In this study, a new Stacked Generalization technique called Fuzzy Stacked Generalization (FSG) is proposed to minimize the difference between N -sample and large-sample classification error of the Nearest Neighbor classifier. The proposed FSG employs a new hierarchical distance learning strategy to minimize the error difference. For this purpose, we first construct an ensemble of base-layer fuzzy k- Nearest Neighbor (k-NN) classifiers, each of which receives a different feature set extracted from the same sample set. The fuzzy membership values computed at the decision space of each fuzzy k-NN classifier are concatenated to form the feature vectors of a fusion space. Finally, the feature vectors are fed to a meta-layer classifier to learn the degree of accuracy of the decisions of the base-layer classifiers for meta-layer classification. Rather than the power of the individual base layer-classifiers, diversity and cooperation of the classifiers become an important issue to improve the overall performance of the proposed FSG. A weak base-layer classifier may boost the overall performance more than a strong classifier, if it is capable of recognizing the samples, which are not recognized by the rest of the classifiers, in its own feature space. The experiments explore the type of the collaboration among the individual classifiers required for an improved performance of the suggested architecture. Experiments on multiple feature real-world datasets show that the proposed FSG performs better than the state of the art ensemble learning algorithms such as Adaboost, Random Subspace and Rotation Forest. On the other hand, compatible performances are observed in the experiments on single feature multi-attribute datasets.
In Section , we define the problem of minimizing the error difference between @math -sample and large-sample error in a single classifier. Then, we introduce the distance learning approach for an ensemble of classifiers considering the distance learning problem as a decision space design problem in Section . Employment of the proposed hierarchical distance learning approach in the FSG and its algorithmic description is given in Section . We discuss expertise of base-layer classifiers and the dimensionality problems of the feature spaces in FSG, and its computational complexity in Section . In order to compare the proposed FSG with the state of the art ensemble learning algorithms, we have implemented Adaboost, Random Subspace and Rotation Forest in the experimental analysis in Section . Moreover, we have used the same multi-attribute benchmark datasets with the same data splitting given in @cite_29 @cite_24 to compare the performance of the proposed hierarchical distance learning approach with that of the aforementioned distance learning methods. Since the classification performances of these distance learning methods are analyzed in @cite_29 @cite_24 in detail, we do not reproduce these results in Section and refer the reader to @cite_29 @cite_24 .
@cite_24 @cite_29
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In order to optimize the accuracy of the nearest-neighbor classification rule, a weighted distance is proposed, along with algorithms to automatically learn the corresponding weights. These weights may be specific for each class and feature, for each individual prototype, or for both. The learning algorithms are derived by (approximately) minimizing the leaving-one-out classification error of the given training set. The proposed approach is assessed through a series of experiments with UCI STATLOG corpora, as well as with a more specific task of text classification which entails very sparse data representation and huge dimensionality. In all these experiments, the proposed approach shows a uniformly good behavior, with results comparable to or better than state-of-the-art results published with the same data so far We study the problem of selecting a subset of big data to train a classifier while incurring minimal performance loss. We show the connection of submodularity to the data likelihood functions for Naive Bayes (NB) and Nearest Neighbor (NN) classifiers, and formulate the data subset selection problems for these classifiers as constrained submodular maximization. Furthermore, we apply this framework to active learning and propose a novel scheme called filtered active submodular selection (FASS), where we combine the uncertainty sampling method with a submodular data subset selection framework. We extensively evaluate the proposed framework on text categorization and handwritten digit recognition tasks with four different classifiers, including deep neural network (DNN) based classifiers. Empirical results indicate that the proposed framework yields significant improvement over the state-of-the-art algorithms on all classifiers. We introduce a new probabilistic proximity search algorithm for range and A"-nearest neighbor (A"-NN) searching in both coordinate and metric spaces. Although there exist solutions for these problems, they boil down to a linear scan when the space is intrinsically high dimensional, as is the case in many pattern recognition tasks. This, for example, renders the A"-NN approach to classification rather slow in large databases. Our novel idea is to predict closeness between elements according to how they order their distances toward a distinguished set of anchor objects. Each element in the space sorts the anchor objects from closest to farthest to it and the similarity between orders turns out to be an excellent predictor of the closeness between the corresponding elements. We present extensive experiments comparing our method against state-of-the-art exact and approximate techniques, both in synthetic and real, metric and nonmetric databases, measuring both CPU time and distance computations. The experiments demonstrate that our technique almost always improves upon the performance of alternative techniques, in some cases by a wide margin. The essence of distantly supervised relation extraction is that it is an incomplete multi-label classification problem with sparse and noisy features. To tackle the sparsity and noise challenges, we propose solving the classification problem using matrix completion on factorized matrix of minimized rank. We formulate relation classification as completing the unknown labels of testing items (entity pairs) in a sparse matrix that concatenates training and testing textual features with training labels. Our algorithmic framework is based on the assumption that the rank of item-by-feature and item-by-label joint matrix is low. We apply two optimization models to recover the underlying low-rank matrix leveraging the sparsity of feature-label matrix. The matrix completion problem is then solved by the fixed point continuation (FPC) algorithm, which can find the global optimum. Experiments on two widely used datasets with different dimensions of textual features demonstrate that our low-rank matrix completion approach significantly outperforms the baseline and the state-of-the-art methods.