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(a) System that approximates, which has divided the input space of a problem into several regions. (b) Straight line that delimits an erroneous zone. (c) Special treatment (approx5) on the erroneous zone that does not take into consideration the previous partitions.
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This article presents a machine learning method for solving classification and approximation problems. This method uses the divide-and-conquer algorithm design technique (taken from machine learning models based on a tree), with the aim of achieving design ease and good results on the training examples and allows semi-global actions on its computat...
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... designing a solver system to overcome the problem inside this zone. This special treat- ment may be one of two types. B1) Special treatment that forgets the previous partitions. For example, let us suppose that a system is avail- able that solves an approximation problem, that it has divided the input space of the problem into sev- eral regions [ Fig. 1(a)] and that a straight line has delimited a zone with erroneous examples that con- tains several previous partitions [ Fig. 1(b)], then the previous approximations of each particular region would be forgotten in this zone and a new approx- imation would be designed for the whole zone (ap- prox5 in Fig. 1(c)). B2) Special treatment that ...
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... treatment that forgets the previous partitions. For example, let us suppose that a system is avail- able that solves an approximation problem, that it has divided the input space of the problem into sev- eral regions [ Fig. 1(a)] and that a straight line has delimited a zone with erroneous examples that con- tains several previous partitions [ Fig. 1(b)], then the previous approximations of each particular region would be forgotten in this zone and a new approx- imation would be designed for the whole zone (ap- prox5 in Fig. 1(c)). B2) Special treatment that takes into consideration the previous partitions. For example, let us suppose that a classifier system is available which has ...
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... of the problem into sev- eral regions [ Fig. 1(a)] and that a straight line has delimited a zone with erroneous examples that con- tains several previous partitions [ Fig. 1(b)], then the previous approximations of each particular region would be forgotten in this zone and a new approx- imation would be designed for the whole zone (ap- prox5 in Fig. 1(c)). B2) Special treatment that takes into consideration the previous partitions. For example, let us suppose that a classifier system is available which has divided Adjust the solver systems that act on incorrect regions that are not inside the erroneous zone. For instance, adjust approx1, approx2, approx3 and approx4 in Fig. 1(c). The ...
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... (ap- prox5 in Fig. 1(c)). B2) Special treatment that takes into consideration the previous partitions. For example, let us suppose that a classifier system is available which has divided Adjust the solver systems that act on incorrect regions that are not inside the erroneous zone. For instance, adjust approx1, approx2, approx3 and approx4 in Fig. 1(c). The main moti- vation for this step is the possible situation of a region that is not able to transform into correct because it has some troubled examples. These examples can be included in the erroneous zone when the region is divided by the processing element. Hence, the solver system that acts on this region can be ad- justed ...
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Citations
... The divide and conquer strategies make use of regions of solution spaces for knowledge extraction, handling noisy instances, and multi-facet decision-making by partitioning the instances into subgroups [11]. The semi-global partitioning to design automatic systems (SEPARATE) algorithm partitions the solution space into different regions using the solver modules, decision nodes, and the index nodes [12]. The solver module (binary perceptron) attempt to correctly classify instances through iteratively dividing solution space into sub-regions that have instances with homogenous outcomes. ...
... Various algorithms have been applied to PIMA dataset in order to improve the generalization accuracy. The SEPARATE algorithm produced a classification accuracy of 79.99% with 78.85% prediction accuracy [12]. The genetic learning of fuzzy rule classifiers produced classification accuracy of 85% with 73% prediction accuracy [30]. ...
A relabeling algorithm for retrieval of noisy instances with binary outcomes is presented. The relabeling algorithm iteratively retrieves, selects, and re-labels data instances (i.e., transforms a decision space) to improve prediction quality. It emphasizes knowledge generalization and confidence rather than classification accuracy. A confidence index incorporating classification accuracy, prediction error, impurities in the relabeled dataset, and cluster purities was designed. The proposed approach is illustrated with a binary outcome dataset and was successfully tested on the standard benchmark four UCI repository dataset as well as bladder cancer immunotherapy data. A subset of the most stable instances (i.e., 7% to 51% of the sample) with high confidence (i.e., between 64%-99.44%) was identified for each application along with most noisy instances. The domain experts and the extracted knowledge validated the relabeled instances and corresponding confidence indexes. The relabeling algorithm with some modifications can be applied to other medical, industrial, and service domains.
