Related papers: Learning gradients on manifolds
Supervised manifold learning methods learn data representations by preserving the geometric structure of data while enhancing the separation between data samples from different classes. In this work, we propose a theoretical study of…
Nonlinear manifold learning from unorganized data points is a very challenging unsupervised learning and data visualization problem with a great variety of applications. In this paper we present a new algorithm for manifold learning and…
Nonlinear dimensionality reduction methods provide a valuable means to visualize and interpret high-dimensional data. However, many popular methods can fail dramatically, even on simple two-dimensional manifolds, due to problems such as…
Manifold learning is a popular and quickly-growing subfield of machine learning based on the assumption that one's observed data lie on a low-dimensional manifold embedded in a higher-dimensional space. This thesis presents a mathematical…
High-dimensional data analysis has been an active area, and the main focuses have been variable selection and dimension reduction. In practice, it occurs often that the variables are located on an unknown, lower-dimensional nonlinear…
Manifold learning (ML), known also as non-linear dimension reduction, is a set of methods to find the low dimensional structure of data. Dimension reduction for large, high dimensional data is not merely a way to reduce the data; the new…
Analyzing large volumes of high-dimensional data requires dimensionality reduction: finding meaningful low-dimensional structures hidden in their high-dimensional observations. Such practice is needed in atomistic simulations of complex…
Ensemble learning has had many successes in supervised learning, but it has been rare in unsupervised learning and dimensionality reduction. This study explores dimensionality reduction ensembles, using principal component analysis and…
It has been shown that gradient descent can yield the zero training loss in the over-parametrized regime (the width of the neural networks is much larger than the number of data points). In this work, combining the ideas of some existing…
Manifold learning techniques have become increasingly valuable as data continues to grow in size. By discovering a lower-dimensional representation (embedding) of the structure of a dataset, manifold learning algorithms can substantially…
Clustering and dimensionality reduction have been crucial topics in machine learning and computer vision. Clustering high-dimensional data has been challenging for a long time due to the curse of dimensionality. For that reason, a more…
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…
Deep learning is the mainstream technique for many machine learning tasks, including image recognition, machine translation, speech recognition, and so on. It has outperformed conventional methods in various fields and achieved great…
Manifold learning is used for dimensionality reduction, with the goal of finding a projection subspace to increase and decrease the inter- and intraclass variances, respectively. However, a bottleneck for subspace learning methods often…
This report concerns the problem of dimensionality reduction through information geometric methods on statistical manifolds. While there has been considerable work recently presented regarding dimensionality reduction for the purposes of…
In this work, we investigate Riemannian geometry based dimensionality reduction methods that respect the underlying manifold structure of the data. In particular, we focus on Principal Geodesic Analysis (PGA) as a nonlinear generalization…
The discovering of low-dimensional manifolds in high-dimensional data is one of the main goals in manifold learning. We propose a new approach to identify the effective dimension (intrinsic dimension) of low-dimensional manifolds. The scale…
We consider machine learning applications that train a model by leveraging data distributed over a trusted network, where communication constraints can create a performance bottleneck. A number of recent approaches propose to overcome this…
The problem of identifying geometric structure in data is a cornerstone of (unsupervised) learning. As a result, Geometric Representation Learning has been widely applied across scientific and engineering domains. In this work, we…
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…