In this work, we propose a novel node splitting method for regression trees and incorporate it into the regression forest framework. Unlike traditional binary splitting, where the splitting rule is selected from a predefined set of binary splitting rules via trial-and-error, the proposed node splitting method first finds clusters of the training data which at least locally minimize the empirical loss without considering the input space. Then splitting rules which preserve the found clusters as much as possible are determined by casting the problem into a classification problem. Consequently, our new node splitting method enjoys more freedom in choosing the splitting rules, resulting in more efficient tree structures. In addition to the Euclidean target space, we present a variant which can naturally deal with a circular target space by the proper use of circular statistics. We apply the regression forest employing our node splitting to head pose estimation (Euclidean target space) and car direction estimation (circular target space) and demonstrate that the proposed method significantly outperforms state-of-the-art methods (38.5 and 22.5 error reduction respectively).
@cite_5 @cite_27 apply k-means clustering to the target space to automatically discretize the target space and assign pseudo-classes. They then solve the classification problem by rule induction algorithms for classification. Though somewhat more sophisticated, these approaches still suffer from problems due to discretization. The difference of our method from approaches discussed above is that in these approaches, pseudo-classes are fixed once determined either by human or clustering algorithms while in our approach, pseudo-classes are redetermined at each node splitting of regression tree training. Similarly to our method, @cite_23 converts node splitting tasks into local classification tasks by applying EM algorithm to the joint input-output space. Since clustering is applied to the joint space, their method is not suitable for tasks with high dimensional input space. In fact there experiments are limited to tasks with upto 20 dimensional input space, where their method performs poorly compared to baseline methods.
@cite_5 @cite_27 @cite_23
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In this paper, we present "k-means+ID3", a method to cascade k-means clustering and the ID3 decision tree learning methods for classifying anomalous and normal activities in a computer network, an active electronic circuit, and a mechanical mass-beam system. The k-means clustering method first partitions the training instances into k clusters using Euclidean distance similarity. On each cluster, representing a density region of normal or anomaly instances, we build an ID3 decision tree. The decision tree on each cluster refines the decision boundaries by learning the subgroups within the cluster. To obtain a final decision on classification, the decisions of the k-means and ID3 methods are combined using two rules: 1) the nearest-neighbor rule and 2) the nearest-consensus rule. We perform experiments on three data sets: 1) network anomaly data (NAD), 2) Duffing equation data (DED), and 3) mechanical system data (MSD), which contain measurements from three distinct application domains of computer networks, an electronic circuit implementing a forced Duffing equation, and a mechanical system, respectively. Results show that the detection accuracy of the k-means+ID3 method is as high as 96.24 percent at a false-positive-rate of 0.03 percent on NAD; the total accuracy is as high as 80.01 percent on MSD and 79.9 percent on DED We propose novel cooperative spectrum sensing (CSS) algorithms for cognitive radio (CR) networks based on machine learning techniques which are used for pattern classification. In this regard, unsupervised (e.g., K-means clustering and Gaussian mixture model (GMM)) and supervised (e.g., support vector machine (SVM) and weighted K-nearest-neighbor (KNN)) learning-based classification techniques are implemented for CSS. For a radio channel, the vector of the energy levels estimated at CR devices is treated as a feature vector and fed into a classifier to decide whether the channel is available or not. The classifier categorizes each feature vector into either of the two classes, namely, the "channel available class" and the "channel unavailable class". Prior to the online classification, the classifier needs to go through a training phase. For classification, the K-means clustering algorithm partitions the training feature vectors into K clusters, where each cluster corresponds to a combined state of primary users (PUs) and then the classifier determines the class the test energy vector belongs to. The GMM obtains a mixture of Gaussian density functions that well describes the training feature vectors. In the case of the SVM, the support vectors (i.e., a subset of training vectors which fully specify the decision function) are obtained by maximizing the margin between the separating hyperplane and the training feature vectors. Furthermore, the weighted KNN classification technique is proposed for CSS for which the weight of each feature vector is calculated by evaluating the area under the receiver operating characteristic (ROC) curve of that feature vector. The performance of each classification technique is quantified in terms of the average training time, the sample classification delay, and the ROC curve. Our comparative results clearly reveal that the proposed algorithms outperform the existing state-of-the-art CSS techniques. In this work we investigate the applicability of unsupervised feature learning methods to the task of automatic genre prediction of music pieces. More specifically we evaluate a framework that recently has been successfully used to recognize objects in images. We first extract local patches from the time-frequency transformed audio signal, which are then pre-processed and used for unsupervised learning of an overcomplete dictionary of local features. For learning we either use a bootstrapped k-means clustering approach or select features randomly. We further extract feature responses in a convolutional manner and train a linear SVM for classification. We extensively evaluate the approach on the GTZAN dataset, emphasizing the influence of important design choices such as dimensionality reduction, pooling and patch dimension on the classification accuracy. We show that convolutional extraction of local feature responses is crucial to reach high performance. Furthermore we find that using this approach, simple and fast learning techniques such as k-means or randomly selected features are competitive with previously published results which also learn features from audio signals. The main purpose of this paper is to describe a process for partitioning an N-dimensional population into k sets on the basis of a sample. The process, which is called 'k-means,' appears to give partitions which are reasonably efficient in the sense of within-class variance. That is, if p is the probability mass function for the population, S = S1, S2, * *, Sk is a partition of EN, and ui, i = 1, 2, * , k, is the conditional mean of p over the set Si, then W2(S) = ff=ISi f z u42 dp(z) tends to be low for the partitions S generated by the method. We say 'tends to be low,' primarily because of intuitive considerations, corroborated to some extent by mathematical analysis and practical computational experience. Also, the k-means procedure is easily programmed and is computationally economical, so that it is feasible to process very large samples on a digital computer. Possible applications include methods for similarity grouping, nonlinear prediction, approximating multivariate distributions, and nonparametric tests for independence among several variables. In addition to suggesting practical classification methods, the study of k-means has proved to be theoretically interesting. The k-means concept represents a generalization of the ordinary sample mean, and one is naturally led to study the pertinent asymptotic behavior, the object being to establish some sort of law of large numbers for the k-means. This problem is sufficiently interesting, in fact, for us to devote a good portion of this paper to it. The k-means are defined in section 2.1, and the main results which have been obtained on the asymptotic behavior are given there. The rest of section 2 is devoted to the proofs of these results. Section 3 describes several specific possible applications, and reports some preliminary results from computer experiments conducted to explore the possibilities inherent in the k-means idea. The extension to general metric spaces is indicated briefly in section 4. The original point of departure for the work described here was a series of problems in optimal classification (MacQueen [9]) which represented special