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Manifold learning techniques have become increasingly valuable as data continues to grow in size. By discovering a lower-dimensional representation (embedding) of the structure of a dataset, manifold learning algorithms can substantially…

In recent years, Rectified flow (RF) has gained considerable popularity largely due to its generation efficiency and state-of-the-art performance. In this paper, we investigate the degree to which RF automatically adapts to the intrinsic…

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 work is about a slow-fast data assimilation system when only slow components are observable. First, we obtain its low dimensional reduction via an invariant slow manifold. Second, we prove that the low dimensional filter on the slow…

This report concerns the problem of dimensionality reduction through information geometric methods on statistical manifolds. While there has been considerable work recently presented regarding dimensionality reduction for the purposes of…

Neural network pruning is an essential approach for reducing the computational complexity of deep models so that they can be well deployed on resource-limited devices. Compared with conventional methods, the recently developed dynamic…

Spectral dimensionality reduction is frequently used to identify low-dimensional structure in high-dimensional data. However, learning manifolds, especially from the streaming data, is computationally and memory expensive. In this paper, we…

Radio frequency (RF) data contain richer information compared to other data types, such as envelope or B-mode, and employing RF data for training deep neural networks has attracted growing interest in ultrasound image processing. However,…

Dimension reduction is the process of embedding high-dimensional data into a lower dimensional space to facilitate its analysis. In the Euclidean setting, one fundamental technique for dimension reduction is to apply a random linear map to…

In recent years, radio frequency (RF) sensing has gained increasing popularity due to its pervasiveness, low cost, non-intrusiveness, and privacy preservation. However, realizing the promises of RF sensing is highly nontrivial, given…

Network filtering is an important form of dimension reduction to isolate the core constituents of large and interconnected complex systems. We introduce a new technique to filter large dimensional networks arising out of dynamical behavior…

Dimension reduction (DR) aims to learn low-dimensional representations of high-dimensional data with the preservation of essential information. In the context of manifold learning, we define that the representation after…

Similarity matching and join of time series data streams has gained a lot of relevance in today's world that has large streaming data. This process finds wide scale application in the areas of location tracking, sensor networks, object…

Data are not only ubiquitous in society, but are increasingly complex both in size and dimensionality. Dimension reduction offers researchers and scholars the ability to make such complex, high dimensional data spaces simpler and more…

Radiography is often used to probe complex, evolving density fields in dynamic systems and in so doing gain insight into the underlying physics. This technique has been used in numerous fields including materials science, shock physics,…

In recent years, manifold methods have moved into focus as tools for dimension reduction. Assuming that the high-dimensional data actually lie on or close to a low-dimensional nonlinear manifold, these methods have shown convincing results…

Spectral dimensionality reduction algorithms are widely used in numerous domains, including for recognition, segmentation, tracking and visualization. However, despite their popularity, these algorithms suffer from a major limitation known…

Visualizing high dimensional data by projecting them into two or three dimensional space is one of the most effective ways to intuitively understand the data's underlying characteristics, for example their class neighborhood structure.…

We introduce Random Projection Flows (RPFs), a principled framework for injective normalizing flows that leverages tools from random matrix theory and the geometry of random projections. RPFs employ random semi-orthogonal matrices, drawn…

Dimensionality reduction is an integral part of data visualization. It is a process that obtains a structure preserving low-dimensional representation of the high-dimensional data. Two common criteria can be used to achieve a dimensionality…