Analysis and convergence of SMO-like decomposition and geometrical algorithms for support vector machines

Tesis doctoral inédita. Universidad Autónoma de Madrid, Escuela Politécnica Superior, noviembre de 201

Algorithms for Automatic Label Placement

Práce popisuje problém automatického umísťování popisků do mapy. Jednotlivé bodové, čárové a plošné objekty v mapě je třeba označit odpovídajícími textovými či obrázkovými popisky. Tyto popisky je nutné rozmístit tak, aby se vzájemně nepřekrývaly a zároveň byly jasně přiřaditelné k odpovídajícím objektům. O problému je známo, že je NP-těžký a nalezení optimálního rozmístění všech popisků je výpočetně velmi náročné i pro nejjednodušší mapy. Pozornost je věnována umísťování popisků označujících bodové a čárové objekty, včetně prvního kroku obnášejícího přípravu možných pozic pro umístění těchto popisků, při dodržení běžných kartografických pravidel pro rozmísťování popisků. Následně jsou na problém aplikovány tři různé druhy algoritmů -- greedy ("hladové") algoritmy v kombinaci s lokálním prohledáváním, matematická optimalizace (v podobě 0-1 celočíselného programování) a genetické algoritmy. Popsané algoritmy jsou v softwarové části práce implementovány a na závěr porovnány na několika různých datových sadách, vycházejících z reálných geografických podkladů a z náhodně vygenerovaných map. Závěrečné srovnání se zaměřuje na kvalitu výsledného rozmístění (dle metrik definovaných v práci), času potřebnému k nalezení řešení a také na determinističnost daných algoritmů.Thesis describes the problem of automatic map label placement. Various point, line or area features in maps must be marked with matching text or graphic labels. These labels have to be placed so they do not overlap with each other and they are clearly associable with corresponding map features. The problem is known to be NP-hard and finding optimal positions of all map labels is highly computationally expensive, even for the simplest maps. Focus is given to the placement of labels describing point and line map features, including the initial phase of enumerating possible label positions, respecting the basic cartographic rules common for those labels. Afterwards, three different algorithm types are applied to the problem itself -- greedy algorithms (in combination with local search optimization), mathematical optimization (0-1 integer programming) and genetic algorithms. Ultimately, the described algorithms are implemented in the software part of the work and compared on various data sets, based on both real world geographical data and randomly generated maps. The final comparison focuses especially on the quality of the result (scored by the metrics defined in the thesis), time needed to find the solution and determinism of the given algorithms

Efficient optimization methods for regularized learning: support vector machines and total-variation regularization

Tesis doctoral inédita. Universidad Autónoma de Madrid, Escuela Politécnica Superior, mayo de 201

Silhouette Mapping

Recent image-based rendering techniques have shown success in approximating detailed models using sampled images over coarser meshes. One limitation of these techniques is that the coarseness of the geometric mesh is apparent in the rough polygonal silhouette of the rendering. In this paper, we present a scheme for accurately capturing the external silhouette of a model in order to clip the approximate geometry. Given a detailed model, silhouettes sampled from a discrete set of viewpoints about the object are collected into a silhouette map. The silhouette from an arbitrary viewpoint is then computed as the interpolation from three nearby viewpoints in the silhouette map. Pairwise silhouette interpolation is based on a visual hull approximation in the epipolar plane. The silhouette map itself is adaptively simplified by removing views whose silhouettes are accurately predicted by interpolation of their neighbors. The model geometry is approximated by a progressive hull construction, and is rendered using projected texture maps. The 3D rendering is clipped to the interpolated silhouette using stencil planes.Engineering and Applied Science

Efficient and High-Quality Rendering of Higher-Order Geometric Data Representations

