Object-Oriented Data Analysis of Cell Images

Lu, Xiaosun; Marron, J. S.; Haaland, Perry D.

doi:10.1080/01621459.2014.884503

Cited by 10 publications

(9 citation statements)

References 25 publications

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“…FDA is interested in the analysis of data points that are complex, such as curves, images, shapes, trees, movies, spectra, sounds or covariance matrices or operators (e.g. Lu et al (2014)). The space Ω (following the paper's notation) in which such data points lie falls (roughly) into four categories.…”

Section: Shahin Tavakoli (University Of Warwick Coventry)mentioning

confidence: 99%

Functional Models for Time-Varying Random Objects

Dubey

Müller

2020

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Summary Functional data analysis provides a popular toolbox of functional models for the analysis of samples of random functions that are real valued. In recent years, samples of time‐varying object data such as time‐varying networks that are not in a vector space have been increasingly collected. These data can be viewed as elements of a general metric space that lacks local or global linear structure and therefore common approaches that have been used with great success for the analysis of functional data, such as functional principal component analysis, cannot be applied. We propose metric covariance, a novel association measure for paired object data lying in a metric space (Ω,d) that we use to define a metric autocovariance function for a sample of random Ω‐valued curves, where Ω generally will not have a vector space or manifold structure. The proposed metric autocovariance function is non‐negative definite when the squared semimetric d2 is of negative type. Then the eigenfunctions of the linear operator with the autocovariance function as kernel can be used as building blocks for an object functional principal component analysis for Ω‐valued functional data, including time‐varying probability distributions, covariance matrices and time dynamic networks. Analogues of functional principal components for time‐varying objects are obtained by applying Fréchet means and projections of distance functions of the random object trajectories in the directions of the eigenfunctions, leading to real‐valued Fréchet scores. Using the notion of generalized Fréchet integrals, we construct object functional principal components that lie in the metric space Ω. We establish asymptotic consistency of the sample‐based estimators for the corresponding population targets under mild metric entropy conditions on Ω and continuity of the Ω‐valued random curves. These concepts are illustrated with samples of time‐varying probability distributions for human mortality, time‐varying covariance matrices derived from trading patterns and time‐varying networks that arise from New York taxi trips.

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Section: Shahin Tavakoli (University Of Warwick Coventry)mentioning

confidence: 99%

Functional Models for Time-Varying Random Objects

Dubey

Müller

2020

Journal of the Royal Statistical Society Series B: Statistical Methodology

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“…This is an emerging area of statistics where the goal is to develop and apply statistical methods to objects such as functions, images, graphs or trees (e.g. [19,21,20,25,27,30]) while respecting the structure of these objects.…”

Section: Related Workmentioning

confidence: 99%

Medians of populations of persistence diagrams

Turner

2020

Homology, Homotopy and Applications

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Persistence diagrams are common objects in the field of Topological Data Analysis. They are topological summaries that capture both topological and geometric structure within data. Recently there has been a surge of interest in developing tools to statistically analyse populations of persistence diagrams, a process hampered by the complicated geometry of the space of persistence diagrams. In this paper we study the median of a set of diagrams, defined as the minimizer of an appropriate cost function analogous to the sum of distances used for samples of real numbers. We then characterize the local minima of this cost function and in doing so characterize the median. We also do some comparative analysis of the properties of the median and the mean.

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“…Only recently, statisticians are considering images as a new source of useful data for statistical analysis. See, for instance, Lu et al (2014).…”

Section: Analyzing New Sources Of Information: Texts Images Videos Audios and Functionsmentioning

confidence: 99%

Data science, big data and statistics

Galeano

Peña

2019

TEST

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This article analyzes how Big Data is changing the way we learn from observations. We describe the changes in statistical methods in seven areas that have been shaped by the Big Data-rich environment: the emergence of new sources of information; visualization in high dimensions; multiple testing problems; analysis of heterogeneity; automatic model selection; estimation methods for sparse models; and merging network information with statistical models. Next, we compare the statistical approach with those in computer science and machine learning and argue that the convergence of different methodologies for data analysis will be the core of the new field of data science. Then, we present two examples of Big Data analysis in which several new tools discussed previously are applied, as using network information or combining different sources of data. Finally, the article concludes with some final remarks.

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Object-Oriented Data Analysis of Cell Images

Cited by 10 publications

References 25 publications

Functional Models for Time-Varying Random Objects

Functional Models for Time-Varying Random Objects

Medians of populations of persistence diagrams

Data science, big data and statistics

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