Related papers: Joint Characterization of Spatiotemporal Data Mani…

Dimension reduction (DR) methods provide systematic approaches for analyzing high-dimensional data. A key requirement for DR is to incorporate global dependencies among original and embedded samples while preserving clusters in the…

We explore two primary classes of approaches to dimensionality reduction (DR): Independent Dimensionality Reduction (IDR) and Simultaneous Dimensionality Reduction (SDR). In IDR methods, of which Principal Components Analysis is a…

High dimensional data can contain multiple scales of variance. Analysis tools that preferentially operate at one scale can be ineffective at capturing all the information present in this cross-scale complexity. We propose a multiscale joint…

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…

Because of high dimensionality, correlation among covariates, and noise contained in data, dimension reduction (DR) techniques are often employed to the application of machine learning algorithms. Principal Component Analysis (PCA), Linear…

$\textbf{This is the conference version of our paper: Spatiotemporal Implicit Neural Representation as a Generalized Traffic Data Learner}$. Spatiotemporal Traffic Data (STTD) measures the complex dynamical behaviors of the multiscale…

Spatiotemporal Traffic Data (STTD) measures the complex dynamical behaviors of the multiscale transportation system. Existing methods aim to reconstruct STTD using low-dimensional models. However, they are limited to data-specific…

Dimensionality reduction (DR) is often used as a preprocessing step in classification, but usually one first fixes the DR mapping, possibly using label information, and then learns a classifier (a filter approach). Best performance would be…

Large scale dynamical systems (e.g. many nonlinear coupled differential equations) can often be summarized in terms of only a few state variables (a few equations), a trait that reduces complexity and facilitates exploration of behavioral…

Among applications of deep learning (DL) involving low cost sensors, remote image classification involves a physical channel that separates edge sensors and cloud classifiers. Traditional DL models must be divided between an encoder for the…

Dimensionality Reduction (DR) techniques can generate 2D projections and enable visual exploration of cluster structures of high-dimensional datasets. However, different DR techniques would yield various patterns, which significantly affect…

Dimensionality reduction (DR) is characterized by two longstanding trade-offs. First, there is a global-local preservation tension: methods such as t-SNE and UMAP prioritize local neighborhood preservation, yet may distort global manifold…

Distribution Regression (DR) on stochastic processes describes the learning task of regression on collections of time series. Path signatures, a technique prevalent in stochastic analysis, have been used to solve the DR problem. Recent…

Signature, lying at the heart of rough path theory, is a central tool for analysing controlled differential equations driven by irregular paths. Recently it has also found extensive applications in machine learning and data science as a…

Individual trajectories, rich in human-environment interaction information across space and time, serve as vital inputs for geospatial foundation models (GeoFMs). However, existing attempts at learning trajectory representations have…

Different unsupervised models for dimensionality reduction like PCA, LLE, Shannon's mapping, tSNE, UMAP, etc. work on different principles, hence, they are difficult to compare on the same ground. Although they are usually good for…

Remote sensing spatiotemporal fusion (STF) addresses the fundamental trade-off between temporal and spatial resolution by combining high temporal-low spatial and high spatial-low temporal imagery. This paper presents the first comprehensive…

Dimensional reduction~(DR) maps high-dimensional data into a lower dimensions latent space with minimized defined optimization objectives. The DR method usually falls into feature selection~(FS) and feature projection~(FP). FS focuses on…

Both Dimensionality Reduction (DR) and Graph Drawing (GD) aim to visualize abstract, non-linear structures, yet rely on different optimization paradigms. This contrast is evident in Multidimensional Scaling (MDS), which typically depends on…

Dimensionality reduction (DR) plays a vital role in the visual analysis of high-dimensional data. One main aim of DR is to reveal hidden patterns that lie on intrinsic low-dimensional manifolds. However, DR often overlooks important…