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We introduce a new method to jointly reduce the dimension of the input and output space of a function between high-dimensional spaces. Choosing a reduced input subspace influences which output subspace is relevant and vice versa.…

Developing an understanding of high-dimensional data can be facilitated by visualizing that data using dimensionality reduction. However, the low-dimensional embeddings are often difficult to interpret. To facilitate the exploration and…

Human brain connectome studies aim at extracting and analyzing relevant features associated to pathologies of interest. Usually this consists in modeling the brain connectome as a graph and in using graph metrics as features. A fine brain…

The unprecedented prowess of measurement techniques provides a detailed, multi-scale look into the depths of living systems. Understanding these avalanches of high-dimensional data -- by distilling underlying principles and mechanisms --…

This work approaches the multidimensional scaling problem from a novel angle. We introduce a scalable method based on the h-plot, which inherently accommodates asymmetric proximity data. Instead of embedding the objects themselves, the…

This paper addresses the problem of mapping high-dimensional data to a low-dimensional space, in the presence of other known features. This problem is ubiquitous in science and engineering as there are often controllable/measurable features…

Dimension reduction and visualization of high-dimensional data have become very important research topics because of the rapid growth of large databases in data science. In this paper, we propose using a generalized sigmoid function to…

Dimensionality reduction (DR) of image features plays an important role in image retrieval and classification tasks. Recently, two types of methods have been proposed to improve the both the accuracy and efficiency for the dimensionality…

The visualization of multi-dimensional data with interpretable methods remains limited by capabilities for both high-dimensional lossless visualizations that do not suffer from occlusion and that are computationally capable by parameterized…

The current data tends to be more complex than conventional data and need dimension reduction. Dimension reduction is important in cluster analysis and creates a smaller data in volume and has the same analytical results as the original…

Integrating functions on discrete domains into neural networks is key to developing their capability to reason about discrete objects. But, discrete domains are (1) not naturally amenable to gradient-based optimization, and (2) incompatible…

DNA storage technology offers new possibilities for addressing massive data storage due to its high storage density, long-term preservation, low maintenance cost, and compact size. To improve the reliability of stored information, base…

Sufficient dimension reduction is widely applied to help model building between the response $Y$ and covariate $X$. While the target of interest is the relationship between $(Y,X)$, in some applications we also collect additional variable…

We present Clusterplot, a multi-class high-dimensional data visualization tool designed to visualize cluster-level information offering an intuitive understanding of the cluster inter-relations. Our unique plots leverage 2D blobs devised to…

Supervised dimensionality reduction has emerged as an important theme in the last decade. Despite the plethora of models and formulations, there is a lack of a simple model which aims to project the set of patterns into a space defined by…

High-content screening uses large collections of unlabeled cell image data to reason about genetics or cell biology. Two important tasks are to identify those cells which bear interesting phenotypes, and to identify sub-populations enriched…

Most linear dimension reduction methods proposed in the literature can be formulated using an appropriate pair of scatter matrices, see e.g. Ye and Weiss (2003), Tyler et al. (2009), Bura and Yang (2011), Liski et al. (2014) and Luo and Li…

Data vectors are obtained from multiple domains. They are feature vectors of images or vector representations of words. Domains may have different numbers of data vectors with different dimensions. These data vectors from multiple domains…

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…

High-dimensional big data appears in many research fields such as image recognition, biology and collaborative filtering. Often, the exploration of such data by classic algorithms is encountered with difficulties due to `curse of…