LIX Campus de l'École Polytechnique 1, rue Honoré d'Estienne d'Orves Bâtiment Alan Turing CS35003 91120 Palaiseau France Phone: (+33) 1 7757 8070 (Office 2028)

Computational Information Geometry for Machine Learning and Imaging

- Research:

The 21st century is revolutionizing

**data analysis**and information processing (cloud, big data, privacy, HPC, data science to cite a few) and open brand new horizons for adding novel "values" to data or extracting "information" thereof, with both industrial and societal impacts. I am addressing those topics under the umbrella of*Computational Information Geometry*(CIG) with applications to*machine learning*,*computational statistics*and*imaging*(including computer vision), mainly. But:- what is information?
- what is computation? and
- what is geometry?

**geometric framework**allows us to perform*intrinsic*analysis that are not biased by the*ad hoc*data representations and to analyze the**data landscape**: We are investigating the geometric structures of data spaces for pure analytics. I am writing software (C++/Java/Processing/R/Python) and applications to demonstrate those capabilities. My contributions and interests are:- Machine learning (classification, clustering)
- Computational statistics
- Computer vision (image segmentation, image retrieval systems, etc.)
- Computational photography (image-based rendering, surround panoramic video, free 3D viewpoint, etc.)
- Human Computer interaction (image editing, login interfaces, etc.)
- Computational geometry
- Information geometry
- Geometric combinatorial optimization (antenna network layout)
- etc.

- Upcoming organizing events:
- Geometric Science of Information (GSI), 2017
- Geometrical and topological structures of information, CIRM, August 28th-September 1st 2017
- Shannon 100th birthday celebration, Oct 2016
- Differential Geometrical Theory of Statistics, Special issue of Entropy, 2016

- Past events:
- ICMS workshop on Computational Information Geometry for Image and Signal Processing (CIGISP), 21-25 September, Edinburgh, UK, 2015.
- Geometric Science of Information (GSI), Oct 28-30 (Wed-Fri), Ecole Polytechnique, France, 2015.

- What is new?
- [publications chronological | reverse] [slides] [video] [DBLP] [software]
- Preprints:
- Computational Information Geometry for Machine Learning (MLSS 2015, Sydney)
- Some demos with source codes:
- Papers:
- Loss factorization, weakly supervised learning and label noise robustness, ICML 2016
- k-variates++: more pluses in the k-means++, ICML 2016
- Which Geometry for Clustering Copulas? (Gimli:Geometry in Machine Learning workshop, ICML 2016)
- Guaranteed bounds on the Kullback-Leibler divergence of univariate mixtures using piecewise log-sum-exp inequalities, preprint, 2016 (arxiv 1606.05850), IEEE Signal Processing Letters, pdf xplore
- Learning on High-dimensional Neuromanifolds with Relative Natural Gradients (Gimli:Geometry in Machine Learning workshop, ICML 2016) (arxiv 1606.06069")
- Clustering Financial Time Series: How Long is Enough? (IJCAI'16)
- Optimal transport vs. Fisher-Rao distance between copulas for clustering multivariate time series (IEEE SSP'16)
- Classification with mixtures of curved Mahalanobis Metrics (IEEE ICIP'16)
- SSSC-AM: A unified framework for video co-segmentation by structured sparse subspace clustering with appearance and motion features (IEEE ICIP'16)
- Quantifying the Invariance and Robustness of Permutation-Based Indexing Schemes (SISAP'16, LNCS)
- Patch Matching with Polynomial Exponential Families and Projective Divergences (SISAP'16, LNCS)
- Optimal Copula Transport for Clustering Multivariate Time Series, IEEE ICASSP 2016.
- Comix: Joint Estimation and Lightspeed Comparison of Mixture Models, IEEE ICASSP 2016.
- Image and information, preprint, 2016
- Bridging weak supervision and privacy aware learning via sufficient statistics NIPS 2015, workshop on Learning and privacy with incomplete data and weak supervision
- A proposal of a methodological framework with experimental guidelines to investigate clustering stability on financial time series, 14th International Conference on Machine Learning and Applications (IEEE ICMLA'15)
- HCMapper: An interactive visualization tool to compare partition-based flat clustering extracted from pairs of dendrograms. CoRR abs/1507.08137 (2015)
- TS-GNPR Clustering Random Walk Time Series slides video
- Bag-of-components an online algorithm for batch learning of mixture models slides video
- Approximating Covering and Minimum Enclosing Balls in Hyperbolic Geometry slides video
- Online k-MLE for mixture modeling with exponential families slides video
- Estimation jointe et en ligne de modèles de mélanges avec les co-mélanges et les sacs de composantes, GRETSI 2015
- Comment partitionner automatiquement des marches aléatoires ? Avec application à la finance quantitative , GRETSI 2015
- TOTAL JENSEN DIVERGENCES: DEFINITION, PROPERTIES AND CLUSTERING (ICASSP'2015)
- On learning statistical mixtures maximizing the
complete likelihood, MaxEnt (video), AIP Proceedings (2014)

