Data mining algorithms are originally designed by assuming the data is available at one centralized site. These algorithms also assume that the whole data is fit into main memory while running the algorithm. But in today's scenario the data has to be handled is distributed even geographically. Bringing the data into a centralized site is a bottleneck in terms of the bandwidth when compared with the size of the data. In this paper for multiclass SVM we propose an algorithm which builds a global SVM model by merging the local SVMs using a distributed approach(DSVM). And the global SVM will be communicated to each site and made it available for further classification. The experimental analysis has shown promising results with better accuracy when compared with both the centralized and ensemble method. The time complexity is also reduced drastically because of the parallel construction of local SVMs. The experiments are conducted by considering the data sets of size 100s to hundred of 100s which also addresses the issue of scalability.
In 1998 Han. discussed the model of coupling the estimation of class probabilities for each pair of classes @cite_5 . The used classifiers include linear discriminant, nearest neighbors and SVM.
@cite_5
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We discuss a strategy for polychotomous classification that involves estimating class probabilities for each pair of classes, and then coupling the estimates together. The coupling model is similar to the Bradley-Terry method for paired comparisons. We study the nature of the class probability estimates that arise, and examine the performance of the procedure in real and simulated data sets. Classifiers used include linear discriminants, nearest neighbors, adaptive nonlinear methods and the support vector machine. Pairwise coupling is a popular multi-class classification method that combines all comparisons for each pair of classes. This paper presents two approaches for obtaining class probabilities. Both methods can be reduced to linear systems and are easy to implement. We show conceptually and experimentally that the proposed approaches are more stable than the two existing popular methods: voting and the method by Hastie and Tibshirani (1998) Nearest neighbour classification expects the class conditional probabilities to be locally constant, and suffers from bias in high dimensions. We propose a locally adaptive form of nearest neighbour classification to try to ameliorate this curse of dimensionality. We use a local linear discriminant analysis to estimate an effective metric for computing neighbourhoods. We determine the local decision boundaries from centroid information, and then shrink neighbourhoods in directions orthogonal to these local decision boundaries, and elongate them parallel to the boundaries. Thereafter, any neighbourhood-based classifier can be employed, using the modified neighbourhoods. The posterior probabilities tend to be more homogeneous in the modified neighbourhoods. We also propose a method for global dimension reduction, that combines local dimension information. In a number of examples, the methods demonstrate the potential for substantial improvements over nearest neighbour classification. We present an algorithm for automatic image orientation estimation using a Bayesian learning framework. We demonstrate that a small codebook (the optimal size of codebook is selected using a modified MDL criterion) extracted from a learning vector quantizer (LVQ) can be used to estimate the class-conditional densities of the observed features needed for the Bayesian methodology. We further show how principal component analysis (PCA) and linear discriminant analysis (LDA) can be used as a feature extraction mechanism to remove redundancies in the high-dimensional feature vectors used for classification. The proposed method is compared with four different commonly used classifiers, namely k-nearest neighbor, support vector machine (SVM), a mixture of Gaussians, and hierarchical discriminating regression (HDR) tree. Experiments on a database of 16 344 images have shown that our proposed algorithm achieves an accuracy of approximately 98 on the training set and over 97 on an independent test set. A slight improvement in classification accuracy is achieved by employing classifier combination techniques. The problem of finding high-dimensional approximate nearest neighbors is considered when the data is generated by some known probabilistic model. A large natural class of algorithms (bucketing codes) is investigated, Bucketing information is defined, and is proven to bound the performance of all bucketing codes. The bucketing information bound is asymptotically attained by some randomly constructed bucketing codes. The example of n Bernoulli(1 2) very long (length d → ∞) sequences of bits is singled out. It is assumed that n - 2m sequences are completely independent, while the remaining 2m sequences are composed of m dependent pairs. The interdependence within each pair is that their bits agree with probability 1 2 0. A specific 2-D inequality (proven in another paper) implies that the exponent 1 p cannot be lowered. Moreover, if one sequence out of each pair belongs to a known set of n(2p-1)2 sequences, pairing can be done