Related papers: An Explicit Nonlinear Mapping for Manifold Learnin…

Modern machine learning algorithms have been adopted in a range of signal-processing applications spanning computer vision, natural language processing, and artificial intelligence. Many relevant problems involve subspace-structured…

Manifold learning is a fundamental problem in machine learning with numerous applications. Most of the existing methods directly learn the low-dimensional embedding of the data in some high-dimensional space, and usually lack the…

Low-dimensional embedding, manifold learning, clustering, classification, and anomaly detection are among the most important problems in machine learning. The existing methods usually consider the case when each instance has a fixed,…

Stochastic neighbor embedding (SNE) and related nonlinear manifold learning algorithms achieve high-quality low-dimensional representations of similarity data, but are notoriously slow to train. We propose a generic formulation of embedding…

Dimensionality reduction (DR) and manifold learning (ManL) have been applied extensively in many machine learning tasks, including signal processing, speech recognition, and neuroinformatics. However, the understanding of whether DR and…

Subspace clustering is an important unsupervised clustering approach. It is based on the assumption that the high-dimensional data points are approximately distributed around several low-dimensional linear subspaces. The majority of the…

The local linear embedding algorithm (LLE) is a non-linear dimension-reducing technique, widely used due to its computational simplicity and intuitive approach. LLE first linearly reconstructs each input point from its nearest neighbors and…

Autoencoders are a widespread tool in machine learning to transform high-dimensional data into a lowerdimensional representation which still exhibits the essential characteristics of the input. The encoder provides an embedding from the…

This paper presents a new framework for manifold learning based on a sequence of principal polynomials that capture the possibly nonlinear nature of the data. The proposed Principal Polynomial Analysis (PPA) generalizes PCA by modeling the…

Neural network representation learning for spatial data is a common need for geographic artificial intelligence (GeoAI) problems. In recent years, many advancements have been made in representation learning for points, polylines, and…

To model manifold data using normalizing flows, we employ isometric autoencoders to design embeddings with explicit inverses that do not distort the probability distribution. Using isometries separates manifold learning and density…

For functional data lying on an unknown nonlinear low-dimensional space, we study manifold learning and introduce the notions of manifold mean, manifold modes of functional variation and of functional manifold components. These constitute…

We consider the ability of deep neural networks to represent data that lies near a low-dimensional manifold in a high-dimensional space. We show that deep networks can efficiently extract the intrinsic, low-dimensional coordinates of such…

Unsupervised homogeneous network embedding (NE) represents every vertex of networks into a low-dimensional vector and meanwhile preserves the network information. Adjacency matrices retain most of the network information, and directly…

The Manifold Hypothesis is a widely accepted tenet of Machine Learning which asserts that nominally high-dimensional data are in fact concentrated near a low-dimensional manifold, embedded in high-dimensional space. This phenomenon is…

Nonlinear partial differential equations (PDEs) are used to model dynamical processes in a large number of scientific fields, ranging from finance to biology. In many applications standard local models are not sufficient to accurately…

Learning discriminative image feature embeddings is of great importance to visual recognition. To achieve better feature embeddings, most current methods focus on designing different network structures or loss functions, and the estimated…

Symmetric positive definite (SPD) matrices used as feature descriptors in image recognition are usually high dimensional. Traditional manifold learning is only applicable for reducing the dimension of high-dimensional vector-form data. For…

Recent literature has shown that symbolic data, such as text and graphs, is often better represented by points on a curved manifold, rather than in Euclidean space. However, geometrical operations on manifolds are generally more complicated…

Autoencoding is a popular method in representation learning. Conventional autoencoders employ symmetric encoding-decoding procedures and a simple Euclidean latent space to detect hidden low-dimensional structures in an unsupervised way.…