
The density of expected persistence diagrams and its kernel based estimation
Persistence diagrams play a fundamental role in Topological Data Analysi...
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Estimation and Quantization of Expected Persistence Diagrams
Persistence diagrams (PDs) are the most common descriptors used to encod...
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Persistence Lenses: Segmentation, Simplification, Vectorization, Scale Space and Fractal Analysis of Images
A persistence lens is a hierarchy of disjoint upper and lower level sets...
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Persistence Atlas for Critical Point Variability in Ensembles
This paper presents a new approach for the visualization and analysis of...
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The Shape of Data and Probability Measures
We introduce the notion of multiscale covariance tensor fields (CTF) ass...
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A computationally efficient framework for vector representation of persistence diagrams
In Topological Data Analysis, a common way of quantifying the shape of d...
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A Randomized Algorithm to Reduce the Support of Discrete Measures
Given a discrete probability measure supported on N atoms and a set of n...
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Optimal quantization of the mean measure and application to clustering of measures
This paper addresses the case where data come as point sets, or more generally as discrete measures. Our motivation is twofold: first we intend to approximate with a compactly supported measure the mean of the measure generating process, that coincides with the intensity measure in the point process framework, or with the expected persistence diagram in the framework of persistencebased topological data analysis. To this aim we provide two algorithms that we prove almost minimax optimal. Second we build from the estimator of the mean measure a vectorization map, that sends every measure into a finitedimensional Euclidean space, and investigate its properties through a clusteringoriented lens. In a nutshell, we show that in a mixture of measure generating process, our technique yields a representation in R^k, for k ∈N^* that guarantees a good clustering of the data points with high probability. Interestingly, our results apply in the framework of persistencebased shape classification via the ATOL procedure described in <cit.>.
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