Manifold Learning for Natural Image Sets, Doctoral Dissertation August 2006

The field of manifold learning provides powerful tools for parameterizing high-dimensional data points with a small number of parameters when this data lies on or near some manifold. Images can be thought of as points in some high-dimensional image space where each coordinate represents the intensity value of a single pixel. These manifold learning techniques have been successfully applied to simple image sets, such as handwriting data and a statue in a tightly controlled environment. However, they fail in the case of natural image sets, even those that only vary due to a single degree of freedom, such as a person walking or a heart beating. Parameterizing data sets such as these will allow for additional constraints on traditional computer vision problems such as segmentation and tracking. This dissertation explores the reasons why classical manifold learning algorithms fail on natural image sets and proposes new algorithms for parameterizing this type of data

Redes neuronales que expresan múltiples estrategias en el videojuego StarCraft 2.

ilustracionesUsing neural networks and supervised learning, we have created models capable of solving problems at a superhuman level. Nevertheless, this training process results in models that learn policies that average the plethora of behaviors usually found in datasets. In this thesis we present and study the Behavioral Repetoires Imitation Learning (BRIL) technique. In BRIL, the user designs a behavior space, the user then projects this behavior space into low coordinates and uses these coordinates as input to the model. Upon deployment, the user can adjust the model to express a behavior by specifying fixed coordinates for these inputs. The main research question ponders on the relationship between the Dimension Reduction algorithm and how much the trained models are able to replicate behaviors. We study three different Dimensionality Reduction algorithms: Principal Component Analysis (PCA), Isometric Feature Mapping (Isomap) and Uniform Manifold Approximation and Projection (UMAP); we design and embed a behavior space in the video game StarCraft 2, we train different models for each embedding and we test the ability of each model to express multiple strategies. Results show that with BRIL we are able to train models that are able to express the multiple behaviors present in the dataset. The geometric structure these methods preserve induce different separations of behaviors, and these separations are reflected in the models' conducts. (Tomado de la fuente)Usando redes neuronales y aprendizaje supervisado, hemos creado modelos capaces de solucionar problemas a nivel súperhumano. Sin embargo, el proceso de entrenamiento de estos modelos es tal que el resultado es una política que promedia todos los diferentes comportamientos presentes en el conjunto de datos. En esta tesis presentamos y estudiamos la técnica Aprendizaje por Imitación de Repertorios de Comportamiento (BRIL), la cual permite entrenar modelos que expresan múltiples comportamientos de forma ajustable. En BRIL, el usuario diseña un espacio de comportamientos, lo proyecta a bajas dimensiones y usa las coordenadas resultantes como entradas del modelo. Para poder expresar cierto comportamiento a la hora de desplegar la red, basta con fijar estas entradas a las coordenadas del respectivo comportamiento. La pregunta principal que investigamos es la relación entre el algoritmo de reducción de dimensionalidad y la capacidad de los modelos entrenados para replicar y expresar las estrategias representadas. Estudiamos tres algoritmos diferentes de reducción de dimensionalidad: Análisis de Componentes Principales (PCA), Mapeo de Características Isométrico (Isomap) y Aproximación y Proyección de Manifolds Uniformes (UMAP); diseñamos y proyectamos un espacio de comportamientos en el videojuego StarCraft 2, entrenamos diferentes modelos para cada embebimiento y probamos la capacidad de cada modelo de expresar múltiples estrategias. Los resultados muestran que, usando BRIL, logramos entrenar modelos que pueden expresar los múltiples comportamientos presentes en el conjunto de datos. La estructura geométrica preservada por cada método de reducción induce diferentes separaciones de los comportamientos, y estas separaciones se ven reflejadas en las conductas de los modelos. (Tomado de la fuente)Maestrí

An intelligent information forwarder for healthcare big data systems with distributed wearable sensors

© 2016 IEEE. An increasing number of the elderly population wish to live an independent lifestyle, rather than rely on intrusive care programmes. A big data solution is presented using wearable sensors capable of carrying out continuous monitoring of the elderly, alerting the relevant caregivers when necessary and forwarding pertinent information to a big data system for analysis. A challenge for such a solution is the development of context-awareness through the multidimensional, dynamic and nonlinear sensor readings that have a weak correlation with observable human behaviours and health conditions. To address this challenge, a wearable sensor system with an intelligent data forwarder is discussed in this paper. The forwarder adopts a Hidden Markov Model for human behaviour recognition. Locality sensitive hashing is proposed as an efficient mechanism to learn sensor patterns. A prototype solution is implemented to monitor health conditions of dispersed users. It is shown that the intelligent forwarders can provide the remote sensors with context-awareness. They transmit only important information to the big data server for analytics when certain behaviours happen and avoid overwhelming communication and data storage. The system functions unobtrusively, whilst giving the users peace of mind in the knowledge that their safety is being monitored and analysed

Modelle reduzierter Ordnung für stationäre, transsonische Strömungen via Methoden des Erlernens von Mannigfaltigkeiten