using order n1+∈ comparisons! This paper addresses the independent assumption issue in classifier fusion process. In the last decade, dependency modeling techniques were developed under some specific assumptions which may not be valid in practical applications. In this paper, using analytical functions on posterior probabilities of each feature, we propose a new framework to model dependency without those assumptions. With the analytical dependency model (ADM), we give an equivalent condition to the independent assumption from the properties of marginal distributions, and show that the proposed ADM can model dependency. Since ADM may contain infinite number of undetermined coefficients, we further propose a reduced form of ADM, based on the convergent properties of analytical functions. Finally, under the regularized least square criterion, an optimal Reduced Analytical Dependency Model (RADM) is learned by approximating posterior probabilities such that all training samples are correctly classified. Experimental results show that the proposed RADM outperforms existing classifier fusion methods on Digit, Flower, Face and Human Action databases. Summary Background—Most machine learning approaches only provide a classification for binary responses. However, probabilities are required for risk estimation using individual patient characteristics. It has been shown recently that every statistical learning machine known to be consistent for a nonparametric regression problem is a probability machine that is provably consistent for this estimation problem. Objectives—The aim of this paper is to show how random forests and nearest neighbors can be used for consistent estimation of individual probabilities. Methods—Two random forest algorithms and two nearest neighbor algorithms are described in detail for estimation of individual probabilities. We discuss the consistency of random forests, nearest neighbors and other learning machines in detail. We conduct a simulation study to illustrate the validity of the methods. We exemplify the algorithms by analyzing two well-known data sets on the diagnosis of appendicitis and the diagnosis of diabetes in Pima Indians. Results—Simulations demonstrate the validity of the method. With the real data application, we show the accuracy and practicality of this approach. We provide sample code from R packages in which the probability estimation is already available. This means that all calculations can be performed using existing software. Conclusions—Random forest algorithms as well as nearest neighbor approaches are valid machine learning methods for estimating individual probabilities for binary responses. Freely available implementations are available in R and may be used for applications. We propose an efficient method to estimate the accuracy of classifiers using only unlabeled data. We consider a setting with multiple classification problems where the target classes may be tied together through logical constraints. For example, a set of classes may be mutually exclusive, meaning that a data instance can belong to at most one of them. The proposed method is based on the intuition that: (i) when classifiers agree, they are more likely to be correct, and (ii) when the classifiers make a prediction that violates the constraints, at least one classifier must be making an error. Experiments on four real-world data sets produce accuracy estimates within a few percent of the true accuracy, using solely unlabeled data. Our models also outperform existing state-of-the-art solutions in both estimating accuracies, and combining multiple classifier outputs. The results emphasize the utility of logical constraints in estimating accuracy, thus validating our intuition. In classification, when the distribution of the training data among classes is uneven, the learning algorithm is generally dominated by the feature of the majority classes. The features in the minority classes are normally difficult to be fully recognized. In this paper, a method is proposed to enhance the classification accuracy for the minority classes. The proposed method combines Synthetic Minority Over-sampling Technique (SMOTE) and Complementary Neural Network (CMTNN) to handle the problem of classifying imbalanced data. In order to demonstrate that the proposed technique can assist classification of imbalanced data, several classification algorithms have been used. They are Artificial Neural Network (ANN), k-Nearest Neighbor (k-NN) and Support Vector Machine (SVM). The benchmark data sets with various ratios between the minority class and the majority class are obtained from the University of California Irvine (UCI) machine learning repository. The results show that the proposed combination techniques can improve the performance for the class imbalance problem. A statistical approach to a posteriori blockmodeling for digraphs and valued digraphs is proposed. The probability model assumes that the vertices of the digraph are partitioned into several unobserved (latent) classes and that the probability distribution of the relation between two vertices depends only on the classes to which they belong. A Bayesian estimator based on Gibbs sampling is proposed. The basic model is not identified, because class labels are arbitrary. The