Analyzing relationships between objects is a pivotal problem within data science. In this context, Dimensionality reduction (DR) techniques are employed to generate smaller and more manageable data representations. This paper proposes a new method for dimensionality reduction, based on optimal transportation theory and the Gromov-Wasserstein distance. We offer a new probabilistic view of the classical Multidimensional Scaling (MDS) algorithm and the nonlinear dimensionality reduction algorithm, Isomap (Isometric Mapping or Isometric Feature Mapping) that extends the classical MDS, in which we use the Gromov-Wasserstein distance between the probability measure of high-dimensional data, and its low-dimensional representation. Through gradient descent, our method embeds high-dimensional data into a lower-dimensional space, providing a robust and efficient solution for analyzing complex high-dimensional datasets.

To make sense of the world our brains must analyze high-dimensional datasets streamed by our sensory organs. Because such analysis begins with dimensionality reduction, modelling early sensory processing requires biologically plausible online dimensionality reduction algorithms. Recently, we derived such an algorithm, termed similarity matching, from a Multidimensional Scaling (MDS) objective function. However, in the existing algorithm, the number of output dimensions is set a priori by the number of output neurons and cannot be changed. Because the number of informative dimensions in sensory inputs is variable there is a need for adaptive dimensionality reduction.

Sleep is crucial for human health, and EEG signals play a significant role in sleep research. Due to the high-dimensional nature of EEG signal data sequences, data visualization and clustering of different sleep stages have been challenges. To address these issues, we propose a two-stage hierarchical and explainable feature selection framework by incorporating a feature selection algorithm to improve the performance of dimensionality reduction. Inspired by topological data analysis, which can analyze the structure of high-dimensional data, we extract topological features from the EEG signals to compensate for the structural information loss that happens in traditional spectro-temporal data analysis. Supported by the topological visualization of the data from different sleep stages and the classification results, the proposed features are proven to be effective supplements to traditional features. Finally, we compare the performances of three dimensionality reduction algorithms: Principal Component Analysis (PCA), t-Distributed Stochastic Neighbor Embedding (t-SNE), and Uniform Manifold Approximation and Projection (UMAP). Among them, t-SNE achieved the highest accuracy of 79.8%, but considering the overall performance in terms of computational resources and metrics, UMAP is the optimal choice.

This paper explores the evolution of word meanings in 19th-century Spanish texts, with an emphasis on Latin American Spanish, using computational linguistics techniques. It addresses the Semantic Shift Detection (SSD) task, which is crucial for understanding linguistic evolution, particularly in historical contexts. The study focuses on analyzing a set of Spanish target words. To achieve this, a 19th-century Spanish corpus is constructed, and a customizable pipeline for SSD tasks is developed. This pipeline helps find the senses of a word and measure their semantic change between two corpora using fine-tuned BERT-like models with old Spanish texts for both Latin American and general Spanish cases. The results provide valuable insights into the cultural and societal shifts reflected in language changes over time

Unsupervised machine learning lacks ground truth by definition. This poses a major difficulty when designing metrics to evaluate the performance of such algorithms. In sharp contrast with supervised learning, for which plenty of quality metrics have been studied in the literature, in the field of dimensionality reduction only a few over-simplistic metrics has been proposed. In this work, we aim to introduce the first highly non-trivial dimensionality reduction performance metric. This metric is based on the sectional curvature behaviour arising from Riemannian geometry. To test its feasibility, this metric has been used to evaluate the performance of the most commonly used dimension reduction algorithms in the state of the art. Furthermore, to make the evaluation of the algorithms robust and representative, using curvature properties of planar curves, a new parameterized problem instance generator has been constructed in the form of a function generator. Experimental results are consistent with what could be expected based on the design and characteristics of the evaluated algorithms and the features of the data instances used to feed the method.

Datasets with non-trivial large scale topology can be hard to embed in low-dimensional Euclidean space with existing dimensionality reduction algorithms. We propose to model topologically complex datasets using vector bundles, in such a way that the base space accounts for the large scale topology, while the fibers account for the local geometry. This allows one to reduce the dimensionality of the fibers, while preserving the large scale topology. We formalize this point of view and, as an application, we describe a dimensionality reduction algorithm based on topological inference for vector bundles. The algorithm takes as input a dataset together with an initial representation in Euclidean space, assumed to recover part of its large scale topology, and outputs a new representation that integrates local representations obtained through local linear dimensionality reduction. We demonstrate this algorithm on examples coming from dynamical systems and chemistry. In these examples, our algorithm is able to learn topologically faithful embeddings of the data in lower target dimension than various well known metric-based dimensionality reduction algorithms.

The children were sitting in circle on the floor. "The flat hat has a number and a label that says parrots and battercakes" -- one of the kids screamed Every single child starts laughing. "Nooooo, it was the black cat is under the table and it eats carrots and pancakes" -- another child replied I realized only then that they were playing telephone (or broken telephone as we call it in Argentina). Human communication is complex, mainly because each person expresses themselves differently. We could speak the same language but use different slang, words, or expressions to convey the same message.

In the age of Big Data in biology, data science and machine learning have flourished and benefitted from their interdisciplinary application to biology. As a graduate student in this discipline, I read a lot of papers to stay up to date on the literature (and still have a large reading list to catch up on!), and thought I would share what have been some of the best papers I've read this year. In about 80–90% of the single-cell papers you'll encounter, depending on the research question, there will be at least one or two tSNE or UMAP plots to visualize the data they've collected, usually single-cell RNA-sequencing (scRNA-seq) data, where individual cells are profiled for their RNA abundance across the genome. These unsupervised dimensionality reduction methods have been more or less accepted as the status quo for data visualization in the world of single-cell genomics, so it took Academic Twitter by storm this summer when a new preprint boldly challenged that norm, arguing that these methods do little to preserve the latent structure of the data it seeks to convey to our 3D minds. Using the extreme example of preserving equidistant cells in high-dimensional space, and later relaxing it to near-equidistance, they show how tSNE and UMAP distort the orientation of groups of cells with near-equidistance spacing in the original space, clustering them with groups of cells that are evenly spread further apart.

There won't be any business insights if the data quality is poor. When preparing data, I often go through many different approaches to reach a level of quality of data that can provide accurate results. In this article, I describe how unsupervised ML can help in data preparation for machine learning projects and how it helps to get more accurate business insights. For accurate predictions, the data must not only be properly labeled, de-deputed, broad, consistent, etc. The point is that the machine learning model should process the "right" data.

The TensorBoard embedding projector is a very powerful tool in data analysis, specifically for interpreting and visualizing low-dimensional embeddings. In order to do so, first, it applies a dimensionality reduction algorithm to the input embeddings, between UMAP, T-SNE, PCA, or a custom one, to reduce their dimension to three and be able to render them in a three-dimensional space. Once the map is generated, this tool can be used, for example, to search for specific keywords associated with the embeddings or highlight similar points in space. Ultimately, its goal is to provide a way to better interpret the embeddings that our machine learning model is generating, to check if the similar ones according to our definition are plotted nearby in the 3D space. When the embeddings we want to display originate from words, plotting the points with the tag it refers is more than enough, which is exactly the use case presented in the TensorBoard documentation.