Dimensionality Reduction with Unsupervised Nearest Neighbors by Oliver Kramer

By Oliver Kramer

This e-book is dedicated to a unique technique for dimensionality aid in keeping with the recognized nearest neighbor process that may be a strong class and regression strategy. It starts off with an advent to computer studying thoughts and a real-world program from the strength area. Then, unsupervised nearest acquaintances (UNN) is brought as effective iterative strategy for dimensionality relief. numerous UNN versions are constructed step-by-step, attaining from an easy iterative process for discrete latent areas to a stochastic kernel-based set of rules for studying submanifolds with autonomous parameterizations. Extensions that permit the embedding of incomplete and noisy styles are brought. quite a few optimization techniques are in comparison, from evolutionary to swarm-based heuristics. Experimental comparisons to comparable methodologies considering man made try out information units and in addition real-world info exhibit the habit of UNN in functional situations. The booklet includes quite a few colour figures to demonstrate the brought suggestions and to spotlight the experimental results.

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6 Experimental Analysis of SVM-KNN-Ensemble 31 be observed that the smallest rate α = 10−1 , corresponding to a training set size of N = 262 patterns, can achieve an accuracy of up to ≈ 95% for the SVM-KNN-ensemble ENS* and also for the SVM with linear kernel. 89%) is achieved with KNN and K = 7. For the SVM approach, we can observe that a linear kernel achieves better results than an RBF-kernel and better results than KNN with K = 5 and K = 7 for training sets smaller and equal to 6−1 . While the SVM with linear kernel takes significantly longer for training with training set sizes larger than 5−1 , it is a good recommendation for small training set sizes.

04 2 (a) 4 6 8 K 10 12 14 (b) Fig. t. training set size 5−1 , 3−1 , and 2−1 for (a) KNN and (b) ENS*. The neighborhood size has a significant influence on the classification error in case of the KNN classifiers, but the effect is compensated in the ensemble. 3 Neighborhood Sizes of KNN In the following, we analyze the influence of neighborhood size K of the KNN classifiers and of ensemble ENS* on the recognition rate. t. different training set sizes. 1(a), we can observe that neighborhood sizes around K = 4 to K = 6 are optimal for small training sets.

In LOO-CV, one pattern is left out for prediction based on the remaining N − 1 training patterns. The whole procedure is repeated N times. 6 Curse of Dimensionality Many machine learning methods have problems in high-dimensional data spaces. The reason is an effect also know as curse of dimensionality or Hughes effect. In high-dimensional data spaces, many patterns are required to cover the whole data space, and our intuition often breaks down. Hastie et al. [40] gives interesting arguments for this effect that we review in the following.

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