resulting identifiability problems are solved by restricting inference to the posterior distributions of invariant functions of the parameters and the vertex class membership. In addition, models are considered where class labels are identified by prior distributions for the class membership of some of the vertices. The model is illustrated by an example from the social networks literature (Kapferer's tailor shop). We investigate the clustering performances of the relaxed @math means in the setting of sub-Gaussian Mixture Model (sGMM) and Stochastic Block Model (SBM). After identifying the appropriate signal-to-noise ratio (SNR), we prove that the misclassification error decay exponentially fast with respect to this SNR. These partial recovery bounds for the relaxed @math means improve upon results currently known in the sGMM setting. In the SBM setting, applying the relaxed @math means SDP allows to handle general connection probabilities whereas other SDPs investigated in the literature are restricted to the assortative case (where within group probabilities are larger than between group probabilities). Again, this partial recovery bound complements the state-of-the-art results. All together, these results put forward the versatility of the relaxed @math means. 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 The perceived success of recent visual recognition approaches has largely been derived from their performance on classification tasks, where all possible classes are known at training time. But what about open set problems, where unknown classes appear at test time? Intuitively, if we could accurately model just the positive data for any known class without overfitting, we could reject the large set of unknown classes even under an assumption of incomplete class knowledge. In this paper, we formulate the problem as one of modeling positive training data at the decision boundary, where we can invoke the statistical extreme value theory. A new algorithm called the P I -SVM is introduced for estimating the unnormalized posterior probability of class inclusion. A class of nonparametric regression function estimates generalizing the nearest neighbor estimate of Cover [ 12] is presented. Under various noise conditions, it is shown that the estimates are strongly uniformly consistent. The uniform convergence of the estimates can be exploited to design a simple random search algorithm for the global minimization of the regression function. Nondeterministic classifiers are defined as those allowed to predict more than one class for some entries from an input space. Given that the true class should be included in predictions and the number of classes predicted should be as small as possible, these kind of classifiers can be considered as Information Retrieval (IR) procedures. In this paper, we propose a family of IR loss functions to measure the performance of nondeterministic learners. After discussing such measures, we derive an algorithm for learning optimal nondeterministic hypotheses. Given an entry from the input space, the algorithm requires the posterior probabilities to compute the subset of classes with the lowest expected loss. From a general point of view, nondeterministic classifiers provide an improvement in the proportion of predictions that include the true class compared to their deterministic counterparts; the price to be paid for this increase is usually a tiny proportion of predictions with more than one class. The paper includes an extensive experimental study using three deterministic learners to estimate posterior probabilities: a multiclass Support Vector Machine (SVM), a Logistic Regression, and a Naive Bayes. The data sets considered comprise both UCI multi-class learning tasks and microarray expressions of different kinds of cancer. We successfully compare nondeterministic classifiers with other alternative approaches. Additionally, we shall see how the quality of posterior probabilities (measured by the Brier score) determines the goodness of nondeterministic predictions. The problem of maximum-likelihood (ML) estimation of discrete tree-structured distributions is considered. Chow and Liu established that ML-estimation reduces to the construction of a maximum-weight spanning tree using the empirical mutual information quantities as the edge weights. Using the theory of large-deviations, we analyze the exponent associated with the error probability of the event that the ML-estimate of the Markov tree structure differs from the true tree structure, given a set of independently drawn samples. By exploiting the fact that the output of ML-estimation is a tree, we establish that the error exponent is equal to the exponential rate of decay of a single dominant crossover event. We prove that in this dominant crossover event, a non-neighbor node pair replaces a true edge of the distribution that is along the path of edges in the true tree graph connecting the nodes in the non-neighbor pair. Using ideas from Euclidean information theory, we then analyze the scenario of ML-estimation in the very noisy learning regime and show that the error exponent can be approximated as a ratio, which is interpreted as the signal-to-noise ratio (SNR) for learning tree distributions. We show via numerical experiments