24 1 Vol. 24 No. 1 ont rol an d Decision 2009 1 Jan. 2009 : 100120920 (2009) 0120113205 1, 1, 2 (1., 100083 ; 2., 100846) :. ;,,. 2.,,. : ; ; ; : F270. 5 : A Research on model of early2warning of enterprise crisis based on entropy TA N G B ao2j un 1, Q I U W an2hua 1, S U N X i ng 2 (1. School of Economics and Management, Beihang University, Beijing 100083, hina ; 2. Information Technology Research Institute, hina enter of Information Industry Development, Beijing 100846, hina. orrespondent : TAN G Bao2jun, E2mail : tang_baojun @126. com Abstract : Based on entropy optimal theory, a new model for early2warning of crisis is established. Firstly, minimum J2divergence entropy is applied to feature extraction. Then the calculating result is classified to judge state of enterprise with a new clustering algorithm, maximum entropy clustering algorithm, which is a development and extension of hard 2means. Finally, an example in early2warning of enterprise crisis is given to validate the model. The result s show the feasibility and validity of the model. The research work supplies a new way for early2warning of enterprise crisis. ey words : Early2warning of enterprise crisis ; Minimum J2divergence entropy ; Feature extraction ; Entropy clustering algorithm 1,,,.,.,.,,. : [1 ] Fisher Logit ; [2 ] ; [3 ] BP ; [4 ].,,. 2., : 2007210210 ; : 2008201229. : (70372011). : (1972 ),,,,,; (1947 ),,,,,.
114 24,. 2 x) ]. : J c [ p ( 1 x), p ( 2 x),, p ( c x) ] = c (2 1 1) 1 [ p ( i x) 1 ], (1),1..,1,L Ho spital, J 1 c [ p ( 1 x), p ( 2 x),, p ( c x) ] = c Shannon. p ( i x) log2 p ( i x), (2) Shannon. 2. 1. 2,.., (),. Shannon ( (2) ), p ( x i) ( x i),, V ( p, ) = p ( x i ) log[ p ( x i) /( x i) ] 0. (3).,;,()., W ( p, q) p ( x i) q( x i), W ( p, q) = V ( p, q) + V ( q, p) = p ( x i ) log p ( x i) q( x i ) logq( x i) + p ( x i ) logq( x i) + q( x i ) log p ( x i) 0. (4) 2. 1 2. 1. 1 Shannon [5 ] W ( p ( i) i j, q ( j) ),, ;( ),.,,,. i, j.,d, d,.,. U ( p, q) = ( pi qi) 2,, i 0 (5) W ( p, q), d.,, p ( 1 x), p ( 2 x),.,, p ( c x),h = J c [ p ( 1 x),, p ( c [5 ], N 1 ( x (1) ki ) 2 ( x (1) p (1) N 1 D ki ) 2 = 1. (6) : k 1, N 1 2, i. pi = 1,. qi. D 2. 2, (5) (6),n,k, X = x11 x12 x1 n x21 x22 x2 n = ( x ij ) k n. (7) ω x k1 x k2 x kn : x ij j i ;,2,, k; j = 1,2,, n. X X = { x1, x2,, x k} < R n. c,c,,x c X 1, X2,, X c., n1, n2,, nc,x j = { x 1 ( j), x 2 ( j),, x ( n j) j }., J, J ( X,V ) = p ( x k) x k x k X j v j. (8),. J,.,., (8).., [6 ].
