Euclidean Distance Matrices: Essential Theory, Algorithms and Applications

Euclidean distance matrices (EDM) are matrices of squared distances between points. The definition is deceivingly simple: thanks to their many useful properties they have found applications in psychometrics, crystallography, machine learning, wireless sensor networks, acoustics, and more. Despite the usefulness of EDMs, they seem to be insufficiently known in the signal processing community. Our goal is to rectify this mishap in a concise tutorial. We review the fundamental properties of EDMs, such as rank or (non)definiteness. We show how various EDM properties can be used to design algorithms for completing and denoising distance data. Along the way, we demonstrate applications to microphone position calibration, ultrasound tomography, room reconstruction from echoes and phase retrieval. By spelling out the essential algorithms, we hope to fast-track the readers in applying EDMs to their own problems. Matlab code for all the described algorithms, and to generate the figures in the paper, is available online. Finally, we suggest directions for further research.Comment: - 17 pages, 12 figures, to appear in IEEE Signal Processing Magazine - change of title in the last revisio

Construction of embedded fMRI resting-state functional connectivity networks using manifold learning

We construct embedded functional connectivity networks (FCN) from benchmark resting-state functional magnetic resonance imaging (rsfMRI) data acquired from patients with schizophrenia and healthy controls based on linear and nonlinear manifold learning algorithms, namely, Multidimensional Scaling, Isometric Feature Mapping, Diffusion Maps, Locally Linear Embedding and kernel PCA. Furthermore, based on key global graph-theoretic properties of the embedded FCN, we compare their classification potential using machine learning. We also assess the performance of two metrics that are widely used for the construction of FCN from fMRI, namely the Euclidean distance and the cross correlation metric. We show that diffusion maps with the cross correlation metric outperform the other combinations

Social Media Text Processing and Semantic Analysis for Smart Cities

With the rise of Social Media, people obtain and share information almost instantly on a 24/7 basis. Many research areas have tried to gain valuable insights from these large volumes of freely available user generated content. With the goal of extracting knowledge from social media streams that might be useful in the context of intelligent transportation systems and smart cities, we designed and developed a framework that provides functionalities for parallel collection of geo-located tweets from multiple pre-defined bounding boxes (cities or regions), including filtering of non-complying tweets, text pre-processing for Portuguese and English language, topic modeling, and transportation-specific text classifiers, as well as, aggregation and data visualization. We performed an exploratory data analysis of geo-located tweets in 5 different cities: Rio de Janeiro, S\~ao Paulo, New York City, London and Melbourne, comprising a total of more than 43 million tweets in a period of 3 months. Furthermore, we performed a large scale topic modelling comparison between Rio de Janeiro and S\~ao Paulo. Interestingly, most of the topics are shared between both cities which despite being in the same country are considered very different regarding population, economy and lifestyle. We take advantage of recent developments in word embeddings and train such representations from the collections of geo-located tweets. We then use a combination of bag-of-embeddings and traditional bag-of-words to train travel-related classifiers in both Portuguese and English to filter travel-related content from non-related. We created specific gold-standard data to perform empirical evaluation of the resulting classifiers. Results are in line with research work in other application areas by showing the robustness of using word embeddings to learn word similarities that bag-of-words is not able to capture

Visualization of Jacques Lacan’s Registers of the Psychoanalytic Field, and Discovery of Metaphor and of Metonymy. Analytical Case Study of Edgar Allan Poe’s “The Purloined Letter”

We start with a description of Lacan’s work that we then take into our analytics methodology. In a first investigation, a Lacan-motivated template of the Poe story is fitted to the data. A segmentation of the storyline is used in order to map out the diachrony. Based on this, it will be shown how synchronous aspects, potentially related to Lacanian registers, can be sought. This demonstrates the effectiveness of an approach based on a model template of the storyline narrative. In a second and more comprehensive investigation, we develop an approach for revealing, that is, uncovering, Lacanian register relationships. Objectives of this work include the wide and general application of our methodology. This methodology is strongly based on the “letting the data speak” Correspondence Analysis analytics platform of Jean-Paul Benzécri, that is also the geometric data analysis, both qualitative and quantitative analytics, developed by Pierre Bourdieu