Grassmann Learning for Recognition and Classification

Computational performance associated with high-dimensional data is a common challenge for real-world classification and recognition systems. Subspace learning has received considerable attention as a means of finding an efficient low-dimensional representation that leads to better classification and efficient processing. A Grassmann manifold is a space that promotes smooth surfaces, where points represent subspaces and the relationship between points is defined by a mapping of an orthogonal matrix. Grassmann learning involves embedding high dimensional subspaces and kernelizing the embedding onto a projection space where distance computations can be effectively performed. In this dissertation, Grassmann learning and its benefits towards action classification and face recognition in terms of accuracy and performance are investigated and evaluated. Grassmannian Sparse Representation (GSR) and Grassmannian Spectral Regression (GRASP) are proposed as Grassmann inspired subspace learning algorithms. GSR is a novel subspace learning algorithm that combines the benefits of Grassmann manifolds with sparse representations using least squares loss §¤1-norm minimization for improved classification. GRASP is a novel subspace learning algorithm that leverages the benefits of Grassmann manifolds and Spectral Regression in a framework that supports high discrimination between classes and achieves computational benefits by using manifold modeling and avoiding eigen-decomposition. The effectiveness of GSR and GRASP is demonstrated for computationally intensive classification problems: (a) multi-view action classification using the IXMAS Multi-View dataset, the i3DPost Multi-View dataset, and the WVU Multi-View dataset, (b) 3D action classification using the MSRAction3D dataset and MSRGesture3D dataset, and (c) face recognition using the ATT Face Database, Labeled Faces in the Wild (LFW), and the Extended Yale Face Database B (YALE). Additional contributions include the definition of Motion History Surfaces (MHS) and Motion Depth Surfaces (MDS) as descriptors suitable for activity representations in video sequences and 3D depth sequences. An in-depth analysis of Grassmann metrics is applied on high dimensional data with different levels of noise and data distributions which reveals that standardized Grassmann kernels are favorable over geodesic metrics on a Grassmann manifold. Finally, an extensive performance analysis is made that supports Grassmann subspace learning as an effective approach for classification and recognition

Statistical and Dynamical Modeling of Riemannian Trajectories with Application to Human Movement Analysis

abstract: The data explosion in the past decade is in part due to the widespread use of rich sensors that measure various physical phenomenon -- gyroscopes that measure orientation in phones and fitness devices, the Microsoft Kinect which measures depth information, etc. A typical application requires inferring the underlying physical phenomenon from data, which is done using machine learning. A fundamental assumption in training models is that the data is Euclidean, i.e. the metric is the standard Euclidean distance governed by the L-2 norm. However in many cases this assumption is violated, when the data lies on non Euclidean spaces such as Riemannian manifolds. While the underlying geometry accounts for the non-linearity, accurate analysis of human activity also requires temporal information to be taken into account. Human movement has a natural interpretation as a trajectory on the underlying feature manifold, as it evolves smoothly in time. A commonly occurring theme in many emerging problems is the need to \emph{represent, compare, and manipulate} such trajectories in a manner that respects the geometric constraints. This dissertation is a comprehensive treatise on modeling Riemannian trajectories to understand and exploit their statistical and dynamical properties. Such properties allow us to formulate novel representations for Riemannian trajectories. For example, the physical constraints on human movement are rarely considered, which results in an unnecessarily large space of features, making search, classification and other applications more complicated. Exploiting statistical properties can help us understand the \emph{true} space of such trajectories. In applications such as stroke rehabilitation where there is a need to differentiate between very similar kinds of movement, dynamical properties can be much more effective. In this regard, we propose a generalization to the Lyapunov exponent to Riemannian manifolds and show its effectiveness for human activity analysis. The theory developed in this thesis naturally leads to several benefits in areas such as data mining, compression, dimensionality reduction, classification, and regression.Dissertation/ThesisDoctoral Dissertation Electrical Engineering 201

Nonparametric Estimation of Distributional Functionals and Applications.

Distributional functionals are integrals of functionals of probability densities and include functionals such as information divergence, mutual information, and entropy. Distributional functionals have many applications in the fields of information theory, statistics, signal processing, and machine learning. Many existing nonparametric distributional functional estimators have either unknown convergence rates or are difficult to implement. In this thesis, we consider the problem of nonparametrically estimating functionals of distributions when only a finite population of independent and identically distributed samples are available from each of the unknown, smooth, d-dimensional distributions. We derive mean squared error (MSE) convergence rates for leave-one-out kernel density plug-in estimators and k-nearest neighbor estimators of these functionals. We then extend the theory of optimally weighted ensemble estimation to obtain estimators that achieve the parametric MSE convergence rate when the densities are sufficiently smooth. These estimators are simple to implement and do not require knowledge of the densities’ support set, in contrast with many competing estimators. The asymptotic distribution of these estimators is also derived. The utility of these estimators is demonstrated through their application to sunspot image data and neural data measured from epilepsy patients. Sunspot images are clustered by estimating the divergence between the underlying probability distributions of image pixel patches. The problem of overfitting is also addressed in both applications by performing dimensionality reduction via intrinsic dimension estimation and by benchmarking classification via Bayes error estimationPhDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/133394/1/krmoon_1.pd

Human-Centric Machine Vision

Recently, the algorithms for the processing of the visual information have greatly evolved, providing efficient and effective solutions to cope with the variability and the complexity of real-world environments. These achievements yield to the development of Machine Vision systems that overcome the typical industrial applications, where the environments are controlled and the tasks are very specific, towards the use of innovative solutions to face with everyday needs of people. The Human-Centric Machine Vision can help to solve the problems raised by the needs of our society, e.g. security and safety, health care, medical imaging, and human machine interface. In such applications it is necessary to handle changing, unpredictable and complex situations, and to take care of the presence of humans

