Related papers: Uniform Manifold Approximation and Projection (UMA…

We discuss a method of parameter reduction in complex models known as the Manifold Boundary Approximation Method (MBAM). This approach, based on a geometric interpretation of statistics, maps the model reduction problem to a geometric…

Distributed learning is commonly used for training deep learning models, especially large models. In distributed learning, manual parallelism (MP) methods demand considerable human effort and have limited flexibility. Hence, automatic…

With the increasing availability of high-dimensional data, analysts often rely on exploratory data analysis to understand complex data sets. A key approach to exploring such data is dimensionality reduction, which embeds high-dimensional…

Recent advances in machine learning allow us to analyze and describe the content of high-dimensional data like text, audio, images or other signals. In order to visualize that data in 2D or 3D, usually Dimensionality Reduction (DR)…

A novel method, named Curvature-Augmented Manifold Embedding and Learning (CAMEL), is proposed for high dimensional data classification, dimension reduction, and visualization. CAMEL utilizes a topology metric defined on the Riemannian…

This is a tutorial and survey paper for Locally Linear Embedding (LLE) and its variants. The idea of LLE is fitting the local structure of manifold in the embedding space. In this paper, we first cover LLE, kernel LLE, inverse LLE, and…

The dimensionality reduction has been widely introduced to use the high-dimensional data for regression, classification, feature analysis, and visualization. As the one technique of dimensionality reduction, a stochastic neighbor embedding…

We study approximation of probability measures supported on $n$-dimensional manifolds embedded in $\mathbb{R}^m$ by injective flows -- neural networks composed of invertible flows and injective layers. We show that in general, injective…

Universal adversarial perturbation (UAP), also known as image-agnostic perturbation, is a fixed perturbation map that can fool the classifier with high probabilities on arbitrary images, making it more practical for attacking deep models in…

Due to the intrinsic complexity of high-dimensional (HD) data, dimensionality reduction (DR) techniques cannot preserve all the structural characteristics of the original data. Therefore, DR techniques focus on preserving either local…

Analyzing high-dimensional data with manifold learning algorithms often requires searching for the nearest neighbors of all observations. This presents a computational bottleneck in statistical manifold learning when observations of…

We propose a novel algorithm for supervised dimensionality reduction named Manifold Partition Discriminant Analysis (MPDA). It aims to find a linear embedding space where the within-class similarity is achieved along the direction that is…

Many data mining and data analysis techniques operate on dense matrices or complete tables of data. Real-world data sets, however, often contain unknown values. Even many classification algorithms that are designed to operate with missing…

Understanding complex phenomena often requires analyzing high-dimensional data to uncover emergent properties that arise from multifactorial interactions. Here, we present EMUSES (Emerging-properties Mapping Using Spatial Embedding…

Learning efficient representations of local features is a key challenge in feature volume-based 3D neural mapping, especially in large-scale environments. In this paper, we introduce Decomposition-based Neural Mapping (DNMap), a…

A key challenge in complex visuomotor control is learning abstract representations that are effective for specifying goals, planning, and generalization. To this end, we introduce universal planning networks (UPN). UPNs embed differentiable…

Dimension reduction (DR) techniques such as t-SNE, UMAP, and TriMAP have demonstrated impressive visualization performance on many real world datasets. One tension that has always faced these methods is the trade-off between preservation of…

Manifold learning is a hot research topic in the field of computer science and has many applications in the real world. A main drawback of manifold learning methods is, however, that there is no explicit mappings from the input data…

Running machine learning analytics over geographically distributed datasets is a rapidly arising problem in the world of data management policies ensuring privacy and data security. Visualizing high dimensional data using tools such as…

Operating units often experience various failure modes in complex systems, leading to distinct degradation paths. Relying on a prognostic model trained on a single failure mode may lead to poor generalization performance across multiple…