that in this regime, our SNR approximation is accurate. We study binary classification in the presence of class-conditional random noise, where the learner gets to see labels that are flipped independently with some probability, and where the flip probability depends on the class. Our goal is to devise learning algorithms that are efficient and statistically consistent with respect to commonly used utility measures. In particular, we look at a family of measures motivated by their application in domains where cost-sensitive learning is necessary (for example, when there is class imbalance). In contrast to most of the existing literature on consistent classification that are limited to the classical 0-1 loss, our analysis includes more general utility measures such as the AM measure (arithmetic mean of True Positive Rate and True Negative Rate). For this problem of cost-sensitive learning under class-conditional random noise, we develop two approaches that are based on suitably modifying surrogate losses. First, we provide a simple unbiased estimator of any loss, and obtain performance bounds for empirical utility maximization in the presence of i.i.d. data with noisy labels. If the loss function satis_es a simple symmetry condition, we show that using unbiased estimator leads to an efficient algorithm for empirical maximization. Second, by leveraging a reduction of risk minimization under noisy labels to classification with weighted 0-1 loss, we suggest the use of a simple weighted surrogate loss, for which we are able to obtain strong utility bounds. This approach implies that methods already used in practice, such as biased SVM and weighted logistic regression, are provably noise-tolerant. For two practically important measures in our family, we show that the proposed methods are competitive with respect to recently proposed methods for dealing with label noise in several benchmark data sets. This paper presents an integrated framework to enable using standard non-sequential machine learning tools for accurate multi-modal activity recognition. We develop a novel framework that contains simple pre- and post-classification strategies to improve the overall performance. We achieve this through class-imbalance correction on the learning data using structure preserving oversampling (SPO), leveraging the sequential nature of sensory data using smoothing of the predicted label sequence and classifier fusion, respectively. Through evaluation on recent publicly available activity datasets comprising of a large amount of multi-dimensional sensory data, we demonstrate that our proposed strategies are effective in improving classification performance over common techniques such as One Nearest Neighbor (1NN) and Support Vector Machines (SVM). Our framework also shows better performance over sequential probabilistic models, such as Conditional Random Field (CRF) and Hidden Markov Model (HMM) and when these models are used as meta-learners. In this paper, a new classifier design methodology, confidence-based classifier design, is proposed to design classifiers with controlled confidence. This methodology is under the guidance of two optimal classification theories, a new classification theory for designing optimal classifiers with controlled error rates and the C.K. Chow's optimal classification theory for designing optimal classifiers with controlled conditional error. The new methodology also takes advantage of the current well-developed classifier's probability preserving and ordering properties. It calibrates the output scores of current classifiers to the conditional error or error rates. Thus, it can either classify input samples or reject them according to the output scores of classifiers. It can achieve some reasonable performance even though it is not an optimal solution. An example is presented to implement the new methodology using support vector machines (SVMs). The empirical cumulative density function method is used to estimate error rates from the output scores of a trained SVM. Furthermore, a new dynamic bin width allocation method is proposed to estimate sample conditional error and this method adapts to the underlying probabilities. The experimental results clearly demonstrate the efficacy of the suggested classifier design methodology. Preface * Introduction * The Bayes Error * Inequalities and alternatedistance measures * Linear discrimination * Nearest neighbor rules *Consistency * Slow rates of convergence Error estimation * The regularhistogram rule * Kernel rules Consistency of the k-nearest neighborrule * Vapnik-Chervonenkis theory * Combinatorial aspects of Vapnik-Chervonenkis theory * Lower bounds for empirical classifier selection* The maximum likelihood principle * Parametric classification *Generalized linear discrimination * Complexity regularization *Condensed and edited nearest neighbor rules * Tree classifiers * Data-dependent partitioning * Splitting the data * The resubstitutionestimate * Deleted estimates of the error probability * Automatickernel rules * Automatic nearest neighbor rules * Hypercubes anddiscrete spaces * Epsilon entropy and totally bounded sets * Uniformlaws of large numbers * Neural networks * Other error estimates *Feature extraction * Appendix * Notation * References * Index