多决策树的模糊积分融合在银行信贷管理系统中的应用

为了提高基于数据挖掘的商业银行信贷管理系统的信贷风险评估水平,将多决策树的Choquet模糊积分融合(MTCFF)模型应用到银行信贷管理系统中。基本思想是采用决策树在已知类型的客户数据上进行挖掘,按照决策树剪枝程度不同形成不同的决策树并产生规则,利用所生成的不同决策树的规则,对未知类型的客户数据进行分类,然后让Choquet模糊积分对多棵决策树的分类结果进行融合,形成最优判断。采用UCI数据库中German客户信用卡数据集进行验证,实验证明Choquet模糊积分的非线性融合效果优于单棵决策树的分类效果,也优于其他线性融合方法,并且Choquet模糊积分要优于Sugeno模糊积分。     

Induction of multiclass multifeature split decision trees from distributed data

The decision tree-based classification is a popular approach for pattern recognition and data mining. Most decision tree induction methods assume training data being present at one central location. Given the growth in distributed databases at geographically dispersed locations, the methods for decision tree induction in distributed settings are gaining importance. This paper describes one such method that generates compact trees using multifeature splits in place of single feature split decision trees generated by most existing methods for distributed data. Our method is based on Fisher's linear discriminant function, and is capable of dealing with multiple classes in the data. For homogeneously distributed data, the decision trees produced by our method are identical to decision trees generated using Fisher's linear discriminant function with centrally stored data. For heterogeneously distributed data, a certain approximation is involved with a small change in performance with respect to the tree generated with centrally stored data. Experimental results for several well-known datasets are presented and compared with decision trees generated using Fisher's linear discriminant function with centrally stored data.     

Omnivariate decision trees.

Univariate decision trees at each decision node consider the value of only one feature leading to axis-aligned splits. In a linear multivariate decision tree, each decision node divides the input space into two with a hyperplane. In a nonlinear multivariate tree, a multilayer perceptron at each node divides the input space arbitrarily, at the expense of increased complexity and higher risk of overfitting. We propose omnivariate trees where the decision node may be univariate, linear, or nonlinear depending on the outcome of comparative statistical tests on accuracy thus matching automatically the complexity of the node with the subproblem defined by the data reaching that node. Such an architecture frees the designer from choosing the appropriate node type, doing model selection automatically at each node. Our simulation results indicate that such a decision tree induction method generalizes better than trees with the same types of nodes everywhere and induces small trees.     

Fisher’s decision tree

Univariate decision trees are classifiers currently used in many data mining applications. This classifier discovers partitions in the input space via hyperplanes that are orthogonal to the axes of attributes, producing a model that can be understood by human experts. One disadvantage of univariate decision trees is that they produce complex and inaccurate models when decision boundaries are not orthogonal to axes. In this paper we introduce the Fisher’s Tree, it is a classifier that takes advantage of dimensionality reduction of Fisher’s linear discriminant and uses the decomposition strategy of decision trees, to come up with an oblique decision tree. Our proposal generates an artificial attribute that is used to split the data in a recursive way.The Fisher’s decision tree induces oblique trees whose accuracy, size, number of leaves and training time are competitive with respect to other decision trees reported in the literature. We use more than ten public available data sets to demonstrate the effectiveness of our method.     

Classifiability-based omnivariate decision trees

Top-down induction of decision trees is a simple and powerful method of pattern classification. In a decision tree, each node partitions the available patterns into two or more sets. New nodes are created to handle each of the resulting partitions and the process continues. A node is considered terminal if it satisfies some stopping criteria (for example, purity, i.e., all patterns at the node are from a single class). Decision trees may be univariate, linear multivariate, or nonlinear multivariate depending on whether a single attribute, a linear function of all the attributes, or a nonlinear function of all the attributes is used for the partitioning at each node of the decision tree. Though nonlinear multivariate decision trees are the most powerful, they are more susceptible to the risks of overfitting. In this paper, we propose to perform model selection at each decision node to build omnivariate decision trees. The model selection is done using a novel classifiability measure that captures the possible sources of misclassification with relative ease and is able to accurately reflect the complexity of the subproblem at each node. The proposed approach is fast and does not suffer from as high a computational burden as that incurred by typical model selection algorithms. Empirical results over 26 data sets indicate that our approach is faster and achieves better classification accuracy compared to statistical model select algorithms.     

