相关论文: nSimplex Zen: A Novel Dimensionality Reduction for…
In this paper, we present a method of embedding physics data manifolds with metric structure into lower dimensional spaces with simpler metrics, such as Euclidean and Hyperbolic spaces. We then demonstrate that it can be a powerful step in…
We developed a Nonlinear Level-set Learning (NLL) method for dimensionality reduction in high-dimensional function approximation with small data. This work is motivated by a variety of design tasks in real-world engineering applications,…
Dimensionality reduction has become an important research topic as demand for interpreting high-dimensional datasets has been increasing rapidly in recent years. There have been many dimensionality reduction methods with good performance in…
Triplet loss is widely used for learning local descriptors from image patch. However, triplet loss only minimizes the Euclidean distance between matching descriptors and maximizes that between the non-matching descriptors, which neglects…
We explore linear and non-linear dimensionality reduction techniques for statistical inference of parameters in cosmology. Given the importance of compressing the increasingly complex data vectors used in cosmology, we address questions…
We present a set of algorithms implementing multidimensional scaling (MDS) for large data sets. MDS is a family of dimensionality reduction techniques using a $n \times n$ distance matrix as input, where $n$ is the number of individuals,…
The weighted Euclidean norm $\|x\|_w$ of a vector $x\in \mathbb{R}^d$ with weights $w\in \mathbb{R}^d$ is the Euclidean norm where the contribution of each dimension is scaled by a given weight. Approaches to dimensionality reduction that…
Advances in computational power and hardware efficiency have enabled tackling increasingly complex, high-dimensional problems. While artificial intelligence (AI) achieves remarkable results, the interpretability of high-dimensional…
The problem of finding suitable point embedding or geometric configurations given only Euclidean distance information of point pairs arises both as a core task and as a sub-problem in a variety of machine learning applications. In this…
A finite set of the Euclidean space is called an $s$-distance set provided the number of Euclidean distances in the set is $s$. Determining the largest possible $s$-distance set for the Euclidean space of a given dimension is challenging.…
Dimensionality reduction is crucial both for visualization and preprocessing high dimensional data for machine learning. We introduce a novel method based on a hierarchy built on 1-nearest neighbor graphs in the original space which is used…
Topology based dimensionality reduction methods such as t-SNE and UMAP have seen increasing success and popularity in high-dimensional data. These methods have strong mathematical foundations and are based on the intuition that the topology…
Dimension reduction techniques typically seek an embedding of a high-dimensional point cloud into a low-dimensional Euclidean space which optimally preserves the geometry of the input data. Based on expert knowledge, one may instead wish to…
Reducing dimension redundancy to find simplifying patterns in high-dimensional datasets and complex networks has become a major endeavor in many scientific fields. However, detecting the dimensionality of their latent space is challenging…
We present a new technique called "DSNE" which learns the velocity embeddings of low dimensional map points when given the high-dimensional data points with its velocities. The technique is a variation of Stochastic Neighbor Embedding,…
High-dimensional imaging is becoming increasingly relevant in many fields from astronomy and cultural heritage to systems biology. Visual exploration of such high-dimensional data is commonly facilitated by dimensionality reduction.…
Nonlinear dimensionality reduction or, equivalently, the approximation of high-dimensional data using a low-dimensional nonlinear manifold is an active area of research. In this paper, we will present a thematically different approach to…
Dimension-varying linear systems are investigated. First, a dimension-free state space is proposed. A cross dimensional distance is constructed to glue vectors of different dimensions together to form a cross-dimensional topological space.…
Multidimensional scaling (MDS) is the act of embedding proximity information about a set of $n$ objects in $d$-dimensional Euclidean space. As originally conceived by the psychometric community, MDS was concerned with embedding a fixed set…
In this work, we study distance metric learning (DML) for high dimensional data. A typical approach for DML with high dimensional data is to perform the dimensionality reduction first before learning the distance metric. The main…