This thesis presents novel parametric ROM based on ML for use in steady transonic aerodynamic applications. The main objective of this work is to derive efficient ROMs that exploit the low-dimensional manifold of the underlying CFD solutions to ensure an improved treatment of the nonlinearities involved in varying the inflow conditions and geometric parameters. In particular, an improved prediction of shocks should be obtained. The reduced-order representation of the underlying CFD data is derived using the ML method Isomap, which is extended to aerodynamic applications. In order to develop a ROM that has the ability to predict approximate CFD solutions at untried parameter combinations, Isomap is coupled with an interpolation method, referred to as Isomap+I, to allow for variations in parameters like the angle of attack or the Mach number. Furthermore, an approximate local inverse mapping from the reduced-order representation to the full CFD solution space is introduced. In addition, the Isomap+I based predictions are further improved by optimizing the corresponding flux residual of the CFD solver used. The low-dimensional representation of the solution manifold discovered by Isomap is also exploited to develop an adaptive sampling strategy. The goal of the method is to obtain a homogenously distributed sampling of the data manifold, which leads to a better description of the underlying manifold and eventually to a more accurate ROM. The proposed Isomap based ROM along with the adaptive sampling strategy are successfully applied to predict CFD solutions of the NACA64A010 airfoil and to a fuselage-wing configuration depending on two and five parameters, respectively. The outcomes are compared to those of the full-order CFD model and, in comparison to predictions obtained by comparable POD based ROM, an improvement of the results is achieved. Particularly, results featuring a shock are more accurately predicted.In dieser Arbeit werden neuartige, parametrische Modelle reduzierter Ordnung (engl. reduced-order models, ROMs) für stationäre, transonische Anwendungen der Aerodynamik vorgestellt. Dabei basieren die entwickelten ROMs auf den Methoden des Erlernens von Mannigfaltigkeiten (engl. manifold learning, ML). Ziel ist die Herleitung effizienter ROMs, welche unter Ausnutzung der niedrig-dimensionalen Mannigfaltigkeit der zugrunde liegenden CFD-Lösungen eine verbesserte Behandlung der Nichtlinearitäten sicherstellen, welche durch variieren von Strömungs- und Geometrieparametern auftreten. Insbesondere soll dies die Vorhersage von Verdichtungsstößen verbessern. Die reduzierte Darstellung der zugrunde liegenden CFD-Daten wird durch die ML-Methode Isomap berechnet, welche für aerodynamische Anwendungen weiterentwickelt wird. Um ein Modell reduzierter Ordnung zu entwickeln, welches approximierte CFD-Lösungen an bisher nicht abgetasteten Parameterkombinationen vorhersagen kann, wird Isomap mit einem Interpolationmodell gekoppelt. Dadurch wird eine Abhängigkeit des Modells von Veränderungen in den Parametern, wie z.B. dem Anstellwinkel oder der Machzahl, erreicht. Um schließlich hoch-dimensionale Vorhersagen treffen zu können, wird eine lokal-inverse Abbildung von der reduzierten Darstellung in den hoch-dimensionalen CFD-Lösungsraum eingeführt. Dieses Modell wird im späteren Isomap+I genannt. Desweiteren wird die Vorhersage der Isomap+I Methode durch Minimierung des entsprechenden CFD-Flussresiduums verbessert. Basierend auf der niedrig-dimensionalen Darstellung der Lösungsmannigfaltigkeit, welche durch Isomap berechnet wurde, wird ein Verfahren zum adaptiven Abtasten des Parameterraums entwickelt. Das Ziel dieser Methode ist es, eine gleichmäßig verteilte Datenmannigfaltigkeit zu generieren, um eine bessere Charakterisierung der zugrundeliegenden Mannigfaltigkeit zu erhalten, wodurch die Genauigkeit der Modelle reduzierter Ordnung gesteigert wird. Die entwickelten ROMs werden, unter anderem in Kombination mit dem Verfahren zum adaptiven Abtasten des Parameterraums, erfolgreich für die Vorhersage von CFD-Lösungen des NACA64A010 Profils und einer Flugzeug-Konfiguration mit zwei respektive fünf Parametern angewendet. Die Ergebnisse werden mit CFD-Referenzlösungen verglichen, mit denen sie besser übereinstimmen als Vorhersagen von ROMs basierend auf der häufig genutzten POD (engl. proper orthogonal decomposition). Insbesondere werden Verdichtungsstöße genauer vorhergesagt

A System for 3D Shape Estimation and Texture Extraction via Structured Light

Shape estimation is a crucial problem in the fields of computer vision, robotics and engineering. This thesis explores a shape from structured light (SFSL) approach using a pyramidal laser projector, and the application of texture extraction. The specific SFSL system is chosen for its hardware simplicity, and efficient software. The shape estimation system is capable of estimating the 3D shape of both static and dynamic objects by relying on a fixed pattern. In order to eliminate the need for precision hardware alignment and to remove human error, novel calibration schemes were developed. In addition, selecting appropriate system geometry reduces the typical correspondence problem to that of a labeling problem. Simulations and experiments verify the effectiveness of the built system. Finally, we perform texture extraction by interpolating and resampling sparse range estimates, and subsequently flattening the 3D triangulated graph into a 2D triangulated graph via graph and manifold methods

Manifold Diffusion Fields

We present Manifold Diffusion Fields (MDF), an approach that unlocks learning of diffusion models of data in general non-Euclidean geometries. Leveraging insights from spectral geometry analysis, we define an intrinsic coordinate system on the manifold via the eigen-functions of the Laplace-Beltrami Operator. MDF represents functions using an explicit parametrization formed by a set of multiple input-output pairs. Our approach allows to sample continuous functions on manifolds and is invariant with respect to rigid and isometric transformations of the manifold. In addition, we show that MDF generalizes to the case where the training set contains functions on different manifolds. Empirical results on multiple datasets and manifolds including challenging scientific problems like weather prediction or molecular conformation show that MDF can capture distributions of such functions with better diversity and fidelity than previous approaches.Comment: ICLR24 pape