Joint segmentation of multivariate time series with hidden process regression for human activity recognition

The problem of human activity recognition is central for understanding and predicting the human behavior, in particular in a prospective of assistive services to humans, such as health monitoring, well being, security, etc. There is therefore a growing need to build accurate models which can take into account the variability of the human activities over time (dynamic models) rather than static ones which can have some limitations in such a dynamic context. In this paper, the problem of activity recognition is analyzed through the segmentation of the multidimensional time series of the acceleration data measured in the 3-d space using body-worn accelerometers. The proposed model for automatic temporal segmentation is a specific statistical latent process model which assumes that the observed acceleration sequence is governed by sequence of hidden (unobserved) activities. More specifically, the proposed approach is based on a specific multiple regression model incorporating a hidden discrete logistic process which governs the switching from one activity to another over time. The model is learned in an unsupervised context by maximizing the observed-data log-likelihood via a dedicated expectation-maximization (EM) algorithm. We applied it on a real-world automatic human activity recognition problem and its performance was assessed by performing comparisons with alternative approaches, including well-known supervised static classifiers and the standard hidden Markov model (HMM). The obtained results are very encouraging and show that the proposed approach is quite competitive even it works in an entirely unsupervised way and does not requires a feature extraction preprocessing step

An Unsupervised Approach for Automatic Activity Recognition based on Hidden Markov Model Regression

Using supervised machine learning approaches to recognize human activities from on-body wearable accelerometers generally requires a large amount of labelled data. When ground truth information is not available, too expensive, time consuming or difficult to collect, one has to rely on unsupervised approaches. This paper presents a new unsupervised approach for human activity recognition from raw acceleration data measured using inertial wearable sensors. The proposed method is based upon joint segmentation of multidimensional time series using a Hidden Markov Model (HMM) in a multiple regression context. The model is learned in an unsupervised framework using the Expectation-Maximization (EM) algorithm where no activity labels are needed. The proposed method takes into account the sequential appearance of the data. It is therefore adapted for the temporal acceleration data to accurately detect the activities. It allows both segmentation and classification of the human activities. Experimental results are provided to demonstrate the efficiency of the proposed approach with respect to standard supervised and unsupervised classification approache

Bandwidth selection for kernel estimation in mixed multi-dimensional spaces

Kernel estimation techniques, such as mean shift, suffer from one major drawback: the kernel bandwidth selection. The bandwidth can be fixed for all the data set or can vary at each points. Automatic bandwidth selection becomes a real challenge in case of multidimensional heterogeneous features. This paper presents a solution to this problem. It is an extension of \cite{Comaniciu03a} which was based on the fundamental property of normal distributions regarding the bias of the normalized density gradient. The selection is done iteratively for each type of features, by looking for the stability of local bandwidth estimates across a predefined range of bandwidths. A pseudo balloon mean shift filtering and partitioning are introduced. The validity of the method is demonstrated in the context of color image segmentation based on a 5-dimensional space

The group fused Lasso for multiple change-point detection

We present the group fused Lasso for detection of multiple change-points shared by a set of co-occurring one-dimensional signals. Change-points are detected by approximating the original signals with a constraint on the multidimensional total variation, leading to piecewise-constant approximations. Fast algorithms are proposed to solve the resulting optimization problems, either exactly or approximately. Conditions are given for consistency of both algorithms as the number of signals increases, and empirical evidence is provided to support the results on simulated and array comparative genomic hybridization data

Automation Process for Morphometric Analysis of Volumetric CT Data from Pulmonary Vasculature in Rats

With advances in medical imaging scanners, it has become commonplace to generate large multidimensional datasets. These datasets require tools for a rapid, thorough analysis. To address this need, we have developed an automated algorithm for morphometric analysis incorporating A Visualization Workshop computational and image processing libraries for three-dimensional segmentation, vascular tree generation and structural hierarchical ordering with a two-stage numeric optimization procedure for estimating vessel diameters. We combine this new technique with our mathematical models of pulmonary vascular morphology to quantify structural and functional attributes of lung arterial trees. Our physiological studies require repeated measurements of vascular structure to determine differences in vessel biomechanical properties between animal models of pulmonary disease. Automation provides many advantages including significantly improved speed and minimized operator interaction and biasing. The results are validated by comparison with previously published rat pulmonary arterial micro-CT data analysis techniques, in which vessels were manually mapped and measured using intense operator intervention

Multiple multidimensional morse wavelets

This paper defines a set of operators that localize a radial image in space and radial frequency simultaneously. The eigenfunctions of the operator are determined and a nonseparable orthogonal set of radial wavelet functions are found. The eigenfunctions are optimally concentrated over a given region of radial space and scale space, defined via a triplet of parameters. Analytic forms for the energy concentration of the functions over the region are given. The radial function localization operator can be generalised to an operator localizing any L-2(R-2) function. It is demonstrated that the latter operator, given an appropriate choice of localization region, approximately has the same radial eigenfunctions as the radial operator. Based on a given radial wavelet function a quaternionic wavelet is defined that can extract the local orientation of discontinuous signals as well as amplitude, orientation and phase structure of locally oscillatory signals. The full set of quaternionic wavelet functions are component by component orthogonal; their statistical properties are tractable, and forms for the variability of the estimators of the local phase and orientation are given, as well as the local energy of the image. By averaging estimators across wavelets, a substantial reduction in the variance is achieved

Joint segmentation of multivariate astronomical time series : bayesian sampling with a hierarchical model

Astronomy and other sciences often face the problem of detecting and characterizing structure in two or more related time series. This paper approaches such problems using Bayesian priors to represent relationships between signals with various degrees of certainty, and not just rigid constraints. The segmentation is conducted by using a hierarchical Bayesian approach to a piecewise constant Poisson rate model. A Gibbs sampling strategy allows joint estimation of the unknown parameters and hyperparameters. Results obtained with synthetic and real photon counting data illustrate the performance of the proposed algorithm

The Data Big Bang and the Expanding Digital Universe: High-Dimensional, Complex and Massive Data Sets in an Inflationary Epoch

Recent and forthcoming advances in instrumentation, and giant new surveys, are creating astronomical data sets that are not amenable to the methods of analysis familiar to astronomers. Traditional methods are often inadequate not merely because of the size in bytes of the data sets, but also because of the complexity of modern data sets. Mathematical limitations of familiar algorithms and techniques in dealing with such data sets create a critical need for new paradigms for the representation, analysis and scientific visualization (as opposed to illustrative visualization) of heterogeneous, multiresolution data across application domains. Some of the problems presented by the new data sets have been addressed by other disciplines such as applied mathematics, statistics and machine learning and have been utilized by other sciences such as space-based geosciences. Unfortunately, valuable results pertaining to these problems are mostly to be found only in publications outside of astronomy. Here we offer brief overviews of a number of concepts, techniques and developments, some "old" and some new. These are generally unknown to most of the astronomical community, but are vital to the analysis and visualization of complex datasets and images. In order for astronomers to take advantage of the richness and complexity of the new era of data, and to be able to identify, adopt, and apply new solutions, the astronomical community needs a certain degree of awareness and understanding of the new concepts. One of the goals of this paper is to help bridge the gap between applied mathematics, artificial intelligence and computer science on the one side and astronomy on the other.Comment: 24 pages, 8 Figures, 1 Table. Accepted for publication: "Advances in Astronomy, special issue "Robotic Astronomy