Dynamic Machine Learning with Least Square Objectives

As of the writing of this thesis, machine learning has become one of the most active research fields. The interest comes from a variety of disciplines which include computer science, statistics, engineering, and medicine. The main idea behind learning from data is that, when an analytical model explaining the observations is hard to find ---often in contrast to the models in physics such as Newton's laws--- a statistical approach can be taken where one or more candidate models are tuned using data. Since the early 2000's this challenge has grown in two ways: (i) The amount of collected data has seen a massive growth due to the proliferation of digital media, and (ii) the data has become more complex. One example for the latter is the high dimensional datasets, which can for example correspond to dyadic interactions between two large groups (such as customer and product information a retailer collects), or to high resolution image/video recordings. Another important issue is the study of dynamic data, which exhibits dependence on time. Virtually all datasets fall into this category as all data collection is performed over time, however I use the term dynamic to hint at a system with an explicit temporal dependence. A traditional example is target tracking from signal processing literature. Here the position of a target is modeled using Newton's laws of motion, which relates it to time via the target's velocity and acceleration. Dynamic data, as I defined above, poses two important challenges. Firstly, the learning setup is different from the standard theoretical learning setup, also known as Probably Approximately Correct (PAC) learning. To derive PAC learning bounds one assumes a collection of data points sampled independently and identically from a distribution which generates the data. On the other hand, dynamic systems produce correlated outputs. The learning systems we use should accordingly take this difference into consideration. Secondly, as the system is dynamic, it might be necessary to perform the learning online. In this case the learning has to be done in a single pass. Typical applications include target tracking and electricity usage forecasting. In this thesis I investigate several important dynamic and online learning problems, where I develop novel tools to address the shortcomings of the previous solutions in the literature. The work is divided into three parts for convenience. The first part is about matrix factorization for time series analysis which is further divided into two chapters. In the first chapter, matrix factorization is used within a Bayesian framework to model time-varying dyadic interactions, with examples in predicting user-movie ratings and stock prices. In the next chapter, a matrix factorization which uses autoregressive models to forecast future values of multivariate time series is proposed, with applications in predicting electricity usage and traffic conditions. Inspired by the machinery we use in the first part, the second part is about nonlinear Kalman filtering, where a hidden state is estimated over time given observations. The nonlinearity of the system generating the observations is the main challenge here, where a divergence minimization approach is used to unify the seemingly unrelated methods in the literature, and propose new ones. This has applications in target tracking and options pricing. The third and last part is about cost sensitive learning, where a novel method for maximizing area under receiver operating characteristics curve is proposed. Our method has theoretical guarantees and favorable sample complexity. The method is tested on a variety of benchmark datasets, and also has applications in online advertising

Image-set, Temporal and Spatiotemporal Representations of Videos for Recognizing, Localizing and Quantifying Actions

This dissertation addresses the problem of learning video representations, which is defined here as transforming the video so that its essential structure is made more visible or accessible for action recognition and quantification. In the literature, a video can be represented by a set of images, by modeling motion or temporal dynamics, and by a 3D graph with pixels as nodes. This dissertation contributes in proposing a set of models to localize, track, segment, recognize and assess actions such as (1) image-set models via aggregating subset features given by regularizing normalized CNNs, (2) image-set models via inter-frame principal recovery and sparsely coding residual actions, (3) temporally local models with spatially global motion estimated by robust feature matching and local motion estimated by action detection with motion model added, (4) spatiotemporal models 3D graph and 3D CNN to model time as a space dimension, (5) supervised hashing by jointly learning embedding and quantization, respectively. State-of-the-art performances are achieved for tasks such as quantifying facial pain and human diving. Primary conclusions of this dissertation are categorized as follows: (i) Image set can capture facial actions that are about collective representation; (ii) Sparse and low-rank representations can have the expression, identity and pose cues untangled and can be learned via an image-set model and also a linear model; (iii) Norm is related with recognizability; similarity metrics and loss functions matter; (v) Combining the MIL based boosting tracker with the Particle Filter motion model induces a good trade-off between the appearance similarity and motion consistence; (iv) Segmenting object locally makes it amenable to assign shape priors; it is feasible to learn knowledge such as shape priors online from Web data with weak supervision; (v) It works locally in both space and time to represent videos as 3D graphs; 3D CNNs work effectively when inputted with temporally meaningful clips; (vi) the rich labeled images or videos help to learn better hash functions after learning binary embedded codes than the random projections. In addition, models proposed for videos can be adapted to other sequential images such as volumetric medical images which are not included in this dissertation

Text Similarity Between Concepts Extracted from Source Code and Documentation

Context: Constant evolution in software systems often results in its documentation losing sync with the content of the source code. The traceability research field has often helped in the past with the aim to recover links between code and documentation, when the two fell out of sync. Objective: The aim of this paper is to compare the concepts contained within the source code of a system with those extracted from its documentation, in order to detect how similar these two sets are. If vastly different, the difference between the two sets might indicate a considerable ageing of the documentation, and a need to update it. Methods: In this paper we reduce the source code of 50 software systems to a set of key terms, each containing the concepts of one of the systems sampled. At the same time, we reduce the documentation of each system to another set of key terms. We then use four different approaches for set comparison to detect how the sets are similar. Results: Using the well known Jaccard index as the benchmark for the comparisons, we have discovered that the cosine distance has excellent comparative powers, and depending on the pre-training of the machine learning model. In particular, the SpaCy and the FastText embeddings offer up to 80% and 90% similarity scores. Conclusion: For most of the sampled systems, the source code and the documentation tend to contain very similar concepts. Given the accuracy for one pre-trained model (e.g., FastText), it becomes also evident that a few systems show a measurable drift between the concepts contained in the documentation and in the source code.</p