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Categorical Exploratory Data Analysis: From Multiclass Classification and Response Manifold Analytics perspectives of baseball pitching dynamics

Authors :
Elizabeth P. Chou
Fushing Hsieh
Source :
Entropy, Volume 23, Issue 7, Entropy, Vol 23, Iss 792, p 792 (2021), Entropy (Basel, Switzerland), vol 23, iss 7
Publication Year :
2020
Publisher :
arXiv, 2020.

Abstract

All features of any data type are universally equipped with categorical nature revealed through histograms. A contingency table framed by two histograms affords directional and mutual associations based on rescaled conditional Shannon entropies for any feature-pair. The heatmap of the mutual association matrix of all features becomes a roadmap showing which features are highly associative with which features. We develop our data analysis paradigm called categorical exploratory data analysis (CEDA) with this heatmap as a foundation. CEDA is demonstrated to provide new resolutions for two topics: multiclass classification (MCC) with one single categorical response variable and response manifold analytics (RMA) with multiple response variables. We compute visible and explainable information contents with multiscale and heterogeneous deterministic and stochastic structures in both topics. MCC involves all feature-group specific mixing geometries of labeled high-dimensional point-clouds. Upon each identified feature-group, we devise an indirect distance measure, a robust label embedding tree (LET), and a series of tree-based binary competitions to discover and present asymmetric mixing geometries. Then, a chain of complementary feature-groups offers a collection of mixing geometric pattern-categories with multiple perspective views. RMA studies a system’s regulating principles via multiple dimensional manifolds jointly constituted by targeted multiple response features and selected major covariate features. This manifold is marked with categorical localities reflecting major effects. Diverse minor effects are checked and identified across all localities for heterogeneity. Both MCC and RMA information contents are computed for data’s information content with predictive inferences as by-products. We illustrate CEDA developments via Iris data and demonstrate its applications on data taken from the PITCHf/x database.

Details

Database :
OpenAIRE
Journal :
Entropy, Volume 23, Issue 7, Entropy, Vol 23, Iss 792, p 792 (2021), Entropy (Basel, Switzerland), vol 23, iss 7
Accession number :
edsair.doi.dedup.....a23c168c3a875c2398cc478c1acf7b57
Full Text :
https://doi.org/10.48550/arxiv.2006.14411