Workshop on Topology: Identifying Order in Complex Systems

Our goal is to describe extensions of the main tools of signal processing, denoising feature extraction, prediction, regression, to deal with more general data sources such as heterogeneous nonlinearly correlated multisensor inputs, questionnaires, text and other digital documents. In particular we introduce functional geometric dualities between data attributes and datasets. We describe general methodologies based on various diffusion geometries for building empirical inferential structures on digital data (such as collaborative filters or recommendation engines ). We indicate natural geometries for fusing information through the combination of several inferential structures. Examples covering questionnaire data analysis, multisensor image processing and data fusion will be described.