In finite set, Choquet fuzzy integral with respect to fuzzy measures can be transferred into linear combination of product, based on this fact we can choose standard optimization technical to determine fuzzy measures....
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In finite set, Choquet fuzzy integral with respect to fuzzy measures can be transferred into linear combination of product, based on this fact we can choose standard optimization technical to determine fuzzy measures. This paper present linear programming and quadratic programming to determine fuzzy measures, the experiments demonstrate that classification accuracy of fuzzy integral with respect to fuzzy measure is better than the classification accuracies of majority voting and weighted average.
Over recent years a huge library of data mining algorithms has been developed to tackle a variety of problems in fields such as medical imaging and network traffic analysis. Many of these techniques are far more flexi...
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ISBN:
(纸本)1424308526
Over recent years a huge library of data mining algorithms has been developed to tackle a variety of problems in fields such as medical imaging and network traffic analysis. Many of these techniques are far more flexible than more classical modelling approaches and could be usefully applied to data-rich environmental problems. Certain techniques such as Artificial Neural Networks, Clustering, Case-Based Reasoning and more recently Bayesian Decision Networks have found application in environmental modelling while other methods, for example classification and association rule extraction, have not yet been taken up on any wide scale. We propose that these and other data mining techniques could be usefully applied to difficult problems in the field. This paper introduces several data mining concepts and briefly discusses their application to environmental modelling, where data may be sparse, incomplete, or heterogenous.
The problem of selecting the best among several alternatives in a stochastic context has been the object of researcli in several domains: stochastic optimization, discrete-event stochastic simulation, experimental des...
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The problem of selecting the best among several alternatives in a stochastic context has been the object of researcli in several domains: stochastic optimization, discrete-event stochastic simulation, experimental design. A particular instance of this problem is of particular relevance in machinelearning where the search of the model which could best represent a finite set of data asks for comparing several alternatives on the basis of a finite set of noisy data. This paper aims to bridge a gap between these different communities by comparing experimentally the effectiveness of techniques proposed in the simulation and in the stochastic dynamic programming community in performing a model selection task. In particular, we will consider here a model selection task in regression where the alternatives are represented by a finite set of K-nearest neighbors models with different values of the structural parameter K. The techniques we compare are i) a two-stage selection technique proposed in the stochastic simulation community, ii) a stochastic dynamic programming approach conceived to address the multi-armed bandit problem, iii) a racing method, iv) a greedy approach, v) a round-search technique.
We present an algorithm for learning a quadratic Gaussian metric (Mahalanobis distance) for use in classification tasks. Our method relies on the simple geometric intuition that a good metric is one under which points...
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ISBN:
(纸本)9780262232531
We present an algorithm for learning a quadratic Gaussian metric (Mahalanobis distance) for use in classification tasks. Our method relies on the simple geometric intuition that a good metric is one under which points in the same class are simultaneously near each other and far from points in the other classes. We construct a convex optimization problem whose solution generates such a metric by trying to collapse all examples in the same class to a single point and push examples in other classes infinitely far away. We show that when the metric we learn is used in simple classifiers, it yields substantial improvements over standard alternatives on a variety of problems. We also discuss how the learned metric may be used to obtain a compact low dimensional feature representation of the original input space, allowing more efficient classification with very little reduction in performance.
Nearest Neighbor Classifier (NNC) is stable to the change of the training data set while sensitive to the variation of the feature set. The combination of multiple NNCs on different subsets of features may outperform ...
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The paper proposes a technique for speeding up the search of the optimal set of features in classification problems where the input variables are discrete or nominal. The approach is based on the definition of an uppe...
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The paper proposes a technique for speeding up the search of the optimal set of features in classification problems where the input variables are discrete or nominal. The approach is based on the definition of an upper bound on the mutual information between the target and a set of d input variables. This bound is derived as a function of the mutual information of its subsets of d - 1 cardinality. The rationale of the algorithm is to proceed to evaluate the mutual information of a subset only if the respective upper bound is sufficiently promising. The computation of the upper bound can thus be seen as a pre-estimation of a subset. We show that the principle of pre-estimating allows to explore a much higher number of combinations of inputs than the classical algorithm of forward selection by preserving the same computational complexity. Some preliminary results showing the effectiveness of the proposed technique with respect to the classical forward search are reported.
We present methods for dealing with missing variables in the context of Gaussian Processes and Support Vector machines. This solves an important problem which has largely been ignored by kernel methods: How to systema...
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ISBN:
(纸本)097273581X
We present methods for dealing with missing variables in the context of Gaussian Processes and Support Vector machines. This solves an important problem which has largely been ignored by kernel methods: How to systematically deal with incomplete data? Our method can also be applied to problems with partially observed labels as well as to the transductive setting where we view the labels as missing data. Our approach relies on casting kernel methods as an estimation problem in exponential families. Hence, estimation with missing variables becomes a problem of computing marginal distributions, and finding efficient optimization methods. To that extent we propose an optimization scheme which extends the Concave Convex Procedure (CCP) of Yuille and Rangarajan, and present a simplified and intuitive proof of its convergence. We show how our algorithm can be specialized to various cases in order to efficiently solve the optimization problems that arise. Encouraging preliminary experimental results on the USPS dataset are also presented.
We propose a convex optimization based strategy to deal with uncertainty in the observations of a classification problem. We assume that instead of a sample (xi;yi) a distribution over (xi;y i) is specified. In partic...
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ISBN:
(纸本)0262195348
We propose a convex optimization based strategy to deal with uncertainty in the observations of a classification problem. We assume that instead of a sample (xi;yi) a distribution over (xi;y i) is specified. In particular, we derive a robust formulation when the distribution is given by a normal distribution. It leads to Second Order Cone Programming formulation. Our method is applied to the problem of missing data, where it outperforms direct imputation.
Many methods based on rough sets to deal with incomplete information system have been proposed in recent years. However, they are only suitable for the nominal datasets. So far only a few methods based on rough sets t...
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The generalization error bounds for the entire input space found by current error models using the number of effective parameters of a classifier and the number of training samples are usually very loose. But classifi...
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