1 : 115,. J = J ( X,V ) = p ( x k) 2 = p ( v j x k) x k v j 2 = p ( x k, v j ) x k v j p ( x k) J (V x k). (9),: p ( v j x k) = 1, x k X j ; 0,. (10) (9) (8),, { v j, p ( v j x k) } (,2,, ;,2,, ) (9) J,., J., X V Shannon, H ( X,V ) = p ( x k, v j ) ln p ( x k, v j ). j 1 (11) Lagrange L ( X,V ) = J ( X,V ) T H ( X,V ), (12) T Lagrange., T, ; T, ;T, J (). (12) Lagrange L. H ( X,V ) = p ( x k, v j ) ln p ( x k, v j ) = H ( X) + p ( x k) H (V x k) = H ( X) + H (V X). (13) H ( X) = p ( x k) ln p ( x k), (14) H (V x k) = H ( v1, v2,, vc x k) = p ( v j x k) ln p ( v j x k), (15) H (V X) = p ( x k) p ( v j x k) ln p ( v j x k) = p ( x k) H (V x k). (16) H ( X),, L H ( X),H (V X)., (8) J,L, H (V X),. H (V X) = p ( x k) H (V x k) p ( x k) ln = ln, min ( H (V H) ) min (ln H (V X) ),(12) min{ L T ( X,V ) = J ( X,V ) + T (ln H (V X) ) = p ( x k) L T (V x k) }, (17) L T (V x k) = J (V x k) + T (ln H (V x k) ). (18) p ( v j x k) L T ( X,V ), p ( v j x k) Gibbs, p ( v j x k) = exp [ x k v j 2 / T ], (19) Zx k Zx k = exp [ x k v j / T ]. (20) (19) (17), L T ( X,V ) L 3 T ( X,V ), L 3 T ( X,V ) = min p( v j x k ) L T ( X,V ) = T p ( x k) [ ln ln exp [ x k v j 2 / T ] ] = p ( x k) L 3 T (V x k). (21) :L 3 T ( X,V ) (), L 3 T (V x k) = Tln exp [ x k v j 2 T ] + Tln. (22) v j L 3 T ( X,V ),, p ( x k) p ( v j x k) ( x k v j ) = 0, (23) p ( x k, v j ) ( x k v j ) = 0. (24)
116 24 v j = p ( x k, v j ) x k/ p ( x k, v j ) = p ( v j ) p ( x k v j ) x k/ p ( v j ) = p ( x k v j ) x k,,2,,. (25), X = { x1, x2,, x k} < R n,p ( x k) = 1/, (23) v j = p ( v j x k) x k/ p ( v j x k),,2,,. (26),,. : 1) c, Lagrange T. 2) v j. 3), p ( v j x k) :,(19) (20) ;, (25) (26).,,. 3 2005,., 10. ( ST). (ST) (ST). 3. 1 1 2005, 12 ST 000505 ST 0. 954 0. 044 90. 830 9. 617 15. 02 0. 068 0. 038 279. 640 69. 720 11. 420 600181 ST 0. 560 0. 035 109. 070 1. 684 1. 385 0. 754 0. 097 166. 640 3 537. 040 21. 870 600338 ST 0. 359 0. 071 115. 810 7. 593 0. 216 3. 467 0. 095 168. 050 321. 910 16. 330 000430 ST 0. 156 0. 018 62. 970 29. 381 13. 654 30. 596 0. 257 46. 620 31. 100 11. 810 600369 ST 0. 822 0. 222 78. 780 3. 222 1. 929 4. 045 0. 042 12. 380 1. 900 0. 180 600753 ST 0. 988 0. 009 68. 240 0. 090 0. 126 0. 053 0. 023 295. 670 22. 780 6. 830 600090 ST 0. 471 0. 068 113. 000 2. 431 2. 504 0. 844 0. 238 2. 100 0. 610 1. 170 000710 ST 1. 023 0. 220 57. 840 2. 993 3. 675 2. 418 0. 510 10. 930 13. 510 5. 57 600695 ST 0. 747 0. 130 80. 460 14. 144 10. 739 2. 066 0. 