performance. Combined with the ability to learn a dictionary from signal examples,…