Related papers: Dimensionality Reduction using Elastic Measures

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…

We propose a stochastic optimization method for minimizing loss functions, expressed as an expected value, that adaptively controls the batch size used in the computation of gradient approximations and the step size used to move along such…

The aerodynamic optimization process of cars requires multiple iterations between aerodynamicists and stylists. Response Surface Modeling and Reduced-Order Modeling are commonly used to eliminate the overhead due to Computational Fluid…

Empirical interpolation method (EIM) is a well-known technique to efficiently approximate parameterized functions. This paper proposes to use EIM algorithm to efficiently reduce the dimension of the training data within supervised machine…

The central aim of this paper is to implement Deep Autoencoder and Neighborhood Components Analysis (NCA) dimensionality reduction methods in Matlab and to observe the application of these algorithms on nine unlike datasets from UCI machine…

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…

An analysis of high-dimensional data can offer a detailed description of a system but is often challenged by the curse of dimensionality. General dimensionality reduction techniques can alleviate such difficulty by extracting a few…

Dimensionality reduction is the essence of many data processing problems, including filtering, data compression, reduced-order modeling and pattern analysis. While traditionally tackled using linear tools in the fluid dynamics community,…

Selecting the appropriate dimensionality reduction (DR) technique and determining its optimal hyperparameter settings that maximize the accuracy of the output projections typically involves extensive trial and error, often resulting in…

This paper proposes a novel paradigm for machine learning that moves beyond traditional parameter optimization. Unlike conventional approaches that search for optimal parameters within a fixed geometric space, our core idea is to treat the…

Metric-based meta-learning has attracted a lot of attention due to its effectiveness and efficiency in few-shot learning. Recent studies show that metric scaling plays a crucial role in the performance of metric-based meta-learning…

Dimension reduction provides a useful tool for analyzing high dimensional data. The recently developed \textit{Envelope} method is a parsimonious version of the classical multivariate regression model through identifying a minimal reducing…

t-Distributed Stochastic Neighbor Embedding (t-SNE) for the visualization of multidimensional data has proven to be a popular approach, with successful applications in a wide range of domains. Despite their usefulness, t-SNE projections can…

The t-distributed Stochastic Neighbor Embedding (t-SNE) is a powerful and popular method for visualizing high-dimensional data. It minimizes the Kullback-Leibler (KL) divergence between the original and embedded data distributions. In this…

Traditional metrics like accuracy, F1-score, and precision are frequently used to evaluate machine learning models, however they may not be sufficient for evaluating performance on tiny, unbalanced, or high-dimensional datasets. A…

We introduce an improved unsupervised clustering protocol specially suited for large-scale structured data. The protocol follows three steps: a dimensionality reduction of the data, a density estimation over the low dimensional…

A new dimension reduction (DR) method for data sets is proposed by autonomous deforming of data manifolds. The deformation is guided by the proposed deforming vector field, which is defined by two kinds of virtual interactions between data…

This article presents a novel application of the t-distributed Stochastic Neighbor Embedding (t-SNE) clustering algorithm to the telecommunication field. t-SNE is a dimensionality reduction (DR) algorithm that allows the visualization of…

We describe a new method called t-ETE for finding a low-dimensional embedding of a set of objects in Euclidean space. We formulate the embedding problem as a joint ranking problem over a set of triplets, where each triplet captures the…

The task of lane detection involves identifying the boundaries of driving areas in real-time. Recognizing lanes with variable and complex geometric structures remains a challenge. In this paper, we explore a novel and flexible way of…