An Application of the ABS Algorithm for Modeling Multiple Regression on Massive Data, Predicting the Most Influencing Factors

Author(s)
Soniya Lalwani,
M. Krishna Mohan,
Pooran Singh Solanki,
Sorabh Singhal,
Sandeep Mathur,
Emilio Spedicato

Affiliation(s)

Advanced Bioinformatics Centre, Birla Institute of Scientific Research, Jaipur, India.

Department of Endocrinology, SMS Medical College and Hospital, Jaipur, India.

Department of Operation Research, University of Bergamo, Bergamo, Italy.

Advanced Bioinformatics Centre, Birla Institute of Scientific Research, Jaipur, India.

Department of Endocrinology, SMS Medical College and Hospital, Jaipur, India.

Department of Operation Research, University of Bergamo, Bergamo, Italy.

ABSTRACT

Linear Least Square (LLS) is an approach for modeling regression analysis, applied for prediction and quantification of the strength of relationship between dependent and independent variables. There are a number of methods for solving the LLS problem but as soon as the data size increases and system becomes ill conditioned, the classical methods become complex at time and space with decreasing level of accuracy. Proposed work is based on prediction and quantification of the strength of relationship between sugar fasting and Post-Prandial (PP) sugar with 73 factors that affect diabetes. Due to the large number of independent variables, presented problem of diabetes prediction also presented similar complexities. ABS method is an approach proven better than other classical approaches for LLS problems. ABS algorithm has been applied for solving LLS problem. Hence, separate regression equations were obtained for sugar fasting and PP severity.

Linear Least Square (LLS) is an approach for modeling regression analysis, applied for prediction and quantification of the strength of relationship between dependent and independent variables. There are a number of methods for solving the LLS problem but as soon as the data size increases and system becomes ill conditioned, the classical methods become complex at time and space with decreasing level of accuracy. Proposed work is based on prediction and quantification of the strength of relationship between sugar fasting and Post-Prandial (PP) sugar with 73 factors that affect diabetes. Due to the large number of independent variables, presented problem of diabetes prediction also presented similar complexities. ABS method is an approach proven better than other classical approaches for LLS problems. ABS algorithm has been applied for solving LLS problem. Hence, separate regression equations were obtained for sugar fasting and PP severity.

Cite this paper

S. Lalwani, M. Mohan, P. Solanki, S. Singhal, S. Mathur and E. Spedicato, "An Application of the ABS Algorithm for Modeling Multiple Regression on Massive Data, Predicting the Most Influencing Factors,"*Applied Mathematics*, Vol. 4 No. 6, 2013, pp. 907-913. doi: 10.4236/am.2013.46126.

S. Lalwani, M. Mohan, P. Solanki, S. Singhal, S. Mathur and E. Spedicato, "An Application of the ABS Algorithm for Modeling Multiple Regression on Massive Data, Predicting the Most Influencing Factors,"

References

[1] E. Spedicato, E. Bodon, Z. Xia and N. Mahdavi-Amiri, “ABS Method for Continuous and Integer Linear Equations and Optimization,” Central European Journal of Operations Research, Vol. 18, No. 1, 2010, pp. 73-95. doi:0.1007/s10100-009-0128-9

[2] S. Lalwani, R. Kumar, E. Spedicato and N. Gupta, “An Application of the ABS LX Algorithm to Multiple Sequence Alignment,” Iranian Journal of Operations Research, Vol. 3, 2012, pp. 31-45.

[3] S. Lalwani, R. Kumar, V. Rastogi and E. Spedicato, “An Application of the ABS LX Algorithm to Schedule Medical Residents,” Journal of Computer and Information Technology, Vol. 1, 2011, pp. 95-118.

[4] S. S. Rich, “Genetics of Diabetes and Its Complications,” Journal of the American Society of Nephrology, Vol. 17, No. 2, 2006, pp, 353-360. doi:0.1681/ASN.2005070770

[5] World Health Statistics Report, 2012. http://www.diabetes24-7.com/?p=1272

[6] A. Ramachandran, C. Snehalatha, A. S. Shetty and A. Nanditha, “Trends in Prevalence of Diabetes in Asian Countries,” World Journal of Diabetes, Vol. 3, No. 6, 2012, 110-117. doi:0.4239/wjd.v3.i6.110

[7] C. L. Lawson and R. J. Hanson, “Solving Least Squares Problems,” Society for Industrial and Applied Mathematics, 1995. doi:0.1137/1.9781611971217

[8] A. Bjorck, “Numerical Methods for Least Squares Problems,” Society for Industrial and Applied Mathematics, 1996. doi:0.1137/1.9781611971484

[9] J. Abaffy, C. G. Broyden and E. Spedicato, “A Class of Direct Methods for Linear Equations,” Numerische Mathematic, Vol. 45, 1984, pp. 361-376.

[10] J. Abaffy and E. Spedicato, “Numerical Experiments with the Symmetric Algorithm in the ABS Class for Linear Systems,” Optimization, Vol. 18, No. 2, 1987, pp. 197212. doi:0.1080/02331938708843232

[11] J. O. Rawlings, S. G. Pantula and D. A. Dickey, “Applied Regression Analysis: A Research Tool,” 2nd Edition, Springer, Berlin, 1998. doi:0.1007/b98890

[12] S. Chatterjee and A. A. S. Hadi, “Regression Analysis by Example,” 4th Edition, Wiley Interscience, 2006. doi:0.1002/0470055464

[13] H. Y. Huang, “A Direct Method for the General Solution of a System of Linear Equations,” Optimization Theory and Application, Vol. 16, No. 5, 1975, pp. 429-445.

