Some Further Evidence about Magnification and Shape in Neural Gas

Neural gas (NG) is a robust vector quantization algorithm with a well-known mathematical model. According to this, the neural gas samples the underlying data distribution following a power law with a magnification exponent that depends on data dimensionality only. The effects of shape in the input data distribution, however, are not entirely covered by the NG model above, due to the technical difficulties involved. The experimental work described here shows that shape is indeed relevant in determining the overall NG behavior; in particular, some experiments reveal richer and complex behaviors induced by shape that cannot be explained by the power law alone. Although a more comprehensive analytical model remains to be defined, the evidence collected in these experiments suggests that the NG algorithm has an interesting potential for detecting complex shapes in noisy datasets

Self-Organized Maps

Se han obtenido los siguientes resultados: (1) Estudio de topologías bidimensionales alternativas: se muestra la importancia de topologías alternativas basadas en áreas ajenas como las teselaciones. (2) Estudio comparativo de topologías en una, dos y tres dimensiones: se revela la influencia de la dimensión en el funcionamiento de una SOM a escala local y global. (3) Estudio de alternativas al movimiento euclídeo: se propone y presenta la alternativa FRSOM al algoritmo SOM clásico. En FRSOM, las neuronas esquivan barreras predefinidas en su movimiento. Las conclusiones más relevantes que emanan de esta Tesis Doctoral son las siguientes: (1) La calidad del clustering y de la preservación topológica de una SOM puede ser mejorada mediante el uso de topologías alternativas y también evitando regiones prohibidas que no contribuyan significativamente al Error Cuadrático Medio (ECM). (2) La dimensióon de la SOM que obtiene mejores resultados es la propia dimensión intrínseca de los datos. Además, en general, valores bajos para la dimensión de la SOM producen mejores resultados en términos del ECM, y valores altos ocasionan mejor aprendizaje de la estructura de los datos.Los mapas auto-organizados o redes de Kohonen (SOM por sus siglas en inglés, self-organizing map) fueron introducidos por el profesor finlandés Teuvo Kalevi Kohonen en los años 80. Un mapa auto-organizado es una herramienta que analiza datos en muchas dimensiones con relaciones complejas entre ellos y los reduce o representa en, usualmente, una, dos o tres dimensiones. La propiedad más importante de una SOM es que preserva las propiedades topológicas de los datos, es decir, que datos próximos aparecen próximos en la representación. La literatura relacionada con los mapas auto-organizados y sus aplicaciones es muy diversa y numerosa. Las neuronas en un mapa auto-organizado clásico están distribuidas en una topología (o malla) bidimensional cuadrada o hexagonal y las distancias entre ellas son distancias euclídeas. Una de las disciplinas de investigación en SOM consiste en la modificación y generalización del algoritmo SOM. Esta Tesis Doctoral por compendio de publicaciones se centra en esta línea de investigación. En concreto, los objetivos desarrollados han sido el estudio de topologías bidimensionales alternativas, el estudio comparativo de topologías de una, dos y tres dimensiones y el estudio de variaciones para la distancia y movimientos euclídeos. Estos objetivos se han abordado mediante el método científico a través de las siguientes fases: aprehensión de resultados conocidos, planteamiento de hipótesis, propuesta de métodos alternativos, confrontación de métodos mediante experimentación, aceptación y rechazo de las diversas hipótesis mediante métodos estadísticos

Principal manifolds and graphs in practice: from molecular biology to dynamical systems

We present several applications of non-linear data modeling, using principal manifolds and principal graphs constructed using the metaphor of elasticity (elastic principal graph approach). These approaches are generalizations of the Kohonen's self-organizing maps, a class of artificial neural networks. On several examples we show advantages of using non-linear objects for data approximation in comparison to the linear ones. We propose four numerical criteria for comparing linear and non-linear mappings of datasets into the spaces of lower dimension. The examples are taken from comparative political science, from analysis of high-throughput data in molecular biology, from analysis of dynamical systems.Comment: 12 pages, 9 figure

Development of artificial neural network-based object detection algorithms for low-cost hardware devices

Finally, the fourth work was published in the “WCCI” conference in 2020 and consisted of an individuals' position estimation algorithm based on a novel neural network model for environments with forbidden regions, named “Forbidden Regions Growing Neural Gas”.The human brain is the most complex, powerful and versatile learning machine ever known. Consequently, many scientists of various disciplines are fascinated by its structures and information processing methods. Due to the quality and quantity of the information extracted from the sense of sight, image is one of the main information channels used by humans. However, the massive amount of video footage generated nowadays makes it difficult to process those data fast enough manually. Thus, computer vision systems represent a fundamental tool in the extraction of information from digital images, as well as a major challenge for scientists and engineers. This thesis' primary objective is automatic foreground object detection and classification through digital image analysis, using artificial neural network-based techniques, specifically designed and optimised to be deployed in low-cost hardware devices. This objective will be complemented by developing individuals' movement estimation methods by using unsupervised learning and artificial neural network-based models. The cited objectives have been addressed through a research work illustrated in four publications supporting this thesis. The first one was published in the “ICAE” journal in 2018 and consists of a neural network-based movement detection system for Pan-Tilt-Zoom (PTZ) cameras deployed in a Raspberry Pi board. The second one was published in the “WCCI” conference in 2018 and consists of a deep learning-based automatic video surveillance system for PTZ cameras deployed in low-cost hardware. The third one was published in the “ICAE” journal in 2020 and consists of an anomalous foreground object detection and classification system for panoramic cameras, based on deep learning and supported by low-cost hardware

