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doi: 10.3934/bdia.2017020
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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

Early access 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$
1180.94290.96930.4797
2460.97820.98770.7718
31080.99070.99390.9076
4192110.9490
Table Options

Download as excel

Original Features$|\mbox{Domain}(X_2, Y)|$$\tau(Y|X_2)$$\lambda(Y|X_2)$$EG$
1180.94290.96930.4797
2460.97820.98770.7718
31080.99070.99390.9076
4192110.9490
Table 2.  Feature selection by the dummy variables
Merged Features$|\mbox{Domain}(X'_2, Y)|$$\tau(Y|X'_2)$$\lambda(Y|X'_2)$$EG$
4160.94450.96930.2098
4240.99080.99390.2143
5300.99620.99790.4669
638110.6638
Table Options

Download as excel

Merged Features$|\mbox{Domain}(X'_2, Y)|$$\tau(Y|X'_2)$$\lambda(Y|X'_2)$$EG$
4160.94450.96930.2098
4240.99080.99390.2143
5300.99620.99790.4669
638110.6638
Table 3.  Feature selection by the original variables
OrigVarFeatures$|\mbox{Domain}(X_2, Y)|$$\tau(Y|X_2)$$\lambda(Y|X_2)$$EG$
1660.30050.34440.8201
22520.39480.43910.9046
318300.43830.46480.9833
Table Options

Download as excel

OrigVarFeatures$|\mbox{Domain}(X_2, Y)|$$\tau(Y|X_2)$$\lambda(Y|X_2)$$EG$
1660.30050.34440.8201
22520.39480.43910.9046
318300.43830.46480.9833
Table 4.  Feature selection by the dummy variables
Merged Features$|\mbox{Domain}(X'_2, Y)|$$\tau(Y|X'_2)$$\lambda(Y|X'_2)$$EG$
2240.32420.39340.5491
2360.35730.41650.6242
2480.37510.42340.6388
3960.39010.42340.7035
41860.40170.42690.7774
42820.41210.43170.8066
55580.42210.45480.8782
69660.43140.47680.8968
717160.44360.48560.9135
Table Options

Download as excel

Merged Features$|\mbox{Domain}(X'_2, Y)|$$\tau(Y|X'_2)$$\lambda(Y|X'_2)$$EG$
2240.32420.39340.5491
2360.35730.41650.6242
2480.37510.42340.6388
3960.39010.42340.7035
41860.40170.42690.7774
42820.41210.43170.8066
55580.42210.45480.8782
69660.43140.47680.8968
717160.44360.48560.9135
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