A category-based probabilistic approach to feature selection

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doi: 10.3934/bdia.2017020

A category-based probabilistic approach to feature selection

Jianguo Dai ^1, , Wenxue Huang ^1, and Yuanyi Pan ^2,

1.	School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China
2.	Clearpier Inc., 1300-121 Richmond St.W., Toronto, Ontario M5H 2K1, Canada

Published August 2018

A high dimensional and large sample categorical data set with a response variable may have many noninformative or redundant categories in its explanatory variables. Identifying and removing these categories usually improve the association but also give rise to significantly higher statistical reliability of selected features. A category-based probabilistic approach is proposed to achieve this goal. Supportive experiments are presented.

Keywords: Association, categorical data, feature selection, statistical reliability.

Mathematics Subject Classification: Primary: 62H20, 62F07; Secondary: 68T30, 58F17.

Citation: Jianguo Dai, Wenxue Huang, Yuanyi Pan. A category-based probabilistic approach to feature selection. Big Data & Information Analytics, doi: 10.3934/bdia.2017020

References:

[1]	A. Daly, T. Dekker and S. Hess, Dummy coding vs effects coding for categorical variables: Clarifications and extensions, J. Choice Modelling, 21 (2014), 36-41. doi: 10.1016/j.jocm.2016.09.005. Google Scholar
[2]	S. Garavaglia and A. Sharma, A Smart Guide to Dummy Variables: Four Applications and a Macro, 1998.Google Scholar
[3]	S. S. Gokhale, Quantifying the variance in application reliability, IEEE Pacific Rim International Symposium on Dependable Computing, (2004), 113-121. doi: 10.1109/PRDC.2004.1276562. Google Scholar
[4]	L. A. Goodman and W. H. Kruskal, Measures of Association for Cross Classifications, Springer-Verlag, New York-Berlin, 1979. Google Scholar
[5]	L. Guttman, The test-retest reliability of qualitative data, Psychometrika, 11 (1946), 81-95. doi: 10.1007/BF02288925. Google Scholar
[6]	W. Huang, X. Li and Y. Pan, Increase statistical reliability without lossing predictive power by merging classes and adding variables, Big Data and Information Analytics, 1 (2016), 341-347. Google Scholar
[7]	W. Huang and Y. Pan, On balancing between optimal and proportional categorical predictions, Big Data and Information Analytics, 1 (2016), 129-137. doi: 10.3934/bdia.2016.1.129. Google Scholar
[8]	W. Huang, Y. Shi and X. Wang, A nominal association matrix with feature selection for categorical data, Communications in Statistics -Theory and Methods, 46 (2017), 7798-7819. doi: 10.1080/03610926.2014.930911. Google Scholar
[9]	S. Kamenshchikov, Variance Ratio as a Measure of Backtest Reliability, Futures, 2015.Google Scholar
[10]	J. Li, K. Cheng, et. al., Feature selection: A data perspective, arXiv: 1601.07996v4, [cs.LG], ACM Computing Surveys 50 (2018), Article No. 94. doi: 10.1145/3136625. Google Scholar
[11]	C. J. Lloyd, Statistical Analysis of Categorical Data, John Wiley & Sons, Inc., New York, 1999. Google Scholar
[12]	STATCAN, 1998. Survey of Family Expenditures-1996.Google Scholar
[13]	http://archive.ics.uci.edu/ml/datasets/Mushroom Google Scholar

show all references

References:

[1]	A. Daly, T. Dekker and S. Hess, Dummy coding vs effects coding for categorical variables: Clarifications and extensions, J. Choice Modelling, 21 (2014), 36-41. doi: 10.1016/j.jocm.2016.09.005. Google Scholar
[2]	S. Garavaglia and A. Sharma, A Smart Guide to Dummy Variables: Four Applications and a Macro, 1998.Google Scholar
[3]	S. S. Gokhale, Quantifying the variance in application reliability, IEEE Pacific Rim International Symposium on Dependable Computing, (2004), 113-121. doi: 10.1109/PRDC.2004.1276562. Google Scholar
[4]	L. A. Goodman and W. H. Kruskal, Measures of Association for Cross Classifications, Springer-Verlag, New York-Berlin, 1979. Google Scholar
[5]	L. Guttman, The test-retest reliability of qualitative data, Psychometrika, 11 (1946), 81-95. doi: 10.1007/BF02288925. Google Scholar
[6]	W. Huang, X. Li and Y. Pan, Increase statistical reliability without lossing predictive power by merging classes and adding variables, Big Data and Information Analytics, 1 (2016), 341-347. Google Scholar
[7]	W. Huang and Y. Pan, On balancing between optimal and proportional categorical predictions, Big Data and Information Analytics, 1 (2016), 129-137. doi: 10.3934/bdia.2016.1.129. Google Scholar
[8]	W. Huang, Y. Shi and X. Wang, A nominal association matrix with feature selection for categorical data, Communications in Statistics -Theory and Methods, 46 (2017), 7798-7819. doi: 10.1080/03610926.2014.930911. Google Scholar
[9]	S. Kamenshchikov, Variance Ratio as a Measure of Backtest Reliability, Futures, 2015.Google Scholar
[10]	J. Li, K. Cheng, et. al., Feature selection: A data perspective, arXiv: 1601.07996v4, [cs.LG], ACM Computing Surveys 50 (2018), Article No. 94. doi: 10.1145/3136625. Google Scholar
[11]	C. J. Lloyd, Statistical Analysis of Categorical Data, John Wiley & Sons, Inc., New York, 1999. Google Scholar
[12]	STATCAN, 1998. Survey of Family Expenditures-1996.Google Scholar
[13]	http://archive.ics.uci.edu/ml/datasets/Mushroom Google Scholar

