Abstract:  Voluminous researches locus on the subspace method of lcature extraction for pattern recogmtion. Particularly, the weighted subspace method is important for feature extraction. But these weights almost arc marr
made set up in these methods, such as the fuzzy inverse Fisher discriminated analysis and the locality preserving protections and linear Laplacian discrimination et al. And the way of embedding weight into scatter matrix cannot
reflect the relation between training sample and subclass. From this，a new weighted scatter matrix is proposed in this paper. We redefine the weighted covariance matrix of principal component analysis and the weighted scatter
matrix of maximum margin criterion. The new weighted definition shows clearly the essential meaning of weight, In weighted kernel principal component analysis，the weights arc embedded into the difference between kernel
transformation of training sample and kernel transformation of subclass center, and the summation operation is replaced with matrix operation when computing kernel matrix in kernel principal component analysis by means of
simply matrix conversion and substitution, In weighted maximum margin criterion, the difference between subclass center and total training sample center is transformed into the difference between training sample and subclass
center, In this case weight much more can embody the relation between training sample and its affiliated subclass. And the weighted betwecrrclass scatter matrix is transformed into the product of some matrix and its transport
matrix, It can ensure that weighted between-class scatter matrix is real symmetric matrix, and is not influenced by the computer accuracy. However, the real symmetry is very important to ensure that the obtained Eigen values are
real number, In order to get more general weighted method，in this paper, a self-learning weighted method is provided.The proposed method updates the weight value of training sample to subclass prototype in both directions
according to some criterion, which incrcate the wci}ht of training sample to its affiliated subclass prototype and decrease the weight of training sample to other subclass prototype. Experiences results show that the proposed
algorithm enjoys more rate of recognition and more stability. At the beginning of a recursion, all of weights are assigned an initial value by equal probability, and then calculating the corresponding transformational operators.To
determine changes direction, the fuzzy memberships of training samples to subclass are used as new weight，and then computing its corresponding transformational operator. And we compute further the offset values of each
training samples to subclass prototype in corresponding subclass. When the learning sample belongs to similar subclass with subclass prototype，the weight is increased if current distance is less than the previous distance and
current weight is greater than the previous weight. When the training samples belong to different subclasses with subclass prototype，the weight is decreased if current distance is greater than the previous distance and current
weight is less than the previous weight. Obviously, this modification strategy is fully consistent with ideas of reducing withirrclass distance while increasing between-class distance. In light of this，the weighted learning
algorithm is convergent. Experiences results show that the proposed algorithm enjoys more rate of recognition and more stability.