678 28. 320 77. 830 20. 11 600093 ST 1. 128 0. 075 57. 010 2. 830 3. 132 1. 678 0. 356 18. 780 16. 640 6. 68 000928 ST 0. 877 0. 061 75. 320 3. 668 6. 312 1. 470 0. 448 15. 340 27. 420 6. 85 600848 ST 0. 913 0. 125 85. 800 3. 216 3. 619 2. 888 0. 849 0. 730 4. 380 0. 85 600597 1. 381 0. 59 38. 84 15. 349 9. 437 12. 113 1. 909 3. 06 10. 14 6. 54 000682 3. 659 1. 408 15. 58 1. 941 5. 145 5. 277 0. 432 2. 23 1. 18 1. 23 600085 2. 797 0. 808 24. 23 9. 642 4. 424 1. 089 0. 711 11. 56 13. 42 12. 58 600811 0. 807 0. 389 52. 43 33. 996 4. 355 10. 748 0. 421 3. 26 3. 11 1. 09 600855 3. 689 2. 041 21. 45 3. 605 8. 763 1. 302 0. 39 10. 92 6. 26 5. 2 000155 1. 016 0. 599 30. 53 92. 906 22. 794 6. 338 0. 705 14. 41 15. 23 12. 74 000768 2. 281 0. 247 24. 62 6. 901 10. 569 1. 198 0. 44 3. 39 2. 04 1. 59 600060 1. 603 0. 642 52. 37 27. 093 5. 756 4. 415 2. 049 1. 01 4. 17 3. 13 000813 1. 451 0. 358 45. 22 4. 64 14. 975 1. 182 0. 54 2. 76 3. 39 0. 84 000585 1. 73 0. 341 29. 24 2. 301 5. 105 5. 523 0. 419 4. 3 3. 01 3. 19 600362 1. 895 0. 412 32. 44 63. 693 28. 096 3. 207 1. 088 13. 88 25. 39 17. 75 000811 0. 885 0. 125 58. 38 8. 342 4. 454 2. 439 0. 799 4. 89 10. 21 5. 11 : : / http :/ / www. stockstar. com/ home. ht m
1 : 117 2 p i 0. 138 89 0. 058 14 0. 133 03 0. 028 99 0. 059 96 0. 018 85 0. 049 88 0. 153 49 0. 249 63 0. 109 15 qi 0. 184 52 0. 071 62 0. 222 44 0. 040 43 0. 067 88 0. 116 92 0. 077 13 0. 105 73 0. 051 92 0. 061 41 ( pi qi) 2 0. 002 08 0. 000 18 0. 007 99 0. 000 13 0. 000 06 0. 009 62 0. 000 74 0. 002 28 0. 039 09 0. 002 28 12 ST ( 1). 10 6, 1 D = 10, N = 12. 1, ( x (1) ki ) 2 = 1. pi 1 ( ST ) i, qi 2 (ST ) i, (6) 2. 2 ( pi qi) 2 6 (5), 6 :. 3. 2 2005 50,50 6. c = 2, Lagrange,,. Lagrange T 1,. [8 ], Lagrange. [7 ], Matlab 5. 2.,, Lagrange T,.,2008 1, 672 860,,,.,. 3. D 3 1 ( ST ) 0. 1 0. 7 0. 1 0. 3 0. 5 0. 3 2 (ST ) 0. 4 0. 2 0. 2 0. 4 0. 9 0. 9 4 2. 4 2 % ( ST) (ST) 2 9. 62 13. 30 8. 01 6. 70,,, 2, 2. 4, 2. 4,,,.,.. : 1), ;2),, ;3),. ( References) [1 ],. [J ]., 2001, 37 (6) : 46255. (Wu S N, L u X Y. A study of models for predicting financial distress in china s listed companies [ J ]. Economic Research Journal, 2001, 37 (6) : 46255. ) [2 ],,. [J ]., 2004, 26 (5) : 1182123. (Li J, Wang W J, Liu X Z. Application of multivariate statistics in early2warning of corporation financial crisis [J ]. J of hongqing Architecture University, 2004, 26 (5) : 1182123. ) (121 )
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