[14] E. Spedicato and E. Bodon, “ABSPACK 1: A Package of ABS Algorithms for Solving Linear Determined, Underdetermined and Overdetermined Systems.” www.unibg.it/dati/persone/636/404.pdf

[15] E. Spedicato, “ABS Algorithm for Linear Systems and Linear Least Squares: Theoretical Results and Computational Performance,” Scientia Iranica, Vol. 1, 1995, pp. 289-303.

[16] J. Abaffy and E. Spedicato, “ABS Projection Algorithms: Mathematical Techniques for Linear and Nonlinear Equations,” Ellis Horwood Ltd., Chichester, 1989.

[17] E. Spedicato and E. Bodon, “Solution of Linear Least Squares via the ABS Algorithms,” Mathematical Programming, Vol. 58, No. 1-3, 1993, pp. 111-136. doi:0.1007/BF01581261

[18] Numerical Algorithms Group (NAG) Codes. http://www.nag.co.uk/

[19] E. Spedicato, “On the Solution of Linear Least Squares through the ABS Class for Linear Systems,” AIRO Conference, 1985, pp. 89-98.

[20] Linear Least Squares (Mathematics), Motivational Example on Wikipedia. http://en.wikipedia.org/wiki/Linear_least_squares_%28mathematics%29#Motivational_example

[1] E. Spedicato, E. Bodon, Z. Xia and N. Mahdavi-Amiri, “ABS Method for Continuous and Integer Linear Equations and Optimization,” Central European Journal of Operations Research, Vol. 18, No. 1, 2010, pp. 73-95. doi:0.1007/s10100-009-0128-9

[2] S. Lalwani, R. Kumar, E. Spedicato and N. Gupta, “An Application of the ABS LX Algorithm to Multiple Sequence Alignment,” Iranian Journal of Operations Research, Vol. 3, 2012, pp. 31-45.

[3] S. Lalwani, R. Kumar, V. Rastogi and E. Spedicato, “An Application of the ABS LX Algorithm to Schedule Medical Residents,” Journal of Computer and Information Technology, Vol. 1, 2011, pp. 95-118.

[4] S. S. Rich, “Genetics of Diabetes and Its Complications,” Journal of the American Society of Nephrology, Vol. 17, No. 2, 2006, pp, 353-360. doi:0.1681/ASN.2005070770

[5] World Health Statistics Report, 2012. http://www.diabetes24-7.com/?p=1272

[6] A. Ramachandran, C. Snehalatha, A. S. Shetty and A. Nanditha, “Trends in Prevalence of Diabetes in Asian Countries,” World Journal of Diabetes, Vol. 3, No. 6, 2012, 110-117. doi:0.4239/wjd.v3.i6.110

[7] C. L. Lawson and R. J. Hanson, “Solving Least Squares Problems,” Society for Industrial and Applied Mathematics, 1995. doi:0.1137/1.9781611971217

[8] A. Bjorck, “Numerical Methods for Least Squares Problems,” Society for Industrial and Applied Mathematics, 1996. doi:0.1137/1.9781611971484

[9] J. Abaffy, C. G. Broyden and E. Spedicato, “A Class of Direct Methods for Linear Equations,” Numerische Mathematic, Vol. 45, 1984, pp. 361-376.

[10] J. Abaffy and E. Spedicato, “Numerical Experiments with the Symmetric Algorithm in the ABS Class for Linear Systems,” Optimization, Vol. 18, No. 2, 1987, pp. 197212. doi:0.1080/02331938708843232

[11] J. O. Rawlings, S. G. Pantula and D. A. Dickey, “Applied Regression Analysis: A Research Tool,” 2nd Edition, Springer, Berlin, 1998. doi:0.1007/b98890

[12] S. Chatterjee and A. A. S. Hadi, “Regression Analysis by Example,” 4th Edition, Wiley Interscience, 2006. doi:0.1002/0470055464

[13] H. Y. Huang, “A Direct Method for the General Solution of a System of Linear Equations,” Optimization Theory and Application, Vol. 16, No. 5, 1975, pp. 429-445.

[14] E. Spedicato and E. Bodon, “ABSPACK 1: A Package of ABS Algorithms for Solving Linear Determined, Underdetermined and Overdetermined Systems.” www.unibg.it/dati/persone/636/404.pdf

[15] E. Spedicato, “ABS Algorithm for Linear Systems and Linear Least Squares: Theoretical Results and Computational Performance,” Scientia Iranica, Vol. 1, 1995, pp. 289-303.

[16] J. Abaffy and E. Spedicato, “ABS Projection Algorithms: Mathematical Techniques for Linear and Nonlinear Equations,” Ellis Horwood Ltd., Chichester, 1989.

[17] E. Spedicato and E. Bodon, “Solution of Linear Least Squares via the ABS Algorithms,” Mathematical Programming, Vol. 58, No. 1-3, 1993, pp. 111-136. doi:0.1007/BF01581261

[18] Numerical Algorithms Group (NAG) Codes. http://www.nag.co.uk/

[19] E. Spedicato, “On the Solution of Linear Least Squares through the ABS Class for Linear Systems,” AIRO Conference, 1985, pp. 89-98.

[20] Linear Least Squares (Mathematics), Motivational Example on Wikipedia. http://en.wikipedia.org/wiki/Linear_least_squares_%28mathematics%29#Motivational_example