Computer-Aided Design (CAD) bezeichnet den Entwurf industrieller Produkte mit Hilfe von virtuellen 3D Modellen. Ein CAD-Modell besteht aus parametrischen Kurven und Flächen, in den meisten Fällen non-uniform rational B-Splines (NURBS). Diese mathematische Beschreibung wird ebenfalls zur Analyse, Optimierung und Präsentation des Modells verwendet. In jeder dieser Entwicklungsphasen wird eine unterschiedliche visuelle Darstellung benötigt, um den entsprechenden Nutzern ein geeignetes Feedback zu geben. Designer bevorzugen beispielsweise illustrative oder realistische Darstellungen, Ingenieure benötigen eine verständliche Visualisierung der Simulationsergebnisse, während eine immersive 3D Darstellung bei einer Benutzbarkeitsanalyse oder der Designauswahl hilfreich sein kann. Die interaktive Darstellung von NURBS-Modellen und -Simulationsdaten ist jedoch aufgrund des hohen Rechenaufwandes und der eingeschränkten Hardwareunterstützung eine große Herausforderung. Diese Arbeit stellt vier neuartige Verfahren vor, welche sich mit der interaktiven Darstellung von NURBS-Modellen und Simulationensdaten befassen. Die vorgestellten Algorithmen nutzen neue Fähigkeiten aktueller Grafikkarten aus, um den Stand der Technik bezüglich Qualität, Effizienz und Darstellungsgeschwindigkeit zu verbessern. Zwei dieser Verfahren befassen sich mit der direkten Darstellung der parametrischen Beschreibung ohne Approximationen oder zeitaufwändige Vorberechnungen. Die dabei vorgestellten Datenstrukturen und Algorithmen ermöglichen die effiziente Unterteilung, Klassifizierung, Tessellierung und Darstellung getrimmter NURBS-Flächen und einen interaktiven Ray-Casting-Algorithmus für die Isoflächenvisualisierung von NURBSbasierten isogeometrischen Analysen. Die weiteren zwei Verfahren beschreiben zum einen das vielseitige Konzept der programmierbaren Transparenz für illustrative und verständliche Visualisierungen tiefenkomplexer CAD-Modelle und zum anderen eine neue hybride Methode zur Reprojektion halbtransparenter und undurchsichtiger Bildinformation für die Beschleunigung der Erzeugung von stereoskopischen Bildpaaren. Die beiden letztgenannten Ansätze basieren auf rasterisierter Geometrie und sind somit ebenfalls für normale Dreiecksmodelle anwendbar, wodurch die Arbeiten auch einen wichtigen Beitrag in den Bereichen der Computergrafik und der virtuellen Realität darstellen. Die Auswertung der Arbeit wurde mit großen, realen NURBS-Datensätzen durchgeführt. Die Resultate zeigen, dass die direkte Darstellung auf Grundlage der parametrischen Beschreibung mit interaktiven Bildwiederholraten und in subpixelgenauer Qualität möglich ist. Die Einführung programmierbarer Transparenz ermöglicht zudem die Umsetzung kollaborativer 3D Interaktionstechniken für die Exploration der Modelle in virtuellenUmgebungen sowie illustrative und verständliche Visualisierungen tiefenkomplexer CAD-Modelle. Die Erzeugung stereoskopischer Bildpaare für die interaktive Visualisierung auf 3D Displays konnte beschleunigt werden. Diese messbare Verbesserung wurde zudem im Rahmen einer Nutzerstudie als wahrnehmbar und vorteilhaft befunden.In computer-aided design (CAD), industrial products are designed using a virtual 3D model. A CAD model typically consists of curves and surfaces in a parametric representation, in most cases, non-uniform rational B-splines (NURBS). The same representation is also used for the analysis, optimization and presentation of the model. In each phase of this process, different visualizations are required to provide an appropriate user feedback. Designers work with illustrative and realistic renderings, engineers need a comprehensible visualization of the simulation results, and usability studies or product presentations benefit from using a 3D display. However, the interactive visualization of NURBS models and corresponding physical simulations is a challenging task because of the computational complexity and the limited graphics hardware support. This thesis proposes four novel rendering approaches that improve the interactive visualization of CAD models and their analysis. The presented algorithms exploit latest graphics hardware capabilities to advance the state-of-the-art in terms of quality, efficiency and performance. In particular, two approaches describe the direct rendering of the parametric representation without precomputed approximations and timeconsuming pre-processing steps. New data structures and algorithms are presented for the efficient partition, classification, tessellation, and rendering of trimmed NURBS surfaces as well as the first direct isosurface ray-casting approach for NURBS-based isogeometric analysis. The other two approaches introduce the versatile concept of programmable order-independent semi-transparency for the illustrative and comprehensible visualization of depth-complex CAD models, and a novel method for the hybrid reprojection of opaque and semi-transparent image information to accelerate stereoscopic rendering. Both approaches are also applicable to standard polygonal geometry which contributes to the computer graphics and virtual reality research communities. The evaluation is based on real-world NURBS-based models and simulation data. The results show that rendering can be performed directly on the underlying parametric representation with interactive frame rates and subpixel-precise image results. The computational costs of additional visualization effects, such as semi-transparency and stereoscopic rendering, are reduced to maintain interactive frame rates. The benefit of this performance gain was confirmed by quantitative measurements and a pilot user study

A Genetic Algorithm for Chromaticity Correction in Diffraction Limited Storage Rings

