tailieunhanh - Supply Chain Management New Perspectives Part 8

Tham khảo tài liệu 'supply chain management new perspectives part 8', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Information Gathering and Classification for Collaborative Logistics Decision Making 267 to be of practical use. One solution to this situation is to map the input space into a feature space of higher dimension and find the optimal hyperplane there. Let z x the corresponding vector notation in the feature space Z. Being w a normal vector perpendicular to the hyperplane we find the hyperplane w X z b 0 defined by the pair w b such that we can separate the point x according to the f xi sign w X zi b subject to yi w X Zi b 0. In the case that the examples are not linearly separable a variable penalty can be introduced into the objective function for mislabeled examples obtaining an objective function f xi sign w X zi b subject to yi w X zi b 1- j. SVM formulations discussed so far require positive and negative examples can be separated linearly . the decision limit should be a hyperplane. However for many data set of real life the decision limits are not linear. To cope with linearly non-separable data the same formulation and solution technique for the linear case are still in use. Just transform your data into the original space to another space usually a much higher dimensional space for a linear decision boundary can separate positive and negative examples in the transformed space which is called feature space. The original data space is called the input space. Thus the basic idea is that the map data in the input space X to a feature space F via a nonlinear mapping 0 0 X F 3 X 0 x 4 The problem with this approach is the computational power required to transform the input data explicitly to a feature space. The number of dimensions in the feature space can be enormous. However with some useful transformations a reasonable number of attributes in the input space can be achieved. Fortunately explicit transformations can be avoided if we realize that the dual representation both the construction of the optimal hyperplane in F and the corresponding function .