Journal of South China University of Technology (Natural Science Edition) ›› 2007, Vol. 35 ›› Issue (1): 123-128.

• Computer Science & Technology • Previous Articles     Next Articles

Determination of Independent Variable Number in Multi -Variable Statistical Analysis

Yao Zhi-xiαng1  Jian Hua li2  Liu Huan-bin1   

  1. 1. State Key Laboratory of Pulp and Paper Engineering , South China Univ. of Tech. , Guangzhou 510640 , Guangdong , China;2. College of Food Science , South China Agricultural Univ. , Guangzhou 510642 , Guangdong , China)
  • Received:2005-12-20 Online:2007-01-25 Published:2007-01-25
  • Contact: 姚志湘(1968-)，男，博士后，广西工学院副教授，主要从事化学计量学方面的研究。 E-mail:zxyao@21cn.com
  • About author:姚志湘(1968-)，男，博士后，广西工学院副教授，主要从事化学计量学方面的研究。
  • Supported by:

    中国博士后科学基金资助项目(2005037583) ;广西自然科学基金资助项目(桂科基0448010)

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Abstract:

In the multi-variable system , there generally exist errors in the determination of independent variable number based on covariance matrix eigenvalues because of the nonuniformity in data space. To solve this problem ,a method is proposed to determine the independent variable number in multi-variable statistical analysis. In this method , sample data are first changed in Mahalanobis distance , and are then added with uniform white noise to shield the nonuniformity in data space. Mter the processing with uniform white noise , by arraying the covariance matrix eigenvalues in descending order and calculating the eigenvalues logarithm , the second difference is obtained.So , a successive value is deduced , which is divided distinctly into two parts , one is related to the noise that is al-most equal to zero , and the other is related to the independent variables that are obviously different from zero , ma-king the independent variable number accurately determined. The simulation example and the experiments all re-veal that the proposed method is exact , distinct and steady.

Key words: multi-variable system, independent variable, number, white noise, independent component analysis