「鑑別式分析特徵萃取法」(Discriminant Analysis Feature Extraction)在最近數十年已經廣泛應用於降低資料維度，萃取資料特徵。雖然，此方法易於使用，然而，此方法所依循的準則存在某些既有之缺點。例如，只利用類別中心(class-mean)鑑別資訊來萃取特徵，以及過度強調類別間之遠距離特徵等問題。在此研究中，我們針對這些問題提出討論及改善。

　　我們提出一個混合式線性特徵萃取法，利用一個新研發之分類錯誤估計法來整合類別中心和共變異矩陣鑑別資訊。待整合之兩種特徵萃取方法分別是aPAC與CMFE。aPAC乃一加權DAFE之特徵萃取法，此法可改善有關類別間遠距離被特徵過度強調之問題。

　　一般而言，這兩種不同的準則是很難直接合併的。為了克服因直接合併所衍生之次佳化(suboptimum)問題，我們利用一個新研發分類錯誤估計法充當媒介使兩者融合。我們亦將此分類錯誤估計法推展出一疊代梯度下降法(iterative gradient descent algorithm)，在定額特徵之需求下，得以微調獲取更有效之特徵組合。實驗的結果顯示提出的方法可以互補aPAC及CMFE兩者所提供的鑑別資訊並且也有不錯的效果。

　　In the past decades, the discriminant analysis feature extraction (DAFE) has been successfully applied to a variety of applications for the purpose of data dimension reduction. Although the DAFE method is easy to use, an ineffective feature extraction often occurs due to the weakness of its criterion. In this study, attentions are focused on the problems caused by the design based only on class-mean discriminant information and its overemphasis upon relatively large distances between classes.

　　We propose a hybrid linear feature extraction that uses both class-mean and covariance discriminant information simultaneously by combining two existing feature extraction methods, the approximate pairwise accuracy criterion (aPAC) and the common mean feature extraction (CMFE). By incorporating a weighting function into the criterion of DAFE, the aPAC can mitigate the problem with an overemphasis upon relatively large distances.

　　A suboptimum problem has emerged from a direct combination of aPAC and CMFE due to the difficulty in fusing their criteria. To overcome the problem, a parametric multiclass error estimation is developed as an intermediary for the combination of aPAC and CMFE. Based on the new parametric multiclass error estimation method, we have also developed an iterative gradient descent algorithm as a fine-tuning for a feature set in a predetermined size.

　　Experiments have shown that our proposed methods can take advantage of the complementary information provided by aPAC and CMFE, leading to a satisfactory performance.

1. N. R. Pal and V. K. Eluri, ”Two Efficient Connectionist Schemes for Structure Preserving Dimensionality Reduction,” IEEE Trans. Neural Networks, vol. 9, no.6, pp. 1142-1154, Nov. 1998.

2. A. Jain and D. Zongker, “Feature selection: Evaluation, application, and small sample performance,” IEEE Trans. Pattern Anal. Machine Intell., vol. 19, no. 2, pp. 153-158, Feb. 1997.

3. K. Fukunaga, Introduction to Statistical Pattern Recognition, second ed., San Diego: Academic Press Inc., 1990.

4. H. M. Lee, C. M. Chen, J. M. Chen and Y. L. Jou, ”An Efficient Fuzzy Classifier with Feature Selection Based on Fuzzy Entropy,” IEEE Trans. Syst. ,Man, Crbern. B., vol. 31, no. 3, pp. 426-432, Jun. 2001.

5. R. Thawonmas and S. Abe, ”A novel approach to feature selection based on analysis of class regions,” IEEE Trans. Syst., Man, Cybern. B., vol. 29, pp. l196-207, Apr. 1997.

6. David Landgrebe, “Information Extraction Principles and Methods for Multispectral and Hyperspectral Image Data,” in information processing for Remote Sensing, C. H. Chen, Ed., World Scientific, 2000, Ch. 1. [Online]. Available: http:// dynamo.ecn.purdue.edu/~landgreb/publications.html

7. J. A. Richards, Remote Sensing Digital Image Analysis. New York: Springer-Verlag, 1993.

8. M. Loog, R. P. W. Duin and R. Haeb-Umbach, “Multiclass Linear Dimension Reduction by weighted Pairwise Fisher Criteria,” IEEE Trans. Patt. Anal. Machine Intell., vol. 23, no. 7, pp. 762-766, Jul. 2001.

9. C. Lee and D. A. Landgrebe, "Feature Extraction Based on Decision Boundaries," IEEE Trans. Patt. Anal. Machine intell., vol. 15, no. 4, pp. 388-400, Apr. 1993.

10. E. Choi and C. Lee, “Optimizing feature extraction for multiclass problems,” IEEE Trans. Geosci. Remote Sens., vol. 39, no. 3, pp. 521-528, Mar. 2001.

11. P. F. Hsieh and D. A. Landgrebe, ”Linear Feature Extraction For Multiclass Problems,” Proc. int. Geoscience and Remote Sensing Symp., ( IGARSS '98), vol. 4, pp. 2050-2052, Jul. 1998.

12. E. Choi and C. Lee, “Bayes Error Evaluation of the Gaussian ML Classifier,” IEEE Trans. Geosc. Remote Sens., vol. 38, no. 3, pp. 1471-1475, May 2000.

13. E. Choi and C. Lee, ”Feature extraction based on the Bhattacharyya distance,” Pattern Recognition, vol. 36, pp. 1703-1709, Aug. 2003.

14. M. Á. Carreira-Perpiñán, “Mode-Finding for Mixtures of Gaussian Distributions”, IEEE Trans. Patt. Anal. Machine intell., vol. 22, no. 11, pp. 1318-1323. Nov. 2000.

15. B.-C. Kuo and D. A. Landgrebe, "A robust classification procedure based on mixture classifiers and nonparametric weighted feature extraction," IEEE Trans. Geosc. Remote Sens., vol. 40, no. 11, pp. 2486-2494, Nov. 2002.

16. Http://shay.ecn.purdue.edu/~frdata/FRData/data/78data/

17. R. Lotlikar and R. Kothari, “Adaptive linear dimensionality reduction for classification,” Pattern Recognition, vol. 33, pp. 185-294, Feb. 2000.

18. D. G. Luenberger, Linear and Nonlinear Programming, Addison-Wesley, 1984.