A multi-objective genetic algorithm is developed for optimizing nonlinearities in diffraction limited storage rings. This algorithm determines sextupole and octupole strengths for chromaticity correction that deliver optimized dynamic aperture and beam lifetime. The algorithm makes use of dominance constraints to breed desirable properties into the early generations. The momentum aperture is optimized indirectly by constraining the chromatic tune footprint and optimizing the off-energy dynamic aperture. The result is an effective and computationally efficient technique for correcting chromaticity in a storage ring while maintaining optimal dynamic aperture and beam lifetime. This framework was developed for the Swiss Light Source (SLS) upgrade project.Comment: 12 pages, 14 figure

Audio computing in the wild: frameworks for big data and small computers

This dissertation presents some machine learning algorithms that are designed to process as much data as needed while spending the least possible amount of resources, such as time, energy, and memory. Examples of those applications, but not limited to, can be a large-scale multimedia information retrieval system where both queries and the items in the database are noisy signals; collaborative audio enhancement from hundreds of user-created clips of a music concert; an event detection system running in a small device that has to process various sensor signals in real time; a lightweight custom chipset for speech enhancement on hand-held devices; instant music analysis engine running on smartphone apps. In all those applications, efficient machine learning algorithms are supposed to achieve not only a good performance, but also a great resource-efficiency. We start from some efficient dictionary-based single-channel source separation algorithms. We can train this kind of source-specific dictionaries by using some matrix factorization or topic modeling, whose elements form a representative set of spectra for the particular source. During the test time, the system estimates the contribution of the participating dictionary items for an unknown mixture spectrum. In this way we can estimate the activation of each source separately, and then recover the source of interest by using that particular source's reconstruction. There are some efficiency issues during this procedure. First off, searching for the optimal dictionary size is time consuming. Although for some very common types of sources, e.g. English speech, we know the optimal rank of the model by trial and error, it is hard to know in advance as to what is the optimal number of dictionary elements for the unknown sources, which are usually modeled during the test time in the semi-supervised separation scenarios. On top of that, when it comes to the non-stationary unknown sources, we had better maintain a dictionary that adapts its size and contents to the change of the source's nature. In this online semi-supervised separation scenario, a mechanism that can efficiently learn the optimal rank is helpful. To this end, a deflation method is proposed for modeling this unknown source with a nonnegative dictionary whose size is optimal. Since it has to be done during the test time, the deflation method that incrementally adds up new dictionary items shows better efficiency than a corresponding na\"ive approach where we simply try a bunch of different models. We have another efficiency issue when we are to use a large dictionary for better separation. It has been known that considering the manifold of the training data can help enhance the performance for the separation. This is because of the symptom that the usual manifold-ignorant convex combination models, such as from low-rank matrix decomposition or topic modeling, tend to result in ambiguous regions in the source-specific subspace defined by the dictionary items as the bases. For example, in those ambiguous regions, the original data samples cannot reside. Although some source separation techniques that respect data manifold could increase the performance, they call for more memory and computational resources due to the fact that the models call for larger dictionaries and involve sparse coding during the test time. This limitation led the development of hashing-based encoding of the audio spectra, so that some computationally heavy routines, such as nearest neighbor searches for sparse coding, can be performed in a cheaper bit-wise fashion. Matching audio signals can be challenging as well, especially if the signals are noisy and the matching task involves a big amount of signals. If it is an information retrieval application, for example, the bigger size of the data leads to a longer response time. On top of that, if the signals are defective, we have to perform the enhancement or separation job in the first place before matching, or we might need a matching mechanism that is robust to all those different kinds of artifacts. Likewise, the noisy nature of signals can add an additional complexity to the system. In this dissertation we will also see some compact integer (and eventually binary) representations for those matching systems. One of the