Multivariate decision trees using linear discriminants and tabu search

A new decision tree method for application in data mining, machine learning, pattern recognition, and other areas is proposed in this paper. The new method incorporates a classical multivariate statistical method, linear discriminant function, into decision trees' recursive partitioning process. The proposed method considers not only the linear combination with all variables, but also combinations with fewer variables. It uses a tabu search technique to find appropriate variable combinations within a reasonable length of time. For problems with more than two classes, the tabu search technique is also used to group the data into two superclasses before each split. The results of our experimental study indicate that the proposed algorithm appears to outperform some of the major classification algorithms in terms of classification accuracy, the proposed algorithm generates decision trees with relatively small sizes, and the proposed algorithm runs faster than most multivariate decision trees and its computing time increases linearly with data size, indicating that the algorithm is scalable to large datasets.     

A Fourier spectrum-based approach to represent decision trees for mining data streams in mobile environments

We present a novel Fourier analysis-based approach to combine, transmit, and visualize decision trees in a mobile environment. Fourier representation of a decision tree has several interesting properties that are particularly useful for mining data streams from small mobile computing devices connected through limited-bandwidth wireless networks. We present algorithms to compute the Fourier spectrum of a decision tree and outlines a technique to construct a decision tree from its Fourier spectrum. It offers a framework to aggregate decision trees in their Fourier representations. It also describes the MobiMine, a mobile data stream mining system, that uses the developed techniques for mining stock-market data from handheld devices.     

融合信息增益与基尼指数的决策树算法

机器学习中的决策树算法具有重要的数据分类功能,但基于信息增益的ID3算法与基于基尼指数的CART算法的分类功效还值得提高.构造信息增益与基尼指数的自适应集成度量,设计有效的决策树算法,以提升ID3与C A RT两类基本算法的性能.分析信息增益信息表示与基尼指数代数表示的异质无关性,采用基于知识的加权线性组合来建立信息增...     

基于代表性数据的决策树集成*

为了获得更好的决策树集成效果,在理论分析的基础上从数据的角度提出了一种基于代表性数据的决策树集成方法。该方法使用围绕中心点的划分(PAM)算法从原始训练集中提取出代表性训练集,由该代表性训练集来训练出多个决策树分类器,并由此建立决策树集成模型。该方法能选取尽可能少的代表性数据来训练出尽可能好的决策树集成模型。实验结果表明,该方法使用更少的代表性数据能获得比Bagging和Boosting还要高的决策树集成精度。     

A connectionist approach to generating oblique decision trees

Neural networks and decision tree methods are two common approaches to pattern classification. While neural networks can achieve high predictive accuracy rates, the decision boundaries they form are highly nonlinear and generally difficult to comprehend. Decision trees, on the other hand, can be readily translated into a set of rules. In this paper, we present a novel algorithm for generating oblique decision trees that capitalizes on the strength of both approaches. Oblique decision trees classify the patterns by testing on linear combinations of the input attributes. As a result, an oblique decision tree is usually much smaller than the univariate tree generated for the same domain. Our algorithm consists of two components: connectionist and symbolic. A three-layer feedforward neural network is constructed and pruned, a decision tree is then built from the hidden unit activation values of the pruned network. An oblique decision tree is obtained by expressing the activation values using the original input attributes. We test our algorithm on a wide range of problems. The oblique decision trees generated by the algorithm preserve the high accuracy of the neural networks, while keeping the explicitness of decision trees. Moreover, they outperform univariate decision trees generated by the symbolic approach and oblique decision trees built by other approaches in accuracy and tree size.     

