ANR PHOENIX

Workgroup IMPERFECT

[IMPrecise Expectation on Random Field Entropy for Clustering Time-series]

 

Context

When analyzing huge datasets for the sake of retrieving a given relevant information, one can distinguish two main situations:

[S1] the information of interest admits a precise representation and the database involves a concise description,

[S2] the information of interest is imprecise or hidden in these data due to:

o   difficulties in deriving a concise representation of this information,

o   measurement uncertainties that affect the data,

o   incomplete knowledge on this information.

 

In the first case study, [S1], (concise information, to be retrieved from a large database), identifying an information of interest is not rocket science: the issue raised is mainly seeking 'optimal data sorting strategies', under computational complexity constraints. This problem has solutions in the form of data mining or machine learning algorithms, among other solutions. An example is the search for an image or a specific video in a multimedia database (by sending a request to a mapping system between descriptors of the query and those of the database elements).

 

In case study [S2], (imprecise or hidden information, incomplete data measurements), information retrieval requires modeling imprecision/incompleteness. Examples of research areas where imprecision affects information processing are:

• finance, where speculative behavior are concealed / hidden in a stream of market data (when undetected, speculations can led to significant financial losses and may cause instability of a financial system),

• astronomy, where observations (comets, planets, constellations, etc.) are usually imprecise / diffuse due to technology limitations with respect to remote objects,

• earth sciences, including satellite remote sensing, where many images are available, but do not make a concise knowledge of glacier/forest/volcano states possible.

 

Imperfect framework

The ‘IMPERFECT’ research project relates to the case study [S2], considering the analysis of inaccurate information in large amounts of data (with application to earth observation and monitoring). The issue addressed is the analysis of information from imprecise random processes through possibilist descriptions associated with functional wavelet representations. Topics include and are not limited to:

·        the analysis of statistical properties of wavelet projections in case of imprecise input stochastic process,

·        identifying relevant wavelet frames for the description of this process, this can be done by:

o   association of a possibilistic distribution to each projection;

o   definition of entropy and mutual information for possibilist stochastic wavelet processes;

o   selection of appropriate similarity measures with respect to wavelet based imprecision nature;

 

Application

The scope chosen for validation of theoretical framework and concepts is earth monitoring by the analysis of remote sensing image time series. The database analyzed consists of multi-source (several satellites and sometimes many acquisition devices for the same satellite), multi-modal (different sensors and several operating wavelengths, mostly optical and synthetic aperture radar) and multi-resolutions images.

From a technical perspective, the exploitation of images in a multi-satellite context (non-synchronized systems for simultaneous observation of a surface or a region) assumes identifying the degree of atomicity of the state called ‘temporal stability'. This atomicity consists in finding a sufficiently short time interval for which the object studied (glacier, volcano or forest) has not been subject to major changes. One then has several images that will be fused according to their imprecise mutual information, without the risk of blurring change information.

 

Team

Literature

[1] A. M. Atto and Y. Berthoumieu, Wavelet Transforms of Nonstationary Random Processes: Contributing Factors for Stationarity and Decorrelation, IEEE Transactions on Information Theory, Vol 58, 2012.

[2] L. Bai, S. Yan, X. Zheng, Ben M. Chen, Market turning points forecasting using wavelet analysis, Physica A: Statistical Mechanics and its Applications, Elsevier, 2015.

[3] T. Kravets and A. Sytienko, Wavelet analysis of the Crisis Effects in Stock Index Returns, Ekonomika / Economics, Vol. 92 Issue 1, p78-96, 2013.

[4] A. M. Atto and E. Trouvé and Y. Berthoumieu and G. Mercier, Multi-Date Divergence Matrices for the Analysis of SAR Image Time Series , IEEE Transactions on Geoscience and Remote Sensing, Special Issue on the Analysis of Multitemporal Remote Sensing Data, 2013.

[5] D. Mondal and D. B. Percival, “Wavelet variance analysis for random fields on a regular lattice,” IEEE Transactions on Image Processing, vol. 21, no. 2, pp. 537 – 549, Febr. 2012.

[6] O. Nicolis, P. Ramirez-Cobo, and B. Vidakovic, 2d wavelet-based spectra with applications, Computational Statistics and Data Analysis, vol.~55,  no.~1, pp. 738 -- 751, 2011.

[7] I. A. Eckley, G. P. Nason, and R. L. Treloar, “Locally stationary wavelet fields with application to the modelling and analysis of image texture,” Journal of the Royal Statistical Society: Applied Statistics, 2010.

 [8] A. Pinheiro and P. K. SEN and H. P. Pinheiro, Decomposability of high-dimensional diversity measures: Quasi-U-statistics, martingales and nonstandard asymptotics, Journal of Multivariate Analysis, v. 100, p. 1645-1656, 2009.

[9] A. M. Atto, Analyse des Séquences de Processus et Champs Aléatoires d'Ondelettes, Habilitation à Diriger des Recherches, Université Savoie Mont Blanc, ComUE Université Grenoble Alpes.

[10] A. M. Atto and K. Salamatian and P. Bolon, Best basis for joint representation: The median of marginal best bases for low cost information exchanges in distributed signal representation , Elsevier Information Sciences, vol. 283, no 1, 2014.

[11] A. M. Atto and Y. Berthoumieu and P. Bolon, 2-Dimensional Wavelet Packet Spectrum for Texture Analysis, Accepted for publication, IEEE Transactions on Image Processing, v. 22, no 6, 2013.

[12] D. Dubois, H. Prade, Formal representation of uncertainty, chapter 3 in D. Bouyssou, D. Dubois, M. Pirlot, H. Prade, eds, Decision-Making Process, ISTE, London, UK & Wiley, Hoboken, N.J. USA, 2009.

[13] Z. Liu, J. Dezert, G. Mercier and Q. Pan, Dynamical Evidential Reasoning For Change Detection In Remote Sensing Images, IEEE Transactions on Geoscience and Remote Sensing, 2012.

[14] A. Imoussaten and J. Montmain and G. Mauris, A Multicriteria Decision Support System using a Possibility Representation for Managing Inconsistent Assessments of Experts Involved in Emergency Situations, 29 (1), pp.50-83, International Journal of Intelligent Systems, Wiley, 2014.

[15] G. Mauris, A review of relationships between possibility and probability representations of uncertainty in measurement, IEEE Transactions on Instrumentation and Measurement, 2013.

[16] ] G. Mauris, Possibility distributions: A unified representation of usual direct-probability-based parameter estimation methods, International Journal of Approximate Reasoning, Vol. 52 , No 9, pp. 1232-1242, 2011.