possible compact representations would be a hashing-based matching method, where we can employ a particular kind of hash functions to preserve the similarity among original signals in the hash code domain. We will see that a variant of Winner Take All hashing can provide Hamming distance from noise-robust binary features, and that matching using the hash codes works well for some keyword spotting tasks. From the fact that some landmark hashes (e.g. local maxima from non-maximum suppression on the magnitudes of a mel-scaled spectrogram) can also robustly represent the time-frequency domain signal efficiently, a matrix decomposition algorithm is also proposed to take those irregular sparse matrices as input. Based on the assumption that the number of landmarks is a lot smaller than the number of all the time-frequency coefficients, we can think of this matching algorithm efficient if it operates entirely on the landmark representation. On the contrary to the usual landmark matching schemes, where matching is defined rigorously, we see the audio matching problem as soft matching where we find a similar constellation of landmarks to the query. In order to perform this soft matching job, the landmark positions are smoothed by a fixed-width Gaussian caps, with which the matching job is reduced down to calculating the amount of overlaps in-between those Gaussians. The Gaussian-based density approximation is also useful when we perform decomposition on this landmark representation, because otherwise the landmarks are usually too sparse to perform an ordinary matrix factorization algorithm, which are originally for a dense input matrix. We also expand this concept to the matrix deconvolution problem as well, where we see the input landmark representation of a source as a two-dimensional convolution between a source pattern and its corresponding sparse activations. If there are more than one source, as a noisy signal, we can think of this problem as factor deconvolution where the mixture is the combination of all the source-specific convolutions. The dissertation also covers Collaborative Audio Enhancement (CAE) algorithms that aim to recover the dominant source at a sound scene (e.g. music signals of a concert rather than the noise from the crowd) from multiple low-quality recordings (e.g. Youtube video clips uploaded by the audience). CAE can be seen as crowdsourcing a recording job, which needs a substantial amount of denoising effort afterward, because the user-created recordings might have been contaminated with various artifacts. In the sense that the recordings are from not-synchronized heterogenous sensors, we can also think of CAE as big ad-hoc sensor array processing. In CAE, each recording is assumed to be uniquely corrupted by a specific frequency response of the microphone, an aggressive audio coding algorithm, interference, band-pass filtering, clipping, etc. To consolidate all these recordings and come up with an enhanced audio, Probabilistic Latent Component Sharing (PLCS) has been proposed as a method of simultaneous probabilistic topic modeling on synchronized input signals. In PLCS, some of the parameters are fixed to be same during and after the learning process to capture common audio content, while the rest of the parameters are for the unwanted recording-specific interference and artifacts. We can speed up PLCS by incorporating a hashing-based nearest neighbor search so that at every EM iteration PLCS can be applied only to a small number of recordings that are closest to the current source estimation. Experiments on a small simulated CAE setup shows that the proposed PLCS can improve the sound quality from variously contaminated recordings. The nearest neighbor search technique during PLCS provides sensible speed-up at larger scaled experiments (up to 1000 recordings). Finally, to describe an extremely optimized deep learning deployment system, Bitwise Neural Networks (BNN) will be also discussed. In the proposed BNN, all the input, hidden, and output nodes are binaries (+1 and -1), and so are all the weights and bias. Consequently, the operations on them during the test time are defined with Boolean algebra, too. BNNs are spatially and computationally efficient in implementations, since (a) we represent a real-valued sample or parameter with a bit (b) the multiplication and addition correspond to bitwise XNOR and bit-counting, respectively. Therefore, BNNs can be used to implement a deep learning system in a resource-constrained environment, so that we can deploy a deep learning system on small devices without using up the power, memory, CPU clocks, etc. The training procedure for BNNs is based on a straightforward extension of backpropagation, which is characterized by the use of the quantization noise injection scheme, and the initialization strategy that learns a weight-compressed real-valued network only for the initialization purpose. Some preliminary results on the MNIST dataset and speech denoising demonstrate that a straightforward extension of backpropagation can successfully train BNNs whose performance is comparable while necessitating vastly fewer computational resources

