Deep Learning And Information Geometry For Time Series Classification
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Deep Learning and Information Geometry for Time-Series Classification
Machine Learning, and in particular Deep Learning, is a powerful tool to model and study the intrinsic statistical foundations of data, allowing the extraction of meaningful, human-interpretable information from otherwise unpalatable arrays of floating points. While it provides a generic solution to many problems, some particular data types exhibit strong underlying physical structure: images have spatial locality, audio has temporal sequentiality, radar has time-frequency structure. Both intuitively and formally, there can be much to gain in leveraging this structure by adapting the subsequent learning models. As convolutional architectures for images, signal properties can be encoded and harnessed within the network. Conceptually, this would allow for a more intrinsic handling of the data, potentially leading to more efficient learning models. Thus, we will aim to use known structures in the signals as model priors. Specifically, we build dedicated deep temporal architectures for time series classification, and explore the use of complex values in neural networks to further refine the analysis of structured data. Going even further, one may wish to directly study the signal's underlying statistical process. As such, Gaussian families constitute a popular candidate. Formally, the covariance of the data fully characterizes such a distribution; developing Machine Learning algorithms on covariance matrices will thus be a central theme throughout this thesis. Statistical distributions inherently diverge from the Euclidean framework; as such, it is necessary to study them on the appropriate, curved Riemannian manifold, as opposed to a flat, Euclidean space. Specifically, we contribute to existing deep architectures by adding normalizations in the form of data-aware mappings, and a Riemannian Batch Normalization algorithm. We showcase empirical validation through a variety of different tasks, including emotion and action recognition from video and Motion Capture data, with a sharpened focus on micro-Doppler radar data for Non-Cooperative Target Recognition drone recognition. Finally, we develop a library for the Deep Learning framework PyTorch, to spur reproducibility and ease of use.
Machine Learning and Knowledge Discovery in Databases. Research Track
This multi-volume set, LNAI 14941 to LNAI 14950, constitutes the refereed proceedings of the European Conference on Machine Learning and Knowledge Discovery in Databases, ECML PKDD 2024, held in Vilnius, Lithuania, in September 2024. The papers presented in these proceedings are from the following three conference tracks: - Research Track: The 202 full papers presented here, from this track, were carefully reviewed and selected from 826 submissions. These papers are present in the following volumes: Part I, II, III, IV, V, VI, VII, VIII. Demo Track: The 14 papers presented here, from this track, were selected from 30 submissions. These papers are present in the following volume: Part VIII. Applied Data Science Track: The 56 full papers presented here, from this track, were carefully reviewed and selected from 224 submissions. These papers are present in the following volumes: Part IX and Part X.
Information Geometry and Its Applications
This is the first comprehensive book on information geometry, written by the founder of the field. It begins with an elementary introduction to dualistic geometry and proceeds to a wide range of applications, covering information science, engineering, and neuroscience. It consists of four parts, which on the whole can be read independently. A manifold with a divergence function is first introduced, leading directly to dualistic structure, the heart of information geometry. This part (Part I) can be apprehended without any knowledge of differential geometry. An intuitive explanation of modern differential geometry then follows in Part II, although the book is for the most part understandable without modern differential geometry. Information geometry of statistical inference, including time series analysis and semiparametric estimation (the Neyman–Scott problem), is demonstrated concisely in Part III. Applications addressed in Part IV include hot current topics in machine learning, signal processing, optimization, and neural networks. The book is interdisciplinary, connecting mathematics, information sciences, physics, and neurosciences, inviting readers to a new world of information and geometry. This book is highly recommended to graduate students and researchers who seek new mathematical methods and tools useful in their own fields.