Related papers: Inductive Global and Local Manifold Approximation …
The recovery of the intrinsic geometric structures of data collections is an important problem in data analysis. Supervised extensions of several manifold learning approaches have been proposed in the recent years. Meanwhile, existing…
Graph Neural Networks (GNNs) have gained popularity in various learning tasks, with successful applications in fields like molecular biology, transportation systems, and electrical grids. These fields naturally use graph data, benefiting…
We present an improved Locality Preserving Projections (LPP) method, named Gloablity-Locality Preserving Projections (GLPP), to preserve both the global and local geometric structures of data. In our approach, an additional constraint of…
Nonlinear dimension reduction (NLDR) techniques such as tSNE, and UMAP provide a low-dimensional representation of high-dimensional data ($p\text{-}D$) by applying a nonlinear transformation. NLDR often exaggerates random patterns. But NLDR…
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…
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…
This work introduces IsUMap, a novel manifold learning technique that enhances data representation by integrating aspects of UMAP and Isomap with Vietoris-Rips filtrations. We present a systematic and detailed construction of a metric…
Exploratory data analysis is a fundamental aspect of knowledge discovery that aims to find the main characteristics of a dataset. Dimensionality reduction, such as manifold learning, is often used to reduce the number of features in a…
For image recognition, an extensive number of methods have been proposed to overcome the high-dimensionality problem of feature vectors being used. These methods vary from unsupervised to supervised, and from statistics to graph-theory…
This paper explores a fully unsupervised deep learning approach for computing distance-preserving maps that generate low-dimensional embeddings for a certain class of manifolds. We use the Siamese configuration to train a neural network to…
Isometric feature mapping (Isomap) is a promising manifold learning method. However, Isomap fails to work on data which distribute on clusters in a single manifold or manifolds. Many works have been done on extending Isomap to…
Understanding the geometric and semantic structure of environments is essential for embodied navigation and reasoning. Existing semantic mapping methods trade off between explicit geometry and multi-scale semantics, and lack a native…
This survey is written in summer, 2016. The purpose of this survey is to briefly introduce nonlinear dimensionality reduction (NLDR) in data reduction. The first two NLDR were respectively published in Science in 2000 in which they solve…
In image set classification, a considerable progress has been made by representing original image sets on Grassmann manifolds. In order to extend the advantages of the Euclidean based dimensionality reduction methods to the Grassmann…
We present Low Distortion Local Eigenmaps (LDLE), a manifold learning technique which constructs a set of low distortion local views of a dataset in lower dimension and registers them to obtain a global embedding. The local views are…
Clustering on the data with multiple aspects, such as multi-view or multi-type relational data, has become popular in recent years due to their wide applicability. The approach using manifold learning with the Non-negative Matrix…
Vision-language models (VLMs) and generative world models are opening new opportunities for embodied navigation. VLMs are increasingly used as direct planners or trajectory predictors, while world models support look-ahead reasoning by…
This paper considers the problem of nonlinear dimensionality reduction. Unlike existing methods, such as LLE, ISOMAP, which attempt to unfold the true manifold in the low dimensional space, our algorithm tries to preserve the nonlinear…
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…
Classical nonlinear dimensionality reduction (NLDR) techniques like t-SNE, Isomap, and LLE excel at creating low-dimensional embeddings for data visualization but fundamentally lack the ability to map these embeddings back to the original…