計算機專業畢業設計文獻翻譯-其他專業(編輯修改稿)

　

【文章內容簡介】 nge in entropy value () is small or the number of iterations is exceeded, otherwise go to (3). (7) Estimate W, E in the primal space after estimating the eigenfunctions from the Nystrom approximation. Illustrative examples are shown in on a noisy sinc function and a double spiral classification problem, both with RBF kernels,. A bad initial choice of the support vectors is intentionally taken, after which a self anizing process is taking place. Corresponding plots for the evolution of the entropy criterion are shown. An important aspect of the algorithm is that the determination of the support vectors is done independently of the regression problem of W, B after estimating E. in other words, not in every iteration step one needs to estimate W, B. This also means that in this algorithm the tuning parameters (R, A) can be determined separately form each other. First, a good choice of Q is determined in relation to the chosen number of support vectors M. Then on may apply . Bayesian learning in order to automatically determine R. note that also in classical radial basis function work learning, methods have been developed where one separates the training of the centers from the training of the output weights. In RBF works the centers are often determined by means of clustering [39。 40] or using w vector quantization method eventually in bination with selfanizing maps [134] to visualize the input space of the work. In a fixed size LSSVM this is done through the explicit primaldual interpretations (). Because the model is estimated in the primal space the estimation problem bees parametric. In this sense, one may also consider applying other methods such as Bayesian learning to the determination of the width of the kernel instead of applying the entropy criterion which only takes into account the input space of the work. The fixed size LSSVM method is also suitable for adaptive signal processing applications where online updating of W, B and recursive methods for the eigenvalue deposition can be applied. Both for recursive least squares and singular value deposition updating, various efficient algorithms have been developed in the past [109。 138。 165。 166。 167。 190。 298], which can be used at this point. Also for transductive inference the use of fixed size LSSVM is very natural due to the fact that the search of support vectors is done in an unsupervised way. In transductive inference [90。 278。 279。 281] one is rather interested in finding a model which is performing well on a specific future data, point (or set of data points) than a general model (as obtained by inductive inference). In other words in transduction one is interested in inference from particular to particular. The future points on which the model should perform well are used in a unlabeled way (for classifiers) or without output target values (for regression), . in an unsupervised way, to improve the quality of the model. If for fixed size LSSVM one knows future data (in addition to the given training data) on which the model should perform well, then one may take these points into account (without class labels or target values) for possible selection of support vectors. In N = 200 training data were generated for a sinc function with zero mean white Gaussian noise with standard deviation . A fixed size M = 10 was taken and an RBF kernel with Q2 = 3. in N = 20210 were generated for a noisy sinc, with the same model. In N = 400 training data were generated and a fixed size LSSVM model with RBF kernel was taken for M = 20. An application of Fixed Size LSSVM with RBF kernel to the UCI adult data set with a training set of 22021 data and a validation set of 11000 data gives the following validation set performance indication: M = 20. The value of R is determined by Bayesian inference. Basis construction in the feature space Another approach to large scale problems is to find a suitable set of basis vectors in the feature space in order to build and span a large subspace (). The following method has been proposed by Cawley [37] for LSSVMs. Fixed Size LSSVM with M = 10 and N = 200 on a noisy sinc function. The support vectors are actively selected by means of entropy criterion (). A bad initial choice of support vectors (grey dots) is intentionally taken, which after a number of iterations leads to a uniform distribution of support vectors over the xaxis. The figures show different stages of this self anizing process. The plete LSSVM model based on N training data for function estimation takes the form () where a, b are the solution (). For the solution vector in the primal weight space one has (). In other words, W is represented by means of a basis 公式 consisting of N vectors. In order to find a sparse representation one expresses W in terms of fewer basis vectors 公式 . These vectors Qk all belong to the set of training data 公式 . One expresses () where typically M N. Such an approach has also been proposed by Scholkopf et al. in [204]. In terms of this reduced set the model takes the form (). (Continued)(Top) entropy with respect to iteration steps。 (Button) Corresponding error on an independent test set for the noisy sinc function of the previous figure. Fixed size LSSVM for a noisy sinc function with M = 10 and N = 20210. (Top) given training set。 (Bottom) true sinc function (solid line), estimate of Fixed Size LSSVM (dashed line), and support vectors (grey dots). Fixed size LSSVM with M = 20 and N = 400 for a double spiral classification problem. The support vectors are actively selected by means of a entropy criterion. The figures show different stages of this selfanizing process of support vector selection. (Continued) corresponding plot of the entropy during the iteration process. In [37] the following