arXiv subjects

Pierre-François Marteau

Publications and source records attributed to Pierre-François Marteau.

28 records · Page 2Linked to original sources

arXiv2011

Discrete Time Elastic Vector Spaces

We propose in this paper a framework dedicated to the construction of what we call time elastic inner products that allows embedding sets of non-uniformly sampled multivariate time series of varying lengths into vector space structures. This framework is based on a recursive definition that covers the case of multiple embedded time elastic dimensions. We prove that such inner products exist in our framework and show how a simple instance of this inner product class operates on some toy applications, while generalizing the Euclidean inner product.

cs.DM↗

arXiv2009

Parallel Random Apollonian Networks

We present and study in this paper a simple algorithm that produces so called growing Parallel Random Apollonian Networks (P-RAN) in any dimension d. Analytical derivations show that these networks still exhibit small-word and scale-free characteristics. To characterize further the structure of P-RAN, we introduce new parameters that we refer to as the parallel degree and the parallel coefficient, that determine locally and in average the number of vertices inside the (d+1)-cliques composing the network. We provide analytical derivations for the computation of the degree and parallel degree distributions, parallel and clustering coefficients. We give an upper bound for the average path lengths for P-RAN and finally show that our derivations are in very good agreement with our simulations.

cs.DM↗

arXiv2009

Weighted Naive Bayes Model for Semi-Structured Document Categorization

The aim of this paper is the supervised classification of semi-structured data. A formal model based on bayesian classification is developed while addressing the integration of the document structure into classification tasks. We define what we call the structural context of occurrence for unstructured data, and we derive a recursive formulation in which parameters are used to weight the contribution of structural element relatively to the others. A simplified version of this formal model is implemented to carry out textual documents classification experiments. First results show, for a adhoc weighting strategy, that the structural context of word occurrences has a significant impact on classification results comparing to the performance of a simple multinomial naive Bayes classifier. The proposed implementation competes on the Reuters-21578 data with the SVM classifier associated or not with the splitting of structural components. These results encourage exploring the learning of acceptable weighting strategies for this model, in particular boosting strategies.

cs.IR↗

arXiv2008

Interprétation vague des contraintes structurelles pour la RI dans des corpus de documents XML - Évaluation d'une méthode approchée de RI structurée

We propose specific data structures designed to the indexing and retrieval of information elements in heterogeneous XML data bases. The indexing scheme is well suited to the management of various contextual searches, expressed either at a structural level or at an information content level. The approximate search mechanisms are based on a modified Levenshtein editing distance and information fusion heuristics. The implementation described highlights the mixing of structured information presented as field/value instances and free text elements. The retrieval performances of the proposed approach are evaluated within the INEX 2005 evaluation campaign. The evaluation results rank the proposed approach among the best evaluated XML IR systems for the VVCAS task.

cs.IR↗

arXiv2008

Time Warp Edit Distance

This technical report details a family of time warp distances on the set of discrete time series. This family is constructed as an editing distance whose elementary operations apply on linear segments. A specific parameter allows controlling the stiffness of the elastic matching. It is well suited for the processing of event data for which each data sample is associated with a timestamp, not necessarily obtained according to a constant sampling rate. Some properties verified by these distances are proposed and proved in this report.

cs.IR↗

arXiv2008

Spiral Walk on Triangular Meshes : Adaptive Replication in Data P2P Networks

We introduce a decentralized replication strategy for peer-to-peer file exchange based on exhaustive exploration of the neighborhood of any node in the network. The replication scheme lets the replicas evenly populate the network mesh, while regulating the total number of replicas at the same time. This is achieved by self adaptation to entering or leaving of nodes. Exhaustive exploration is achieved by a spiral walk algorithm that generates a number of messages linearly proportional to the number of visited nodes. It requires a dedicated topology (a triangular mesh on a closed surface). We introduce protocols for node connection and departure that maintain the triangular mesh at low computational and bandwidth cost. Search efficiency is increased using a mechanism based on dynamically allocated super peers. We conclude with a discussion on experimental validation results.

cs.NI↗

arXiv2008

Time Warp Edit Distance with Stiffness Adjustment for Time Series Matching

In a way similar to the string-to-string correction problem we address time series similarity in the light of a time-series-to-time-series-correction problem for which the similarity between two time series is measured as the minimum cost sequence of "edit operations" needed to transform one time series into another. To define the "edit operations" we use the paradigm of a graphical editing process and end up with a dynamic programming algorithm that we call Time Warp Edit Distance (TWED). TWED is slightly different in form from Dynamic Time Warping, Longest Common Subsequence or Edit Distance with Real Penalty algorithms. In particular, it highlights a parameter which drives a kind of stiffness of the elastic measure along the time axis. We show that the similarity provided by TWED is a metric potentially useful in time series retrieval applications since it could benefit from the triangular inequality property to speed up the retrieval process while tuning the parameters of the elastic measure. In that context, a lower bound is derived to relate the matching of time series into down sampled representation spaces to the matching into the original space. Empiric quality of the TWED distance is evaluated on a simple classification task. Compared to Edit Distance, Dynamic Time Warping, Longest Common Subsequnce and Edit Distance with Real Penalty, TWED has proven to be quite effective on the considered experimental task.

cs.IR↗

arXiv2008

Speeding up Simplification of Polygonal Curves using Nested Approximations

We develop a multiresolution approach to the problem of polygonal curve approximation. We show theoretically and experimentally that, if the simplification algorithm A used between any two successive levels of resolution satisfies some conditions, the multiresolution algorithm MR will have a complexity lower than the complexity of A. In particular, we show that if A has a O(N2/K) complexity (the complexity of a reduced search dynamic solution approach), where N and K are respectively the initial and the final number of segments, the complexity of MR is in O(N).We experimentally compare the outcomes of MR with those of the optimal "full search" dynamic programming solution and of classical merge and split approaches. The experimental evaluations confirm the theoretical derivations and show that the proposed approach evaluated on 2D coastal maps either shows a lower complexity or provides polygonal approximations closer to the initial curves.

cs.CG↗

arXiv2007

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.

cs.IR↗

arXiv2007

Multiresolution Approximation of Polygonal Curves in Linear Complexity

We propose a new algorithm to the problem of polygonal curve approximation based on a multiresolution approach. This algorithm is suboptimal but still maintains some optimality between successive levels of resolution using dynamic programming. We show theoretically and experimentally that this algorithm has a linear complexity in time and space. We experimentally compare the outcomes of our algorithm to the optimal "full search" dynamic programming solution and finally to classical merge and split approaches. The experimental evaluations confirm the theoretical derivations and show that the proposed approach evaluated on 2D coastal maps either show a lower time complexity or provide polygonal approximations closer to the input discrete curves.

cs.CV↗