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

Point triangulation through polyhedron collapse using the l∞ norm

Multi-camera triangulation of feature points based on a minimisation of the overall l(2) reprojection error can get stuck in suboptimal local minima or require slow global optimisation. For this reason, researchers have proposed optimising the l(infinity) norm of the l(2) single view reprojection errors, which avoids the problem of local minima entirely. In this paper we present a novel method for l(infinity) triangulation that minimizes the l(infinity) norm of the l(infinity) reprojection errors: this apparently small difference leads to a much faster but equally accurate solution which is related to the MLE under the assumption of uniform noise. The proposed method adopts a new optimisation strategy based on solving simple quadratic equations. This stands in contrast with the fastest existing methods, which solve a sequence of more complex auxiliary Linear Programming or Second Order Cone Problems. The proposed algorithm performs well: for triangulation, it achieves the same accuracy as existing techniques while executing faster and being straightforward to implement

The Extended Edit Distance Metric

Similarity search is an important problem in information retrieval. This similarity is based on a distance. Symbolic representation of time series has attracted many researchers recently, since it reduces the dimensionality of these high dimensional data objects. We propose a new distance metric that is applied to symbolic data objects and we test it on time series data bases in a classification task. We compare it to other distances that are well known in the literature for symbolic data objects. We also prove, mathematically, that our distance is metric.Comment: Technical repor