Methods of Information Geometry to model complex shapes

The aim of this study is to model shapes from complex systems using Information Geometry tools. It is well-known that the Fisher information endows the statistical manifold, defined by a family of probability distributions, with a Riemannian metric, called the Fisher-Rao metric. With respect to this, geodesic paths are determined, minimizing information in Fisher sense. Under the hypothesis that it is possible to extract from the shape a finite number of representing points, called landmarks, we propose to model each of them with a probability distribution, as for example a multivariate Gaussian distribution. Then using the geodesic distance, induced by the Fisher-Rao metric, we can define a shape metric which enables us to quantify differences between shapes. The discriminative power of the proposed shape metric is tested performing a cluster analysis on the shapes of three different groups of specimens corresponding to three species of flatfish. Results show a better ability in recovering the true cluster structure with respect to other existing shape distances.

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“…As a conclusion, we only remark that the proposed shape representation allows also to study and predict the evolution in time of a shape [15].…”

Section: Shape Metrics Based On Geodesic Distancementioning

confidence: 85%

Fisher Information Geometry for Shape Analysis

Sanctis

Gattone

2016

Proceedings of 3rd International Electronic and Flipped Conference on Entropy and Its Applications

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“…The authors of [ 4 ] develop several distribution based clustering techniques using the

norm between distributions as a similarity measure. In [ 5 , 6 , 7 ], the authors explore information geometry based clustering methods using the Fisher-Rao distance distributions as a similarity measure. The authors also mention that the development of clustering algorithms based upon probability distributions is a relatively unexplored area.…”

Section: Introductionmentioning

confidence: 99%

Clustering Financial Return Distributions Using the Fisher Information Metric

Taylor

2019

Entropy

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Information geometry provides a correspondence between differential geometry and statistics through the Fisher information matrix. In particular, given two models from the same parametric family of distributions, one can define the distance between these models as the length of the geodesic connecting them in a Riemannian manifold whose metric is given by the model's Fisher information matrix. One limitation that has hindered the adoption of this similarity measure in practical applications is that the Fisher distance is typically difficult to compute in a robust manner. We review such complications and provide a general form for the distance function for one parameter model. We next focus on higher dimensional extreme value models including the generalized Pareto and generalized extreme value distributions that will be used in financial risk applications. Specifically, we first develop a technique to identify the nearest neighbors of a target security in the sense that their best fit model distributions have minimal Fisher distance to the target. Second, we develop a hierarchical clustering technique that utilizes the Fisher distance. Specifically, we compare generalized extreme value distributions fit to block maxima of a set of equity loss distributions and group together securities whose worst single day yearly loss distributions exhibit similarities.

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A new approach for modeling bone response to dental implant materials

Sanctis

Gattone

2017

Bone Response to Dental Implant Materials

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Methods of Information Geometry to model complex shapes

Cited by 6 publications

References 5 publications

Fisher Information Geometry for Shape Analysis

Fisher Information Geometry for Shape Analysis

Clustering Financial Return Distributions Using the Fisher Information Metric

A new approach for modeling bone response to dental implant materials

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