What governs star formation in galaxies? A modern statistical approach

Understanding the process of star formation is one of the key steps in understanding the formation and evolution of galaxies. In this thesis, I address the empirical star formation laws, and study the properties of galaxies that can affect the star formation rate. The Andromeda galaxy (M31) is the nearest large spiral galaxy, and Therefore, high resolution images of this galaxy are available. These images provide data from various regions with different physical properties. Star formation rate and gas mass surface densities of M31have been measured using three different methods, and have been used to compare different star formation laws over the whole galaxy and in spatially-resolved regions. Using hierarchical Bayesian regression analysis, I conclude that there is a correlation between surface density of star formation and the stellar mass surface density. A weak correlation between star formation rate, stellar mass and metallicity is also found. To study the effect of other properties a galaxy on the star formation rate, I utilize an unsupervised data mining method (specifically the self-organizing map) on measurements of both nearby and high-redshift galaxies. Both observed data and derived quantities (e.g. star formation rate, stellar mass) of star-forming regions in M31 and the nearby spiral galaxy M101 are used as inputs to the self-organizing map. Clustering the M31 regions in the feature space reveals some (anti)-correlations between the properties the galaxy, which are not apparent when considering data from all regions in the galaxy. The self-organizing map can be used to predict star formation rates for spatially-resolved regions in galaxies using other properties of those regions. I also apply the self-organizing map method to spectral energy distributions of high-redshift galaxies. Template spectra made from galaxies with known morphological type are used to train self-organizing maps. The trained maps are used to classify a sample of galaxy spectral energy distributions derived from fitting models to photometry data of 142 high-redshift galaxies. The grouped properties of the classified galaxies are found to be more tightly correlated in mean values of age, specific star formation rate, stellar mass, and far-UV extinction than in previous studies

Evaluating indoor positioning systems in a shopping mall : the lessons learned from the IPIN 2018 competition

The Indoor Positioning and Indoor Navigation (IPIN) conference holds an annual competition in which indoor localization systems from different research groups worldwide are evaluated empirically. The objective of this competition is to establish a systematic evaluation methodology with rigorous metrics both for real-time (on-site) and post-processing (off-site) situations, in a realistic environment unfamiliar to the prototype developers. For the IPIN 2018 conference, this competition was held on September 22nd, 2018, in Atlantis, a large shopping mall in Nantes (France). Four competition tracks (two on-site and two off-site) were designed. They consisted of several 1 km routes traversing several floors of the mall. Along these paths, 180 points were topographically surveyed with a 10 cm accuracy, to serve as ground truth landmarks, combining theodolite measurements, differential global navigation satellite system (GNSS) and 3D scanner systems. 34 teams effectively competed. The accuracy score corresponds to the third quartile (75th percentile) of an error metric that combines the horizontal positioning error and the floor detection. The best results for the on-site tracks showed an accuracy score of 11.70 m (Track 1) and 5.50 m (Track 2), while the best results for the off-site tracks showed an accuracy score of 0.90 m (Track 3) and 1.30 m (Track 4). These results showed that it is possible to obtain high accuracy indoor positioning solutions in large, realistic environments using wearable light-weight sensors without deploying any beacon. This paper describes the organization work of the tracks, analyzes the methodology used to quantify the results, reviews the lessons learned from the competition and discusses its future

A sequential algorithm for training the SOM prototypes based on higher-order recursive equations

A novel training algorithm is proposed for the formation of Self-Organizing Maps (SOM). In the proposed model, the weights are updated incrementally by using a higher-order difference equation, which implements a low-pass digital filter. It is possible to improve selected features of the self-organization process with respect to the basic SOM by suitably designing the filter. Moreover, from this model, new visualization tools can be derived for cluster visualization and for monitoring the quality of the map

Robust modelling and tracking of NonRigid objects using Active-GNG

This paper presents a robust approach to nonrigid modelling and tracking. The contour of the object is described by an active growing neural gas (A-GNG) network which allows the model to re-deform locally. The approach is novel in that the nodes of the network are described by their geometrical position, the underlying local feature structure of the image, and the distance vector between the modal image and any successive images. A second contribution is the correspondence of the nodes which is measured through the calculation of the topographic product, a topology preserving objective function which quantifies the neighbourhood preservation before and after the mapping. As a result, we can achieve the automatic modelling and tracking of objects without using any annotated training sets. Experimental results have shown the superiority of our proposed method over the original growing neural gas (GNG) network