On landmark selection and sampling in high-dimensional data analysis

In recent years, the spectral analysis of appropriately defined kernel matrices has emerged as a principled way to extract the low-dimensional structure often prevalent in high-dimensional data. Here we provide an introduction to spectral methods for linear and nonlinear dimension reduction, emphasizing ways to overcome the computational limitations currently faced by practitioners with massive datasets. In particular, a data subsampling or landmark selection process is often employed to construct a kernel based on partial information, followed by an approximate spectral analysis termed the Nystrom extension. We provide a quantitative framework to analyse this procedure, and use it to demonstrate algorithmic performance bounds on a range of practical approaches designed to optimize the landmark selection process. We compare the practical implications of these bounds by way of real-world examples drawn from the field of computer vision, whereby low-dimensional manifold structure is shown to emerge from high-dimensional video data streams.Comment: 18 pages, 6 figures, submitted for publicatio

Semi-Supervised First-Person Activity Recognition in Body-Worn Video

Body-worn cameras are now commonly used for logging daily life, sports, and law enforcement activities, creating a large volume of archived footage. This paper studies the problem of classifying frames of footage according to the activity of the camera-wearer with an emphasis on application to real-world police body-worn video. Real-world datasets pose a different set of challenges from existing egocentric vision datasets: the amount of footage of different activities is unbalanced, the data contains personally identifiable information, and in practice it is difficult to provide substantial training footage for a supervised approach. We address these challenges by extracting features based exclusively on motion information then segmenting the video footage using a semi-supervised classification algorithm. On publicly available datasets, our method achieves results comparable to, if not better than, supervised and/or deep learning methods using a fraction of the training data. It also shows promising results on real-world police body-worn video

Multiclass Data Segmentation using Diffuse Interface Methods on Graphs

We present two graph-based algorithms for multiclass segmentation of high-dimensional data. The algorithms use a diffuse interface model based on the Ginzburg-Landau functional, related to total variation compressed sensing and image processing. A multiclass extension is introduced using the Gibbs simplex, with the functional's double-well potential modified to handle the multiclass case. The first algorithm minimizes the functional using a convex splitting numerical scheme. The second algorithm is a uses a graph adaptation of the classical numerical Merriman-Bence-Osher (MBO) scheme, which alternates between diffusion and thresholding. We demonstrate the performance of both algorithms experimentally on synthetic data, grayscale and color images, and several benchmark data sets such as MNIST, COIL and WebKB. We also make use of fast numerical solvers for finding the eigenvectors and eigenvalues of the graph Laplacian, and take advantage of the sparsity of the matrix. Experiments indicate that the results are competitive with or better than the current state-of-the-art multiclass segmentation algorithms.Comment: 14 page

Scale-Adaptive Video Understanding.

The recent rise of large-scale, diverse video data has urged a new era of high-level video understanding. It is increasingly critical for intelligent systems to extract semantics from videos. In this dissertation, we explore the use of supervoxel hierarchies as a type of video representation for high-level video understanding. The supervoxel hierarchies contain rich multiscale decompositions of video content, where various structures can be found at various levels. However, no single level of scale contains all the desired structures we need. It is essential to adaptively choose the scales for subsequent video analysis. Thus, we present a set of tools to manipulate scales in supervoxel hierarchies including both scale generation and scale selection methods. In our scale generation work, we evaluate a set of seven supervoxel methods in the context of what we consider to be a good supervoxel for video representation. We address a key limitation that has traditionally prevented supervoxel scale generation on long videos. We do so by proposing an approximation framework for streaming hierarchical scale generation that is able to generate multiscale decompositions for arbitrarily-long videos using constant memory. Subsequently, we present two scale selection methods that are able to adaptively choose the scales according to application needs. The first method flattens the entire supervoxel hierarchy into a single segmentation that overcomes the limitation induced by trivial selection of a single scale. We show that the selection can be driven by various post hoc feature criteria. The second scale selection method combines the supervoxel hierarchy with a conditional random field for the task of labeling actors and actions in videos. We formulate the scale selection problem and the video labeling problem in a joint framework. Experiments on a novel large-scale video dataset demonstrate the effectiveness of the explicit consideration of scale selection in video understanding. Aside from the computational methods, we present a visual psychophysical study to quantify how well the actor and action semantics in high-level video understanding are retained in supervoxel hierarchies. The ultimate findings suggest that some semantics are well-retained in the supervoxel hierarchies and can be used for further video analysis.PhDComputer Science and EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/133202/1/cliangxu_1.pd

