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We present a theoretical foundation regarding the boundedness of the t-SNE algorithm. t-SNE employs gradient descent iteration with Kullback-Leibler (KL) divergence as the objective function, aiming to identify a set of points that closely…

An increasing number of multi-view data are being published by studies in several fields. This type of data corresponds to multiple data-views, each representing a different aspect of the same set of samples. We have recently proposed…

With the recent surge in big data analytics for hyper-dimensional data there is a renewed interest in dimensionality reduction techniques for machine learning applications. In order for these methods to improve performance gains and…

Tensor decomposition of high-dimensional data often struggles to capture semantically or physically meaningful structures, particularly when relying on reconstruction objectives and fixed-rank constraints. We introduce a no-rank tensor…

Visualizing high-dimensional data has been a focus in data analysis communities for decades, which has led to the design of many algorithms, some of which are now considered references (such as t-SNE for example). In our era of overwhelming…

In this work, we discuss low-parametric approaches for approximating SimRank matrices, which estimate the similarity between pairs of nodes in a graph. Although SimRank matrices and their computation require a significant amount of memory,…

We present the self-encoder, a neural network trained to guess the identity of each data sample. Despite its simplicity, it learns a very useful representation of data, in a self-supervised way. Specifically, the self-encoder learns to…

Relational data mining is becoming ubiquitous in many fields of study. It offers insights into behaviour of complex, real-world systems which cannot be modeled directly using propositional learning. We propose Symbolic Graph Embedding…

t-SNE and hierarchical clustering are popular methods of exploratory data analysis, particularly in biology. Building on recent advances in speeding up t-SNE and obtaining finer-grained structure, we combine the two to create tree-SNE, a…

Unsupervised dimensionality reduction is one of the commonly used techniques in the field of high dimensional data recognition problems. The deep autoencoder network which constrains the weights to be non-negative, can learn a low…

Embedding high-dimensional data onto a low-dimensional manifold is of both theoretical and practical value. In this paper, we propose to combine deep neural networks (DNN) with mathematics-guided embedding rules for high-dimensional data…

We train three convolutional neural networks (CNNs) to classify galaxies with Galaxy Zoo 2 dataset and extract the activations from the last fully connected layer or the last average pooling layer of CNNs to study the high-dimensional…

The task of dimensionality reduction and visualization of high-dimensional datasets remains a challenging problem since long. Modern high-throughput technologies produce newer high-dimensional datasets having multiple views with relatively…

Embedding network data into a low-dimensional vector space has shown promising performance for many real-world applications, such as node classification and entity retrieval. However, most existing methods focused only on leveraging network…

Quantum embedding is a fundamental prerequisite for applying quantum machine learning techniques to classical data, and has substantial impacts on performance outcomes. In this study, we present Neural Quantum Embedding (NQE), a method that…

Sensor data analysis plays a key role in health assessment of critical equipment. Such data are multivariate and exhibit nonlinear relationships. This paper describes how one can exploit nonlinear dimension reduction techniques, such as the…

Unsupervised text embedding methods, such as Skip-gram and Paragraph Vector, have been attracting increasing attention due to their simplicity, scalability, and effectiveness. However, comparing to sophisticated deep learning architectures…

Network Embeddings (NEs) map the nodes of a given network into $d$-dimensional Euclidean space $\mathbb{R}^d$. Ideally, this mapping is such that `similar' nodes are mapped onto nearby points, such that the NE can be used for purposes such…

A representation technique that allows encoding music in a way that contains musical meaning would improve the results of any model trained for computer music tasks like generation of melodies and harmonies of better quality. The field of…

Representing the nodes of continuous-time temporal graphs in a low-dimensional latent space has wide-ranging applications, from prediction to visualization. Yet, analyzing continuous-time relational data with timestamped interactions…