Research on model of early2warning of enterprise crisis based on entropy

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1 24 1 Vol. 24 No. 1 ont rol an d Decision Jan : (2009) , 1, 2 (1., ; 2., ) :. ;,,. 2.,,. : ; ; ; : F : 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 , hina ; 2. Information Technology Research Institute, hina enter of Information Industry Development, Beijing , hina. orrespondent : TAN G Bao2jun, E2mail : 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., : ; : : ( ). : (1972 ),,,,,; (1947 ),,,,,.

2 114 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 ,.., (),. 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) 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 ].

3 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)

4 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).,, ,., 10. ( ST). (ST) (ST) , 12 ST ST ST ST ST ST ST ST ST ST ST ST ST : : / http :/ / www. stockstar. com/ home. ht m

5 1 : p i qi ( pi qi) 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 : ,50 6. c = 2, Lagrange,,. Lagrange T 1,. [8 ], Lagrange. [7 ], Matlab 5. 2.,, Lagrange T,.,2008 1, ,,,.,. 3. D 3 1 ( ST ) (ST ) % ( ST) (ST) ,,, 2, 2. 4, 2. 4,,,.,.. : 1), ;2),, ;3),. ( References) [1 ],. [J ]., 2001, 37 (6) : (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) : ) [2 ],,. [J ]., 2004, 26 (5) : (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) : ) (121 )

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