[Paper] [BibTeX] [Summary] [Slides] [Video] - On Clustering Histograms with k-Means by Using Mixed \alpha-Divergences.
MDPI Entropy 16(6): 3273-3301 (2014)

[Paper] [BibTeX] [Summary] [Slides] [code Java/Processing] - Generalized Bhattacharyya and Chernoff upper bounds on Bayes error using quasi-arithmetic means. Elsevier Pattern Recognition Letters 42: 25-34 (2014)

[paper] [BibTeX] [Summary] [Slides] [Code Java] - On the Chi Square and Higher-Order Chi Distances for Approximating f-Divergences. IEEE Signal Process. Lett. 21(1): 10-13 (2014)

[Paper] [BibTeX] [Summary] [Slides] [Code Java] [code Java] - Optimal Interval Clustering: Application to Bregman Clustering and Statistical Mixture Learning. IEEE Signal Process. Lett. 21(10): 1289-1292 (2014)

[BibTeX] [Summary] [Slides] [Poster] [code Java] - Visualizing hyperbolic Voronoi diagrams. ACM Symposium on Computational Geometry (2014)

[BibTeX] [Paper] [Video] [Web] - On approximating the Riemannian 1-center. Comput. Geom. 46(1): 93-104 (2013)

[BibTeX] [Paper] [Slides] [code Java/Processing] - An Information-Geometric Characterization of Chernoff Information. IEEE Signal Process. Lett. 20(3): 269-272 (2013)

[BibTeX] [Paper] [Slides] [code Java] - Jeffreys Centroids: A Closed-Form Expression for Positive Histograms and a Guaranteed Tight Approximation for Frequency Histograms. IEEE Signal Process. Lett. 20(7): 657-660 (2013)

[BibTeX] [Paper] [Slides] [code Java/R] - Consensus Region Merging for Image Segmentation. ACPR 2013: 325-329 (2013)

[BibTeX] [Paper] [code Java] - Perspective click-and-drag area selections in pictures. MVA 2013: 29-32

[BibTeX] [Paper] [Slides] [Video] [code Java/Processing]

Best Practical Paper Award - Logging safely in public spaces using color PINs. CoRR abs/1304.6499 (2013)

[Paper] [Video] [code Java/Processing]

- more from DBLP

- Overview:
- Computational Information Geometry for Machine Learning (MLSS 2015, Sydney) video
- Pattern learning and recognition on statistical manifolds: An information-geometric review (slides)
- Voronoi diagrams in information geometry, MaxEnt 2014 tutorial. [Video]

- Editors: Journal of Mathematical Imaging and Vision (JMIV) MDPI Entropy (JMIV)

- A GPU Panorama Viewer for Generic Camera Models
- Interactive image segmentation based on gpu cellular automata (ShaderX5)
- An interactive tour of Voronoi diagrams on the gpu (ShaderX6)
- A volume shader for quantum voronoi diagrams inside the 3d Bloch ball (ShaderX7)
- Teaching:

- Traitement massif des données (INF442), Projets scientifiques collectifs (PSCs), tuteur pour les projets informatiques en laboratoire INF571 (Laboratory Personal Project)
- I taught INF311 (Introduction to algorithms and Java), INF555 (Visual Computing, see book), computational photography, Unix/C (Essi), Algorithms and data-structures (ISIA), etc.

GPU:

© 2014 Frank Nielsen, all rights reserved. former home page

November 2014, gs bib 09/2016