Related papers: Modern Dimension Reduction
The high-dimensional data setting, in which p >> n, is a challenging statistical paradigm that appears in many real-world problems. In this setting, learning a compact, low-dimensional representation of the data can substantially help…
Multidimensional scaling (MDS) is a popular dimensionality reduction techniques that has been widely used for network visualization and cooperative localization. However, the traditional stress minimization formulation of MDS necessitates…
Suppose the data consist of a set $S$ of points $x_j$, $1\leq j \leq J$, distributed in a bounded domain $D\subset R^N$, where $N$ is a large number. An algorithm is given for finding the sets $L_k$ of dimension $k\ll N$, $k=1,2,...K$, in a…
Dimension reduction is a common strategy to study non-linear dynamical systems composed by a large number of variables. The goal is to find a smaller version of the system whose time evolution is easier to predict while preserving some of…
Embedding and visualizing large-scale high-dimensional data in a two-dimensional space is an important problem since such visualization can reveal deep insights out of complex data. Most of the existing embedding approaches, however, run on…
We first show that the commonly used dimensionality reduction (DR) methods such as t-SNE and LargeVis poorly capture the global structure of the data in the low dimensional embedding. We show this via a number of tests for the DR methods…
Dimensionality reduction methods are unsupervised approaches which learn low-dimensional spaces where some properties of the initial space, typically the notion of "neighborhood", are preserved. Such methods usually require propagation on…
Networks of interconnected agents are essential to study complex networked systems' state evolution, stability, resilience, and control. Nevertheless, the high dimensionality and nonlinear dynamics are vital factors preventing us from…
Dimensionality reduction (DR) techniques map high-dimensional data into lower-dimensional spaces. Yet, current DR techniques are not designed to explore semantic structure that is not directly available in the form of variables or class…
The rise in data has led to the need for dimension reduction techniques, especially in the area of non-scalar variables, including time series, natural language processing, and computer vision. In this paper, we specifically investigate…
Sufficient dimension reduction (SDR) is continuing an active research field nowadays for high dimensional data. It aims to estimate the central subspace (CS) without making distributional assumption. To overcome the large-$p$-small-$n$…
We propose a novel framework for learning a low-dimensional representation of data based on nonlinear dynamical systems, which we call dynamical dimension reduction (DDR). In the DDR model, each point is evolved via a nonlinear flow towards…
Dimension reduction algorithms are a crucial part of many data science pipelines, including data exploration, feature creation and selection, and denoising. Despite their wide utilization, many non-linear dimension reduction algorithms are…
This paper investigates the theoretical foundations of the t-distributed stochastic neighbor embedding (t-SNE) algorithm, a popular nonlinear dimension reduction and data visualization method. A novel theoretical framework for the analysis…
Dimensionality reduction is a fundamental technique in machine learning and data analysis, enabling efficient representation and visualization of high-dimensional data. This paper explores five key methods: Principal Component Analysis…
The monitoring and management of high-volume feature-rich traffic in large networks offers significant challenges in storage, transmission and computational costs. The predominant approach to reducing these costs is based on performing a…
Unsupervised machine learning has recently gained much attention in the field of molecular dynamics (MD). Particularly, dimensionality reduction techniques have been regularly employed to analyze large volumes of high-dimensional MD data to…
Across many scientific fields, measurements often represent the number of times an event occurs. For example, a document can be represented by word occurrence counts, neural activity by spike counts per time window, or online communication…
Non-linear dimensionality reduction can be performed by \textit{manifold learning} approaches, such as Stochastic Neighbour Embedding (SNE), Locally Linear Embedding (LLE) and Isometric Feature Mapping (ISOMAP). These methods aim to produce…
The goal of dimension reduction tools is to construct a low-dimensional representation of high-dimensional data. These tools are employed for a variety of reasons such as noise reduction, visualization, and to lower computational costs.…