Table 1. Feature selection by the original variables

Original Features	$\|\mbox{Domain}(X_2, Y)\|$	$\tau(Y\|X_2)$	$\lambda(Y\|X_2)$	$EG$
1	18	0.9429	0.9693	0.4797
2	46	0.9782	0.9877	0.7718
3	108	0.9907	0.9939	0.9076
4	192	1	1	0.9490

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Original Features	$\|\mbox{Domain}(X_2, Y)\|$	$\tau(Y\|X_2)$	$\lambda(Y\|X_2)$	$EG$
1	18	0.9429	0.9693	0.4797
2	46	0.9782	0.9877	0.7718
3	108	0.9907	0.9939	0.9076
4	192	1	1	0.9490

Table 2. Feature selection by the dummy variables

Merged Features	$\|\mbox{Domain}(X'_2, Y)\|$	$\tau(Y\|X'_2)$	$\lambda(Y\|X'_2)$	$EG$
4	16	0.9445	0.9693	0.2098
4	24	0.9908	0.9939	0.2143
5	30	0.9962	0.9979	0.4669
6	38	1	1	0.6638

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Merged Features	$\|\mbox{Domain}(X'_2, Y)\|$	$\tau(Y\|X'_2)$	$\lambda(Y\|X'_2)$	$EG$
4	16	0.9445	0.9693	0.2098
4	24	0.9908	0.9939	0.2143
5	30	0.9962	0.9979	0.4669
6	38	1	1	0.6638

Table 3. Feature selection by the original variables

OrigVarFeatures	$\|\mbox{Domain}(X_2, Y)\|$	$\tau(Y\|X_2)$	$\lambda(Y\|X_2)$	$EG$
1	66	0.3005	0.3444	0.8201
2	252	0.3948	0.4391	0.9046
3	1830	0.4383	0.4648	0.9833

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OrigVarFeatures	$\|\mbox{Domain}(X_2, Y)\|$	$\tau(Y\|X_2)$	$\lambda(Y\|X_2)$	$EG$
1	66	0.3005	0.3444	0.8201
2	252	0.3948	0.4391	0.9046
3	1830	0.4383	0.4648	0.9833

Table 4. Feature selection by the dummy variables

Merged Features	$\|\mbox{Domain}(X'_2, Y)\|$	$\tau(Y\|X'_2)$	$\lambda(Y\|X'_2)$	$EG$
2	24	0.3242	0.3934	0.5491
2	36	0.3573	0.4165	0.6242
2	48	0.3751	0.4234	0.6388
3	96	0.3901	0.4234	0.7035
4	186	0.4017	0.4269	0.7774
4	282	0.4121	0.4317	0.8066
5	558	0.4221	0.4548	0.8782
6	966	0.4314	0.4768	0.8968
7	1716	0.4436	0.4856	0.9135

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Merged Features	$\|\mbox{Domain}(X'_2, Y)\|$	$\tau(Y\|X'_2)$	$\lambda(Y\|X'_2)$	$EG$
2	24	0.3242	0.3934	0.5491
2	36	0.3573	0.4165	0.6242
2	48	0.3751	0.4234	0.6388
3	96	0.3901	0.4234	0.7035
4	186	0.4017	0.4269	0.7774
4	282	0.4121	0.4317	0.8066
5	558	0.4221	0.4548	0.8782
6	966	0.4314	0.4768	0.8968
7	1716	0.4436	0.4856	0.9135

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