{"responseHeader":{"status":0,"QTime":6,"params":{"q":"{!q.op=AND}id:\"102867\"","hl":"true","hl.simple.post":"","hl.fragsize":"5000","fq":"!embargo_tdt:[NOW TO *]","hl.fl":"ocr_t","hl.method":"unified","wt":"json","hl.simple.pre":""}},"response":{"numFound":1,"start":0,"docs":[{"file_name_t":"Soller-Automated_Detection.pdf","thumb_s":"/fd/35/fd35aae69b21d7ea6d1494b0450ed68984a16573.jpg","oldid_t":"compsci 10980","setname_s":"ir_computersa","restricted_i":0,"format_t":"application/pdf","modified_tdt":"2016-05-26T00:00:00Z","file_s":"/61/56/61564df8900eb1d7fabe27fa74a133de364c50e6.pdf","title_t":"Page 110","ocr_t":"95 2. The initialization of U and W requires ( m'Qi - %-) multiplications and approximately the same number of additions [29] . 3. The iterative reduction of the bidiagonal matrix to diagonal form, which produces the singular values, requires less than 2m'Qi J multiplications, where J is the number of iterations required to reduce an element. Once the singular value decomposition has completed, the algorithm constructs a generalized inverse and multiplies it by the Y vector. This requires O(m'Qi) operations. A more efficient algorithm for the least squares solution calculates projections after the singular value decomposition [29] [56]. The overall asymptotic worst-case time complexity of both variations of singular value decomposition is O(m'QiJ). Therefore, the time complexity results from the choice of least squares algorithm, and the utilization of more efficient least squares algorithms provide the greatest time complexity improvement in finding the optimal solution. The asymptotic worst-case space complexity is O(m'Q1). Therefore, the time complexity of the STP networks is comparable to the RBF networks and lower than multilayer perceptrons. 11.8 Introduction to Regularization Theory The weighted least squares solutions presented in this chapter attempt to optimize a performance measure over the training data set. In many cases, the system has many degrees of freedom, and the resulting solution overfits the training data. The solution of ill-conditioned systems, where the solution often overfits the data, is sensitive to small perturbations. Regularization methods apply a degree of smoothing to the problem by filtering the solution or imposing constraints. The small solution norm constraint is one form of regularization. Methods for achieving this, while the squared error performance measure remains small, include the following: • linear equality or inequality constraint equations [65],","id":102867,"created_tdt":"2016-05-26T00:00:00Z","parent_i":102961,"_version_":1642982670139916289}]},"highlighting":{"102867":{"ocr_t":[]}}}