Mining Heterogeneous Multivariate Time-Series for Learning Meaningful Patterns: Application to Home Health Telecare

For the last years, time-series mining has become a challenging issue for researchers. An important application lies in most monitoring purposes, which require analyzing large sets of time-series for learning usual patterns. Any deviation from this learned profile is then considered as an unexpected situation. Moreover, complex applications may involve the temporal study of several heterogeneous parameters. In that paper, we propose a method for mining heterogeneous multivariate time-series for learning meaningful patterns. The proposed approach allows for mixed time-series -- containing both pattern and non-pattern data -- such as for imprecise matches, outliers, stretching and global translating of patterns instances in time. We present the early results of our approach in the context of monitoring the health status of a person at home. The purpose is to build a behavioral profile of a person by analyzing the time variations of several quantitative or qualitative parameters recorded through a provision of sensors installed in the home

Subseries Join and Compression of Time Series Data Based on Non-uniform Segmentation

A time series is composed of a sequence of data items that are measured at uniform intervals. Many application areas generate or manipulate time series, including finance, medicine, digital audio, and motion capture. Efficiently searching a large time series database is still a challenging problem, especially when partial or subseries matches are needed. This thesis proposes a new denition of subseries join, a symmetric generalization of subseries matching, which finds similar subseries in two or more time series datasets. A solution is proposed to compute the subseries join based on a hierarchical feature representation. This hierarchical feature representation is generated by an anisotropic diffusion scale-space analysis and a non-uniform segmentation method. Each segment is represented by a minimal polynomial envelope in a reduced-dimensionality space. Based on the hierarchical feature representation, all features in a dataset are indexed in an R-tree, and candidate matching features of two datasets are found by an R-tree join operation. Given candidate matching features, a dynamic programming algorithm is developed to compute the final subseries join. To improve storage efficiency, a hierarchical compression scheme is proposed to compress features. The minimal polynomial envelope representation is transformed to a Bezier spline envelope representation. The control points of each Bezier spline are then hierarchically differenced and an arithmetic coding is used to compress these differences. To empirically evaluate their effectiveness, the proposed subseries join and compression techniques are tested on various publicly available datasets. A large motion capture database is also used to verify the techniques in a real-world application. The experiments show that the proposed subseries join technique can better tolerate noise and local scaling than previous work, and the proposed compression technique can also achieve about 85% higher compression rates than previous work with the same distortion error

Robust Temporally Coherent Laplacian Protrusion Segmentation of 3D Articulated Bodies

In motion analysis and understanding it is important to be able to fit a suitable model or structure to the temporal series of observed data, in order to describe motion patterns in a compact way, and to discriminate between them. In an unsupervised context, i.e., no prior model of the moving object(s) is available, such a structure has to be learned from the data in a bottom-up fashion. In recent times, volumetric approaches in which the motion is captured from a number of cameras and a voxel-set representation of the body is built from the camera views, have gained ground due to attractive features such as inherent view-invariance and robustness to occlusions. Automatic, unsupervised segmentation of moving bodies along entire sequences, in a temporally-coherent and robust way, has the potential to provide a means of constructing a bottom-up model of the moving body, and track motion cues that may be later exploited for motion classification. Spectral methods such as locally linear embedding (LLE) can be useful in this context, as they preserve "protrusions", i.e., high-curvature regions of the 3D volume, of articulated shapes, while improving their separation in a lower dimensional space, making them in this way easier to cluster. In this paper we therefore propose a spectral approach to unsupervised and temporally-coherent body-protrusion segmentation along time sequences. Volumetric shapes are clustered in an embedding space, clusters are propagated in time to ensure coherence, and merged or split to accommodate changes in the body's topology. Experiments on both synthetic and real sequences of dense voxel-set data are shown. This supports the ability of the proposed method to cluster body-parts consistently over time in a totally unsupervised fashion, its robustness to sampling density and shape quality, and its potential for bottom-up model constructionComment: 31 pages, 26 figure

Optimization with learning-informed differential equation constraints and its applications

Inspired by applications in optimal control of semilinear elliptic partial differential equations and physics-integrated imaging, differential equation constrained optimization problems with constituents that are only accessible through data-driven techniques are studied. A particular focus is on the analysis and on numerical methods for problems with machine-learned components. For a rather general context, an error analysis is provided, and particular properties resulting from artificial neural network based approximations are addressed. Moreover, for each of the two inspiring applications analytical details are presented and numerical results are provided

Optimization with learning-informed differential equation constraints and its applications

Inspired by applications in optimal control of semilinear elliptic partial differential equations and physics-integrated imaging, differential equation constrained optimization problems with constituents that are only accessible through data-driven techniques are studied. A particular focus is on the analysis and on numerical methods for problems with machine-learned components. For a rather general context, an error analysis is provided, and particular properties resulting from artificial neural network based approximations are addressed. Moreover, for each of the two inspiring applications analytical details are presented and numerical results are provided