On the Geodesic Distance in Shapes K-means Clustering

Gattone, Stefano Antonio; Sanctis, Angela De; Puechmorel, Stéphane; Nicol, Florence

doi:10.3390/e20090647

Cited by 9 publications

(5 citation statements)

References 23 publications

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“…A major advantage of Hash-Combs when compared to classic techniques [29] [20] is that our approach is not limited to Euclidean data spaces, where distances represent the shortest path between two points along a straight line. In fact, Hash-Combs are also suitable for approximating non-Euclidean geodesic distances [37], which have applications to network security [38], to tracing paths on 3D mesh objects [39], to clustering [40] and training Machine Learning models [41]. Revisiting the example in Figure 4, we can define a simple distance measure based on an element-wise equality check.…”

Section: Hash-combmentioning

confidence: 99%

Hash-Comb: A Hierarchical Distance-Preserving Multi-Hash Data Representation for Collaborative Analytics

2022

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Data privacy regulations like the EU GDPR allow the use of hashing techniques to anonymize data that may contain personal information. However, hashing is well-known to destroy any possibility of performing analytics. Homomorphic crypto-systems allow computing analytics over encrypted data, but cannot guarantee privacy compliance without being coupled with specific privacy-preservation provisions. In this work, we present a novel distance-preserving hashing scheme supporting both regulatory compliance and collaborative analytics. Our scheme achieves regulatory compliance by relying on standard cryptographic hashes while preserving a controllable notion of distance between data points.

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Section: Hash-combmentioning

confidence: 99%

Hash-Comb: A Hierarchical Distance-Preserving Multi-Hash Data Representation for Collaborative Analytics

2022

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“…A Riemannian metric given in [22] is adopted here with Differential Geometry since deployment area is manifold with probability distributions. Riemannian metric A with differential manifold would be brought by matrix f, which describes an internal product on each and every single tangent area of manifold for example.…”

Section: Geometrical Deployment Structure With Probability Distributionsmentioning

confidence: 99%

A geodesic deployment and radial shaped clustering (RSC) algorithm with statistical aggregation in sensor networks

Krishnasamy¹,

Ramasamy²,

Dhanaraj³

et al. 2021

Turkish Journal of Electrical Engineering and Computer Sciences

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Wireless Sensor Networks (WSN) comprise a large number of connected tiny or small sensor devices to sense physical phenomenon. In WSN, prolonging the network's lifetime is a biggest challenge due to absence of power harvesting facility and irreplaceable batteries of the sensor devices. Clustering is one of the widely accepted and standard technique to solve the energy issues faced in WSN. In addition to clustering, the shape of the deployment area also plays the major role especially for large scale sensor deployment. This paper proposes a Radial Shaped Clustering (RSC) algorithm with angular inclination routing. The radial shaped deployed area is divided into virtual concentric layers and each layer is further divided into a set of sectors called clusters. Angular routing is applied to achieve multi-hop routing of packets towards the Sink node. In comparison to Fan Shaped Clustering (FSC), RSC performs better in terms of residual energy and packet received ratio.

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“…The Fisher-Rao distance between multivariate normal distributions in specific cases, such as distributions with a common mean, was considered in diffusion tensor image analysis [29][30][31], in color texture discrimination in several classification experiments [32], in the problem of distributed estimation fusion with unknown correlations [33], and in the machine learning technique [34]. In [35,36], the authors described shapes representing landmarks by a Gaussian model with diagonal covariance matrices and used the Fisher-Rao distance to quantify the difference between two shapes. In [17], this model was applied to statistical inference.…”

Section: Introductionmentioning

confidence: 99%

The Fisher–Rao Distance between Multivariate Normal Distributions: Special Cases, Bounds and Applications

Pinele

Strapasson

Costa

2020

Entropy

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The Fisher–Rao distance is a measure of dissimilarity between probability distributions, which, under certain regularity conditions of the statistical model, is up to a scaling factor the unique Riemannian metric invariant under Markov morphisms. It is related to the Shannon entropy and has been used to enlarge the perspective of analysis in a wide variety of domains such as image processing, radar systems, and morphological classification. Here, we approach this metric considered in the statistical model of normal multivariate probability distributions, for which there is not an explicit expression in general, by gathering known results (closed forms for submanifolds and bounds) and derive expressions for the distance between distributions with the same covariance matrix and between distributions with mirrored covariance matrices. An application of the Fisher–Rao distance to the simplification of Gaussian mixtures using the hierarchical clustering algorithm is also presented.

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On the Geodesic Distance in Shapes K-means Clustering

Cited by 9 publications

References 23 publications

Hash-Comb: A Hierarchical Distance-Preserving Multi-Hash Data Representation for Collaborative Analytics

Hash-Comb: A Hierarchical Distance-Preserving Multi-Hash Data Representation for Collaborative Analytics

A geodesic deployment and radial shaped clustering (RSC) algorithm with statistical aggregation in sensor networks

The Fisher–Rao Distance between Multivariate Normal Distributions: Special Cases, Bounds and Applications

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