Machine Learning for Intelligent Processing of Printed Documents

A paper document processing system is an information system component which transforms information on printed or handwritten documents into a computer-revisable form. In intelligent systems for paper document processing this information capture process is based on knowledge of the specific layout and logical structures of the documents. This article proposes the application of machine learning techniques to acquire the specific knowledge required by an intelligent document processing system, named WISDOM++, that manages printed documents, such as letters and journals. Knowledge is represented by means of decision trees and first-order rules automatically generated from a set of training documents. In particular, an incremental decision tree learning system is applied for the acquisition of decision trees used for the classification of segmented blocks, while a first-order learning system is applied for the induction of rules used for the layout-based classification and understanding of documents. Issues concerning the incremental induction of decision trees and the handling of both numeric and symbolic data in first-order rule learning are discussed, and the validity of the proposed solutions is empirically evaluated by processing a set of real printed documents.     

Theoretical and practical considerations of uncertainty andcomplexity in automated knowledge acquisition

Inductive machine learning has become an important approach to automated knowledge acquisition from databases. The disjunctive normal form (DNF), as the common analytic representation of decision trees and decision tables (rules), provides a basis for formal analysis of uncertainty and complexity in inductive learning. A theory for general decision trees is developed based on C. Shannon's (1949) expansion of the discrete DNF, and a probabilistic induction system PIK is further developed for extracting knowledge from real world data. Then we combine formal and practical approaches to study how data characteristics affect the uncertainty and complexity in inductive learning. Three important data characteristics, namely, disjunctiveness, noise and incompleteness, are studied. The combination of leveled pruning, leveled condensing and resampling estimation turns out to be a very powerful method for dealing with highly disjunctive and inadequate data. Finally the PIK system is compared with other recent inductive learning systems on a number of real world domains     

Extracting decision trees from trained neural networks

In this paper we present a methodology for extracting decision trees from input data generated from trained neural networks instead of doing it directly from the data. A genetic algorithm is used to query the trained network and extract prototypes. A prototype selection mechanism is then used to select a subset of the prototypes. Finally, a standard induction method like ID3 or C5.0 is used to extract the decision tree. The extracted decision trees can be used to understand the working of the neural network besides performing classification. This method is able to extract different decision trees of high accuracy and comprehensibility from the trained neural network.     

Generalized haar DWT and transformations between decision trees and neural networks

The core contribution of this paper is a three-fold improvement of the Haar discrete wavelet transform (DWT). It is modified to efficiently transform a multiclass- (rather than numerical-) valued function over a multidimensional (rather than low dimensional) domain, or transform a multiclass-valued decision tree into another useful representation. We prove that this multidimensional, multiclass DWT uses dynamic programming to minimize (within its framework) the number of nontrivial wavelet coefficients needed to summarize a training set or decision tree. It is a spatially localized algorithm that takes linear time in the number of training samples, after a sort. Convergence of the DWT to benchmark training sets seems to degrade with rising dimension in this test of high dimensional wavelets, which have been seen as difficult to implement. This multiclass multidimensional DWT has tightly coupled applications from learning "dyadic" decision trees directly from training data, rebalancing or converting preexisting decision trees to fixed depth boolean or threshold neural networks (in effect parallelizing the evaluation of the trees), or learning rule/exception sets represented as a new form of tree called an "E-tree," which could greatly help interpretation/visualization of a dataset.     

Upper bounds for error rates of linear combinations of classifiers

A useful notion of weak dependence between many classifiers constructed with the same training data is introduced. It is shown that if both this weak dependence is low and the expected margins are large, then decision rules based on linear combinations of these classifiers can achieve error rates that decrease exponentially fast. Empirical results with randomized trees and trees constructed via boosting and bagging show that weak dependence is present in these type of trees. Furthermore, these results also suggest that there is a trade-off between weak dependence and expected margins, in the sense that to compensate for low expected margins, there should be low mutual dependence between the classifiers involved in the linear combination     

Learning from examples: generation and evaluation of decision treesfor software resource analysis

