Algorithms for feature selection and pattern recognition on Grassmann manifolds

Includes bibliographical references.2015 Summer.This dissertation presents three distinct application-driven research projects united by ideas and topics from geometric data analysis, optimization, computational topology, and machine learning. We first consider hyperspectral band selection problem solved by using sparse support vector machines (SSVMs). A supervised embedded approach is proposed using the property of SSVMs to exhibit a model structure that includes a clearly identifiable gap between zero and non-zero feature vector weights that permits important bands to be definitively selected in conjunction with the classification problem. An SSVM is trained using bootstrap aggregating to obtain a sample of SSVM models to reduce variability in the band selection process. This preliminary sample approach for band selection is followed by a secondary band selection which involves retraining the SSVM to further reduce the set of bands retained. We propose and compare three adaptations of the SSVM band selection algorithm for the multiclass problem. We illustrate the performance of these methods on two benchmark hyperspectral data sets. Second, we propose an approach for capturing the signal variability in data using the framework of the Grassmann manifold (Grassmannian). Labeled points from each class are sampled and used to form abstract points on the Grassmannian. The resulting points have representations as orthonormal matrices and as such do not reside in Euclidean space in the usual sense. There are a variety of metrics which allow us to determine distance matrices that can be used to realize the Grassmannian as an embedding in Euclidean space. Multidimensional scaling (MDS) determines a low dimensional Euclidean embedding of the manifold, preserving or approximating the Grassmannian geometry based on the distance measure. We illustrate that we can achieve an isometric embedding of the Grassmann manifold using the chordal metric while this is not the case with other distances. However, non-isometric embeddings generated by using the smallest principal angle pseudometric on the Grassmannian lead to the best classification results: we observe that as the dimension of the Grassmannian grows, the accuracy of the classification grows to 100% in binary classification experiments. To build a classification model, we use SSVMs to perform simultaneous dimension selection. The resulting classifier selects a subset of dimensions of the embedding without loss in classification performance. Lastly, we present an application of persistent homology to the detection of chemical plumes in hyperspectral movies. The pixels of the raw hyperspectral data cubes are mapped to the geometric framework of the Grassmann manifold where they are analyzed, contrasting our approach with the more standard framework in Euclidean space. An advantage of this approach is that it allows the time slices in a hyperspectral movie to be collapsed to a sequence of points in such a way that some of the key structure within and between the slices is encoded by the points on the Grassmannian. This motivates the search for topological structure, associated with the evolution of the frames of a hyperspectral movie, within the corresponding points on the manifold. The proposed framework affords the processing of large data sets, such as the hyperspectral movies explored in this investigation, while retaining valuable discriminative information. For a particular choice of a distance metric on the Grassmannian, it is possible to generate topological signals that capture changes in the scene after a chemical release

Modelos de aprendizaje automático en la detección e identificación de personas: una revisión de literatura

Introduction: This article is the result of research entitled "Development of a prototype to optimize access conditions to the SENA-Pescadero using artificial intelligence and open-source tools", developed at the Servicio Nacional de Aprendizaje in 2020.   Problem: How to identify Machine Learning Techniques applied to computer vision processes through a literature review? Objective: Determine the application, as well as advantages and disadvantages of machine learning techniques focused on the detection and identification of people. Methodology: Systematic literature review in 4 high-impact bibliographic and scientific databases, using search filters and information selection criteria. Results: Machine Learning techniques defined as Principal Component Analysis, Weak Label Regularized Local Coordinate Coding, Support Vector Machines, Haar Cascade Classifiers and EigenFaces and FisherFaces, as well as their applicability in detection and identification processes.   Conclusion: The research led to the identification of the main computational intelligence techniques based on machine learning, applied to the detection and identification of people. Their influence was shown in several application cases, but most of them were focused on the implementation and optimization of access control systems, or tasks in which the identification of people was required for the execution of processes. Originality: Through this research, we studied and defined the main machine learning techniques currently used for the detection and identification of people. Limitations: The systematic review is limited to information available in the 4 databases consulted, and the amount of information is variable as articles are deposited in the databases.Introducción: Este artículo es el resultado de la investigación titulada " Desarrollo de un prototipo para optimizar las condiciones de acceso al SENA-Pescadero utilizando inteligencia artificial y herramientas de código abierto", desarrollada en el Servicio Nacional de Aprendizaje en 2020. Problema: ¿Cómo identificar las técnicas de aprendizaje automático aplicadas a los procesos de visión por computador a través de una revisión bibliográfica? Objetivo: Determinar la aplicación, así como las ventajas y desventajas de las técnicas de aprendizaje automático enfocadas a la detección e identificación de personas. Metodología: Revisión sistemática de la literatura en 4 bases de datos bibliográficas y científicas de alto impacto, utilizando filtros de búsqueda y criterios de selección de información. Resultados: Técnicas de aprendizaje automático definidas como Análisis de Componentes Principales, Codificación Local de Coordenadas Regularizada de Etiquetas Débiles, Máquinas de Vectores de Soporte, Clasificadores en Cascada de Haar y EigenFaces y FisherFaces, así como su aplicabilidad en procesos de detección e identificación. Conclusiones: La investigación permitió identificar las principales técnicas de inteligencia computacional basadas en machine learning aplicadas a la detección e identificación de personas. Su influencia se mostró en varios casos de aplicación, pero la mayoría de ellos se centraron en la implementación y optimización de sistemas de control de acceso, o tareas en las que se requería la identificación de personas para la ejecución de procesos Originalidad: A través de esta investigación se estudiaron y definieron las principales técnicas de machine learning utilizadas actualmente para la detección e identificación de personas

Fast Numerical and Machine Learning Algorithms for Spatial Audio Reproduction

Audio reproduction technologies have underwent several revolutions from a purely mechanical, to electromagnetic, and into a digital process. These changes have resulted in steady improvements in the objective qualities of sound capture/playback on increasingly portable devices. However, most mobile playback devices remove important spatial-directional components of externalized sound which are natural to the subjective experience of human hearing. Fortunately, the missing spatial-directional parts can be integrated back into audio through a combination of computational methods and physical knowledge of how sound scatters off of the listener's anthropometry in the sound-field. The former employs signal processing techniques for rendering the sound-field. The latter employs approximations of the sound-field through the measurement of so-called Head-Related Impulse Responses/Transfer Functions (HRIRs/HRTFs). This dissertation develops several numerical and machine learning algorithms for accelerating and personalizing spatial audio reproduction in light of available mobile computing power. First, spatial audio synthesis between a sound-source and sound-field requires fast convolution algorithms between the audio-stream and the HRIRs. We introduce a novel sparse decomposition algorithm for HRIRs based on non-negative matrix factorization that allows for faster time-domain convolution than frequency-domain fast-Fourier-transform variants. Second, the full sound-field over the spherical coordinate domain must be efficiently approximated from a finite collection of HRTFs. We develop a joint spatial-frequency covariance model for Gaussian process regression (GPR) and sparse-GPR methods that supports the fast interpolation and data fusion of HRTFs across multiple data-sets. Third, the direct measurement of HRTFs requires specialized equipment that is unsuited for widespread acquisition. We ``bootstrap'' the human ability to localize sound in listening tests with Gaussian process active-learning techniques over graphical user interfaces that allows the listener to infer his/her own HRTFs. Experiments are conducted on publicly available HRTF datasets and human listeners