Overview of object oriented data analysis

Abstract

Object oriented data analysis is the statistical analysis of populations of complex objects. In the special case of functional data analysis, these data objects are curves, where a variety of Euclidean approaches, such as principal components analysis, have been very successful. Challenges in modern medical image analysis motivate the statistical analysis of populations of more complex data objects that are elements of mildly non-Euclidean spaces, such as lie groups and symmetric spaces, or of strongly non-Euclidean spaces, such as spaces of tree-structured data objects. These new contexts for object oriented data analysis create several potentially large new interfaces between mathematics and statistics. The notion of object oriented data analysis also impacts data analysis, through providing a framework for discussion of the many choices needed in many modern complex data analyses, especially in interdisciplinary contexts.

Persistence Terrace for Topological Inference of Point Cloud Data

“…Accordingly, recent years have seen the development of methods for functional (Ramsay and Silverman, 2005), object-oriented (Marron and Alonso, 2014), and symbolic (Billard and Diday, 2007) data. All of these aim to tackle situations where the basic unit of analysis is something other than a traditional observation; rather, it can now be an entire image, or a histogram, or a function.…”

Object oriented data analysis under spatial correlation

“…Then we can use such measures to summarize and describe collections of repeated realizations of an object (point pattern) via prototypes or multidimensional scaling (MDS). Extending the link between MDS and PCA, as mentioned by Marron and Alonso (2014), into the context where objects are spatial patterns, and even more interesting, when these patterns or objects are defined on spheres or other manifolds is worth exploring in the near future.…”

Different perspectives on object oriented data analysis

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The paper by Marron and Alonso (2014) provides valuable insights into the statistics of the near future. I found it thought-provoking, stimulating, and full of ideas and suggestions.

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