Automated Digital Machining for Parallel Processors

When a process engineer creates a tool path a number of fixed decisions are made that inevitably produce sub-optimal results. This is because it is impossible to process all of the tradeoffs before generating the tool path. The research presents a methodology to support a process engineers attempt to generate optimal tool paths by performing automated digital machining and analysis. This methodology automatically generates and evaluates tool paths based on parallel processing of digital part models and generalized cutting geometry. Digital part models are created by voxelizing STL files and the resulting digital part surfaces are obtained based on casting rays into the part model. Tool paths are generated based on a general path template and updated based on generalized tool geometry and part surface information. The material removed by the generalized cutter as it follows the path is used to obtain path metrics. The paths are evaluated based on the path metrics of material removal rate, machining time, and amount of scallop. This methodology is a parallel processing accelerated framework suitable for generating tool paths in parallel enabling the process engineer to rank and select the best tool path for the job

Acceleration Methods for Classic Convex Optimization Algorithms

Tesis doctoral inédita leída en la Universidad Autónoma de Madrid, Escuela Politécnica Superior, Departamento de Ingeniería Informática. Fecha de lectura : 12-09-2017Most Machine Learning models are defined in terms of a convex optimization problem. Thus, developing algorithms to quickly solve such problems its of great interest to the field. We focus in this thesis on two of the most widely used models, the Lasso and Support Vector Machines. The former belongs to the family of regularization methods, and it was introduced in 1996 to perform both variable selection and regression at the same time. This is accomplished by adding a `1-regularization term to the least squares model, achieving interpretability and also a good generalization error. Support Vector Machines were originally formulated to solve a classification problem by finding the maximum-margin hyperplane, that is, the hyperplane which separates two sets of points and its at equal distance from both of them. SVMs were later extended to handle non-separable classes and non-linear classification problems, applying the kernel-trick. A first contribution of this work is to carefully analyze all the existing algorithms to solve both problems, describing not only the theory behind them but also pointing out possible advantages and disadvantages of each one. Although the Lasso and SVMs solve very different problems, we show in this thesis that they are both equivalent. Following a recent result by Jaggi, given an instance of one model we can construct an instance of the other having the same solution, and vice versa. This equivalence allows us to translate theoretical and practical results, such as algorithms, from one field to the other, that have been otherwise being developed independently. We will give in this thesis not only the theoretical result but also a practical application, that consists on solving the Lasso problem using the SMO algorithm, the state-of-the-art solver for non-linear SVMs. We also perform experiments comparing SMO to GLMNet, one of the most popular solvers for the Lasso. The results obtained show that SMO is competitive with GLMNet, and sometimes even faster. Furthermore, motivated by a recent trend where classical optimization methods are being re-discovered in improved forms and successfully applied to many problems, we have also analyzed two classical momentum-based methods: the Heavy Ball algorithm, introduced by Polyak in 1963 and Nesterov’s Accelerated Gradient, discovered by Nesterov in 1983. In this thesis we develop practical versions of Conjugate Gradient, which is essentially equivalent to the Heavy Ball method, and Nesterov’s Acceleration for the SMO algorithm. Experiments comparing the convergence of all the methods are also carried out. The results show that the proposed algorithms can achieve a faster convergence both in terms of iterations and execution time.La mayoría de modelos de Aprendizaje Automático se definen en términos de un problema de optimización convexo. Por tanto, desarrollar algoritmos para resolver rápidamente dichos problemas es de gran interés para este campo. En esta tesis nos centramos en dos de los modelos más usados, Lasso y Support Vector Machines. El primero pertenece a la familia de métodos de regularización, y fue introducido en 1996 para realizar selección de características y regresión al mismo tiempo. Esto se consigue añadiendo una penalización `1al modelo de mínimos cuadrados, obteniendo interpretabilidad y un buen error de generalización. Las Máquinas de Vectores de Soporte fueron formuladas originalmente para resolver un problema de clasificación buscando el hiper-plano de máximo margen, es decir, el hiper-plano que separa los dos conjuntos de puntos y está a la misma distancia de ambos. Las SVMs se han extendido posteriormente para manejar clases no separables y problemas de clasificación no lineales, mediante el uso de núcleos. Una primera contribución de este trabajo es analizar cuidadosamente los algoritmos existentes para resolver ambos problemas, describiendo no solo la teoría detrás de los mismos sino también mencionando las posibles ventajas y desventajas de cada uno. A pesar de que el Lasso y las SVMs resuelven problemas muy diferentes, en esta tesis demostramos que ambos son equivalentes. Continuando con un resultado reciente de Jaggi, dada una instancia de uno de los modelos podemos construir una instancia del otro que tiene la misma solución, y viceversa. Esta equivalencia nos permite trasladar resultados teóricos y prácticos, como por ejemplo algoritmos, de un campo al otro, que se han desarrollado de forma independiente. En esta tesis mostraremos no solo la equivalencia teórica sino también una aplicación práctica, que consiste en resolver el problema Lasso usando el algoritmo SMO, que es el estado del arte para la resolución de SVM no lineales. También realizamos experimentos comparando SMO a GLMNet, uno de los algoritmos más populares para resolver el Lasso. Los resultados obtenidos muestran que SMO es competitivo con GLMNet, y en ocasiones incluso más rápido. Además, motivado por una tendencia reciente donde métodos clásicos de optimización se están re- descubriendo y aplicando satisfactoriamente en muchos problemas, también hemos analizado dos métodos clásicos basados en “momento”: el algoritmo Heavy Ball, creado por Polyak en 1963 y el Gradiente Acelerado de Nesterov, descubierto por Nesterov en 1983. En esta tesis desarrollamos versiones prácticas de Gradiente Conjugado, que es equivalente a Heavy Ball, y Aceleración de Nesterov para el algortimo SMO. Además, también se realizan experimentos comparando todos los métodos. Los resultados muestran que los algoritmos propuestos a menudo convergen más rápido, tanto en términos de iteraciones como de tiempo de ejecución