A general solution method for the automatic generation of decision (or classification) trees is investigated. The approach is to provide insights through in-depth empirical characterization and evaluation of decision trees for one problem domain, specifically, that of software resource data analysis. The purpose of the decision trees is to identify classes of objects (software modules) that had high development effort, i.e. in the uppermost quartile relative to past data. Sixteen software systems ranging from 3000 to 112000 source lines have been selected for analysis from a NASA production environment. The collection and analysis of 74 attributes (or metrics), for over 4700 objects, capture a multitude of information about the objects: development effort, faults, changes, design style, and implementation style. A total of 9600 decision trees are automatically generated and evaluated. The analysis focuses on the characterization and evaluation of decision tree accuracy, complexity, and composition. The decision trees correctly identified 79.3% of the software modules that had high development effort or faults, on the average across all 9600 trees. The decision trees generated from the best parameter combinations correctly identified 88.4% of the modules on the average. Visualization of the results is emphasized, and sample decision trees are included     

Fuzzy rule based decision trees

This paper presents a new architecture of a fuzzy decision tree based on fuzzy rules – fuzzy rule based decision tree (FRDT) and provides a learning algorithm. In contrast with “traditional” axis-parallel decision trees in which only a single feature (variable) is taken into account at each node, the node of the proposed decision trees involves a fuzzy rule which involves multiple features. Fuzzy rules are employed to produce leaves of high purity. Using multiple features for a node helps us minimize the size of the trees. The growth of the FRDT is realized by expanding an additional node composed of a mixture of data coming from different classes, which is the only non-leaf node of each layer. This gives rise to a new geometric structure endowed with linguistic terms which are quite different from the “traditional” oblique decision trees endowed with hyperplanes as decision functions. A series of numeric studies are reported using data coming from UCI machine learning data sets. The comparison is carried out with regard to “traditional” decision trees such as C4.5, LADtree, BFTree, SimpleCart, and NBTree. The results of statistical tests have shown that the proposed FRDT exhibits the best performance in terms of both accuracy and the size of the produced trees.     

Using artificial neural networks to enhance CART

Accuracy is a critical factor in predictive modeling. A predictive model such as a decision tree must be accurate to draw conclusions about the system being modeled. This research aims at analyzing and improving the performance of classification and regression trees (CART), a decision tree algorithm, by evaluating and deriving a new methodology based on the performance of real-world data sets that were studied. This paper introduces a new approach to tree induction to improve the efficiency of the CART algorithm by combining the existing functionality of CART with the addition of artificial neural networks (ANNs). Trained ANNs are utilized by the tree induction algorithm by generating new, synthetic data, which have been shown to improve the overall accuracy of the decision tree model when actual training samples are limited. In this paper, traditional decision trees developed by the standard CART methodology are compared with the enhanced decision trees that utilize the ANN’s synthetic data generation, or CART+. This research demonstrates the improved accuracies that can be obtained with CART+, which can ultimately improve the knowledge that can be extracted by researchers about a system being modeled.     

Creating Decision Trees from Rules using RBDT‐1

Most of the methods that generate decision trees for a specific problem use the examples of data instances in the decision tree–generation process. This article proposes a method called RBDT‐1—rule‐based decision tree—for learning a decision tree from a set of decision rules that cover the data instances rather than from the data instances themselves. The goal is to create on demand a short and accurate decision tree from a stable or dynamically changing set of rules. The rules could be generated by an expert, by an inductive rule learning program that induces decision rules from the examples of decision instances such as AQ‐type rule induction programs, or extracted from a tree generated by another method, such as the ID3 or C4.5. In terms of tree complexity (number of nodes and leaves in the decision tree), RBDT‐1 compares favorably with AQDT‐1 and AQDT‐2, which are methods that create decision trees from rules. RBDT‐1 also compares favorably with ID3 while it is as effective as C4.5 where both (ID3 and C4.5) are well‐known methods that generate decision trees from data examples. Experiments show that the classification accuracies of the decision trees produced by all methods under comparison are indistinguishable.