Related papers: Nested subspace learning with flags
Manifold Learning is a class of algorithms seeking a low-dimensional non-linear representation of high-dimensional data. Thus manifold learning algorithms are, at least in theory, most applicable to high-dimensional data and sample sizes to…
The Wasserstein distance received a lot of attention recently in the community of machine learning, especially for its principled way of comparing distributions. It has found numerous applications in several hard problems, such as domain…
In the machine learning field, dimensionality reduction is an important task. It mitigates the undesired properties of high-dimensional spaces to facilitate classification, compression, and visualization of high-dimensional data. During the…
Manifold learning is a fundamental task at the core of data analysis and visualisation. It aims to capture the simple underlying structure of complex high-dimensional data by preserving pairwise dissimilarities in low-dimensional…
Visual domain adaptation aims to learn robust classifiers for the target domain by leveraging knowledge from a source domain. Existing methods either attempt to align the cross-domain distributions, or perform manifold subspace learning.…
In this paper, we propose a point cloud classification method based on graph neural network and manifold learning. Different from the conventional point cloud analysis methods, this paper uses manifold learning algorithms to embed point…
Nested space-filling designs are nested designs with attractive low-dimensional stratification. Such designs are gaining popularity in statistics, applied mathematics and engineering. Their applications include multi-fidelity computer…
Representation learning on graphs has emerged as a powerful mechanism to automate feature vector generation for downstream machine learning tasks. The advances in representation on graphs have centered on both homogeneous and heterogeneous…
Modeling videos and image-sets as linear subspaces has proven beneficial for many visual recognition tasks. However, it also incurs challenges arising from the fact that linear subspaces do not obey Euclidean geometry, but lie on a special…
Federated learning is a rapidly-growing area of research which enables a large number of clients to jointly train a machine learning model on privately-held data. One of the largest barriers to wider adoption of federated learning is the…
Semi-supervised learning algorithms typically construct a weighted graph of data points to represent a manifold. However, an explicit graph representation is problematic for neural networks operating in the online setting. Here, we propose…
While Bayesian neural networks (BNNs) have drawn increasing attention, their posterior inference remains challenging, due to the high-dimensional and over-parameterized nature. To address this issue, several highly flexible and scalable…
We explore the use of a topological manifold, represented as a collection of charts, as the target space of neural network based representation learning tasks. This is achieved by a simple adjustment to the output of an encoder's network…
Modern data analysis pipelines are becoming increasingly complex due to the presence of multi-view information sources. While graphs are effective in modeling complex relationships, in many scenarios a single graph is rarely sufficient to…
The goal of Feature Selection - comprising filter, wrapper, and embedded approaches - is to find the optimal feature subset for designated downstream tasks. Nevertheless, current feature selection methods are limited by: 1) the selection…
Constructing good representations is critical for learning complex tasks in a sample efficient manner. In the context of meta-learning, representations can be constructed from common patterns of previously seen tasks so that a future task…
Real world data often lie on low-dimensional Riemannian manifolds embedded in high-dimensional spaces. This motivates learning degenerate normalizing flows that map between the ambient space and a low-dimensional latent space. However, if…
Subspace clustering methods based on expressing each data point as a linear combination of all other points in a dataset are popular unsupervised learning techniques. However, existing methods incur high computational complexity on…
Dynamic subspace estimation, or subspace tracking, is a fundamental problem in statistical signal processing and machine learning. This paper considers a geodesic model for time-varying subspaces. The natural objective function for this…
We consider the problem of simultaneously clustering and learning a linear representation of data lying close to a union of low-dimensional manifolds, a fundamental task in machine learning and computer vision. When the manifolds are…