A time series distance measure for efficient clustering of input output signals by their underlying dynamics

Starting from a dataset with input/output time series generated by multiple deterministic linear dynamical systems, this paper tackles the problem of automatically clustering these time series. We propose an extension to the so-called Martin cepstral distance, that allows to efficiently cluster these time series, and apply it to simulated electrical circuits data. Traditionally, two ways of handling the problem are used. The first class of methods employs a distance measure on time series (e.g. Euclidean, Dynamic Time Warping) and a clustering technique (e.g. k-means, k-medoids, hierarchical clustering) to find natural groups in the dataset. It is, however, often not clear whether these distance measures effectively take into account the specific temporal correlations in these time series. The second class of methods uses the input/output data to identify a dynamic system using an identification scheme, and then applies a model norm-based distance (e.g. H2, H-infinity) to find out which systems are similar. This, however, can be very time consuming for large amounts of long time series data. We show that the new distance measure presented in this paper performs as good as when every input/output pair is modelled explicitly, but remains computationally much less complex. The complexity of calculating this distance between two time series of length N is O(N logN).Comment: 6 pages, 4 figures, sent in for review to IEEE L-CSS (CDC 2017 option

Nilpotent Approximations of Sub-Riemannian Distances for Fast Perceptual Grouping of Blood Vessels in 2D and 3D

We propose an efficient approach for the grouping of local orientations (points on vessels) via nilpotent approximations of sub-Riemannian distances in the 2D and 3D roto-translation groups $SE(2)$ and $SE(3)$. In our distance approximations we consider homogeneous norms on nilpotent groups that locally approximate $SE(n)$, and which are obtained via the exponential and logarithmic map on $SE(n)$. In a qualitative validation we show that the norms provide accurate approximations of the true sub-Riemannian distances, and we discuss their relations to the fundamental solution of the sub-Laplacian on $SE(n)$. The quantitative experiments further confirm the accuracy of the approximations. Quantitative results are obtained by evaluating perceptual grouping performance of retinal blood vessels in 2D images and curves in challenging 3D synthetic volumes. The results show that 1) sub-Riemannian geometry is essential in achieving top performance and 2) that grouping via the fast analytic approximations performs almost equally, or better, than data-adaptive fast marching approaches on $\mathbb{R}^n$ and $SE(n)$.Comment: 18 pages, 9 figures, 3 tables, in review at JMI

Generic Subsequence Matching Framework: Modularity, Flexibility, Efficiency

Subsequence matching has appeared to be an ideal approach for solving many problems related to the fields of data mining and similarity retrieval. It has been shown that almost any data class (audio, image, biometrics, signals) is or can be represented by some kind of time series or string of symbols, which can be seen as an input for various subsequence matching approaches. The variety of data types, specific tasks and their partial or full solutions is so wide that the choice, implementation and parametrization of a suitable solution for a given task might be complicated and time-consuming; a possibly fruitful combination of fragments from different research areas may not be obvious nor easy to realize. The leading authors of this field also mention the implementation bias that makes difficult a proper comparison of competing approaches. Therefore we present a new generic Subsequence Matching Framework (SMF) that tries to overcome the aforementioned problems by a uniform frame that simplifies and speeds up the design, development and evaluation of subsequence matching related systems. We identify several relatively separate subtasks solved differently over the literature and SMF enables to combine them in straightforward manner achieving new quality and efficiency. This framework can be used in many application domains and its components can be reused effectively. Its strictly modular architecture and openness enables also involvement of efficient solutions from different fields, for instance efficient metric-based indexes. This is an extended version of a paper published on DEXA 2012.Comment: This is an extended version of a paper published on DEXA 201

LocNet: Global localization in 3D point clouds for mobile vehicles

Global localization in 3D point clouds is a challenging problem of estimating the pose of vehicles without any prior knowledge. In this paper, a solution to this problem is presented by achieving place recognition and metric pose estimation in the global prior map. Specifically, we present a semi-handcrafted representation learning method for LiDAR point clouds using siamese LocNets, which states the place recognition problem to a similarity modeling problem. With the final learned representations by LocNet, a global localization framework with range-only observations is proposed. To demonstrate the performance and effectiveness of our global localization system, KITTI dataset is employed for comparison with other algorithms, and also on our long-time multi-session datasets for evaluation. The result shows that our system can achieve high accuracy.Comment: 6 pages, IV 2018 accepte

The Bregman Variational Dual-Tree Framework

Graph-based methods provide a powerful tool set for many non-parametric frameworks in Machine Learning. In general, the memory and computational complexity of these methods is quadratic in the number of examples in the data which makes them quickly infeasible for moderate to large scale datasets. A significant effort to find more efficient solutions to the problem has been made in the literature. One of the state-of-the-art methods that has been recently introduced is the Variational Dual-Tree (VDT) framework. Despite some of its unique features, VDT is currently restricted only to Euclidean spaces where the Euclidean distance quantifies the similarity. In this paper, we extend the VDT framework beyond the Euclidean distance to more general Bregman divergences that include the Euclidean distance as a special case. By exploiting the properties of the general Bregman divergence, we show how the new framework can maintain all the pivotal features of the VDT framework and yet significantly improve its performance in non-Euclidean domains. We apply the proposed framework to different text categorization problems and demonstrate its benefits over the original VDT.Comment: Appears in Proceedings of the Twenty-Ninth Conference on Uncertainty in Artificial Intelligence (UAI2013