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We present a novel, domain-agnostic, model-independent, unsupervised, and universally applicable Machine Learning approach for dimensionality reduction based on the principles of algorithmic complexity. Specifically, but without loss of…

We provide a rigorous mathematical treatment to the crowding issue in data visualization when high dimensional data sets are projected down to low dimensions for visualization. By properly adjusting the capacity of high dimensional balls,…

The multidimensional databases often use compression techniques in order to decrease the size of the database. This paper introduces a new method called difference sequence compression. Under some conditions, this new technique is able to…

Semantic segmentation requires methods capable of learning high-level features while dealing with large volume of data. Towards such goal, Convolutional Networks can learn specific and adaptable features based on the data. However, these…

A key obstacle in automated analytics and meta-learning is the inability to recognize when different datasets contain measurements of the same variable. Because provided attribute labels are often uninformative in practice, this task may be…

High-dimensional data, characterized by many features, can be difficult to visualize effectively. Dimensionality reduction techniques, such as PCA, UMAP, and t-SNE, address this challenge by projecting the data into a lower-dimensional…

High-dimensional classification has become an increasingly important problem. In this paper we propose a "Multivariate Adaptive Stochastic Search" (MASS) approach which first reduces the dimension of the data space and then applies a…

Johnson-Lindenstrauss embeddings are widely used to reduce the dimension and thus the processing time of data. To reduce the total complexity, also fast algorithms for applying these embeddings are necessary. To date, such fast algorithms…

Clustering of high-dimensional data sets is a growing need in artificial intelligence, machine learning and pattern recognition. In this paper, we propose a new clustering method based on a combinatorial-topological approach applied to…

Bayesian change-point detection, together with latent variable models, allows to perform segmentation over high-dimensional time-series. We assume that change-points lie on a lower-dimensional manifold where we aim to infer subsets of…

Selecting relevant features is an important and necessary step for intelligent machines to maximize their chances of success. However, intelligent machines generally have no enough computing resources when faced with huge volume of data.…

In this paper, we address the challenging task of achieving multi-view dimensionality reduction. The goal is to effectively use the availability of multiple views for extracting a coherent low-dimensional representation of the data. The…

The basic problem of semantic compression is to minimize the length of a message while preserving its meaning. This differs from classical notions of compression in that the distortion is not measured directly at the level of bits, but…

Supervised manifold learning methods learn data representations by preserving the geometric structure of data while enhancing the separation between data samples from different classes. In this work, we propose a theoretical study of…

The rapid growth of dataset scales has been a key driver in advancing deep learning research. However, as dataset scale increases, the training process becomes increasingly inefficient due to the presence of low-value samples, including…

We propose a novel algorithm for supervised dimensionality reduction named Manifold Partition Discriminant Analysis (MPDA). It aims to find a linear embedding space where the within-class similarity is achieved along the direction that is…

Dataset pruning has been widely studied for 2D images to remove redundancy and accelerate training, while particular pruning methods for 3D data remain largely unexplored. In this work, we study dataset pruning for 3D data, where its…

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 $N$ and $J$ are large numbers. In this paper an algorithm is proposed for checking whether there exists a…

Scientists in many fields have the common and basic need of dimensionality reduction: visualizing the underlying structure of the massive multivariate data in a low-dimensional space. However, many dimensionality reduction methods confront…

One of the fundamental problems within the field of machine learning is dimensionality reduction. Dimensionality reduction methods make it possible to combat the so-called curse of dimensionality, visualize high-dimensional data and, in…