Quadratic Programming Feature Selection

Identifying a subset of features that preserves classification accuracy is a problem of growing importance, because of the increasing size and dimensionality of real-world data sets. We propose a new feature selection method, named Quadratic Programming Feature Selection (QPFS), that reduces the task to a quadratic optimization problem. In order to limit the computational complexity of solving the optimization problem, QPFS uses the Nystr¨om method for approximate matrix diagonalization. QPFS is thus capable of dealing with very large data sets, for which the use of other methods is computationally expensive. In experiments with small and medium data sets, the QPFS method leads to classification accuracy similar to that of other successful techniques. For large data sets, QPFS is superior in terms of computational efficiency.I.R.-L. is supported by an FPU grant from Universidad Autónoma de Madrid, and partially supported by the Universidad Autónoma de Madrid-IIC Chair. R.H. acknowledges partial support by ONR N00014-07-1-074

Feature-aware uniform tessellations on video manifold for content-sensitive supervoxels

Over-segmenting a video into supervoxels has strong potential to reduce the complexity of computer vision applications. Content-sensitive supervoxels (CSS) are typically smaller in content-dense regionsand larger in content-sparse regions. In this paper, we propose to compute feature-aware CSS (FCSS) that are regularly shaped 3D primitive volumes well aligned with local object/region/motion boundaries in video.To compute FCSS, we map a video to a 3-dimensional manifold, in which the volume elements of video manifold give a good measure of the video content density. Then any uniform tessellation on manifold can induce CSS. Our idea is that among all possible uniform tessellations, FCSS find one whose cell boundaries well align with local video boundaries. To achieve this goal, we propose a novel tessellation method that simultaneously minimizes the tessellation energy and maximizes the average boundary distance.Theoretically our method has an optimal competitive ratio O(1). We also present a simple extension of FCSS to streaming FCSS for processing long videos that cannot be loaded into main memory at once. We evaluate FCSS, streaming FCSS and ten representative supervoxel methods on four video datasets and two novel video applications. The results show that our method simultaneously achieves state-of-the-art performance with respect to various evaluation criteria

Activity representation with motion hierarchies

International audienceComplex activities, e.g., pole vaulting, are composed of a variable number of sub-events connected by complex spatio-temporal relations, whereas simple actions can be represented as sequences of short temporal parts. In this paper, we learn hierarchical representations of activity videos in an unsupervised manner. These hierarchies of mid-level motion components are data-driven decompositions specific to each video. We introduce a spectral divisive clustering algorithm to efficiently extract a hierarchy over a large number of tracklets (i.e., local trajectories). We use this structure to represent a video as an unordered binary tree. We model this tree using nested histograms of local motion features. We provide an efficient positive definite kernel that computes the structural and visual similarity of two hierarchical decompositions by relying on models of their parent-child relations. We present experimental results on four recent challenging benchmarks: the High Five dataset [Patron-Perez et al, 2010], the Olympics Sports dataset [Niebles et al, 2010], the Hollywood 2 dataset [Marszalek et al, 2009], and the HMDB dataset [Kuehne et al, 2011]. We show that pervideo hierarchies provide additional information for activity recognition. Our approach improves over unstructured activity models, baselines using other motion decomposition algorithms, and the state of the art