Download e-book for iPad: Dimensionality Reduction with Unsupervised Nearest Neighbors by Oliver Kramer

By Oliver Kramer

ISBN-10: 3642386512

ISBN-13: 9783642386510

ISBN-10: 3642386520

ISBN-13: 9783642386527

This ebook is dedicated to a unique method for dimensionality relief in line with the recognized nearest neighbor approach that could be a strong category and regression procedure. It begins with an creation to desktop studying strategies and a real-world program from the power area. Then, unsupervised nearest friends (UNN) is brought as effective iterative process for dimensionality relief. a variety of UNN versions are built step-by-step, achieving from an easy iterative technique for discrete latent areas to a stochastic kernel-based set of rules for studying submanifolds with self reliant parameterizations. Extensions that permit the embedding of incomplete and noisy styles are brought. numerous optimization techniques are in comparison, from evolutionary to swarm-based heuristics. Experimental comparisons to comparable methodologies bearing in mind man made try facts units and likewise real-world info display the habit of UNN in sensible eventualities. The publication includes various colour figures to demonstrate the brought strategies and to focus on the experimental results.

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Xl , yl )} and a set of unlabeled patterns U = {˜ The idea of semi-supervised learning is that the unlabeled data enriches the learning process by yielding implicit information about the underlying data distributions. Propagating 1-nearest neighbor works as follows. In each step, the unlabeled pattern closest to any of the (already) labeled patterns is selected ˜ ∗ = min min x ˜ − x 2. 15) ˜ ∈U x∈L x Its label y is determined by the label of the nearest neighbor x in the set of labeled patterns L.

1(a), we can observe that neighborhood sizes around K = 4 to K = 6 are optimal for small training sets. On larger training 32 3 Ensemble Learning sets (2−1 ), the influence of the neighborhood size is less significant. If many patterns are available, KNN can average over more training patterns without a deterioration of the classification error. In case of the ensemble ENS*, the neighborhood size of KNN is less important for both larger training sets 3−1 and 2−1 . The SVM classifiers compensate the negative effect of too large neighborhoods, which is a good motivation for the employment of ensembles.

Further, for highdimensional and non-linear data, SVMs use kernel functions that project the data into a feature space of higher dimensions. In this transformed feature space, the patterns become linearly separable, and the decision hyperplane can be computed. We will employ kernel functions in Chapter 7 for dimensionality reduction tasks. , high dimensions and sparse data [40], while KNN is a local method, appropriate for low-dimensional data spaces and a large number of training patterns. Hence, the hybridization of both classifiers is a reasonable undertaking in practical applications, where training set sizes and numbers of features may vary.

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Dimensionality Reduction with Unsupervised Nearest Neighbors by Oliver Kramer

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