... The concept of data set partitioning or divide and conquer was employed by a large number of neural network studies which included tests on the spirals data (Whitley and Karunanithi, 1991; Smieja, 1996; Chen et al., 1997; Lu and Ito, 1999; Fu et al., 2001; Castro et al., 2000; Chen and Chang, 2000; de Souza et al., 2002). The concept of partitioning can successfully be employed to solve the two-spiral task without using neural networks at all. ...
The two-spiral task is a well-known benchmark for binary classification. The data consist of points on two intertwined spirals which cannot be linearly separated. This article reviews how this task and some of its variations have significantly inspired the development of several important methods in the history of artificial neural networks. The two-spiral task became popular for several different reasons: (1) it was regarded as extremely challenging; (2) it belonged to a suite of standard benchmark tasks; and (3) it had visual appeal and was convenient to use in pilot studies. The article also presents an example which demonstrates how small variations of the two-spiral task such as relative rotations of the two spirals can lead to qualitatively different generalisation results.
... In the literature, many well-known models such as modular classifiers [26], [32], [33], ensemble classifiers [1], [34], [35], and neural networks [27]–[29] are based on this strategy. However , most of these models follow the way of mixture experts that decisions are made by a decision-making framework such as voting schemes, gating or weighted output approaches, etc. [31] Another category of divide and conquered based model is classification tree [3]–[6], [23]–[25], [30]. Against previous multimodel methods and other category methods, the advantage is, classification tree can naturally partition the feature space into disjoint regions for a single class, and reduce the classification difficulty. ...
This paper presents a new membership authentication method by face classification using a support vector machine (SVM) classification tree, in which the size of membership group and the members in the membership group can be changed dynamically. Unlike our previous SVM ensemble-based method, which performed only one face classification in the whole feature space, the proposed method employed a divide and conquer strategy that first performs a recursive data partition by membership-based locally linear embedding (LLE) data clustering, then does the SVM classification in each partitioned feature subset. Our experimental results show that the proposed SVM tree not only keeps the good properties that the SVM ensemble method has, such as a good authentication accuracy and the robustness to the change of members, but also has a considerable improvement on the stability under the change of membership group size.
... On the other hand, it is observed that the presented method has been able to improve the generalization results of a neural tree (from 67.18% to 72.91%), without using test samples during the training. In order to compare the presented method with other machine learning methods, Table 3 presents the results obtained by an adjusted neural tree, a feedforward neural network with six neurons into its hidden layer (taken from [5]) and the C4.5 algorithm with pruning (taken from [5]), when the PIMA problem is solved. It can be observed that the adjusted neural tree obtains generalization results better than other tree based method optimized for attaining good generalization (C4.5 algorithm with pruning). ...
... On the other hand, it is observed that the presented method has been able to improve the generalization results of a neural tree (from 67.18% to 72.91%), without using test samples during the training. In order to compare the presented method with other machine learning methods, Table 3 presents the results obtained by an adjusted neural tree, a feedforward neural network with six neurons into its hidden layer (taken from [5]) and the C4.5 algorithm with pruning (taken from [5]), when the PIMA problem is solved. It can be observed that the adjusted neural tree obtains generalization results better than other tree based method optimized for attaining good generalization (C4.5 algorithm with pruning). ...
This article presents a procedure for improving generalization in classification trees. This procedure consists of adjusting the nodes of a tree with the aim of moving the borders between regions in the problem space away from the neighboring training samples. The objective of this process is to place the borders in an optimal position inside the problem space and to detect some noisy training samples. In this way, results on training samples are worse (noisy training samples are not successfully classified) and results on validation samples are better. These facts are experimentally confirmed with several examples.
... El segundo método de análisis aplicado se basa en el empleo de técnicas de Inteligencia Artificial con objeto de seleccionar las características más relevantes, y ajustar el modelo cuya obtención se pretende alcanzar. En concreto, se ha tomado la metodología propuesta en SEPARATE (SEmiglobal PARtition to design Authomatic sysTEms) (Castro, 2000), adaptándola para considerar tanto variables discretas como continuas, y combinándola con la metodología de selección de características del algoritmo FOCUS (Almuallim, 1994). ...
... El segundo método de análisis aplicado se basa en el empleo de un método híbrido con objeto de seleccionar las características más relevantes, y ajustar el modelo QU se pretende. Se parte de la metodología propuesta en SEPARATE (SEmiglobal PARtition to design Authomatic sysTEms) [10], adaptándola para considerar tanto variables discretas como continuas, y combinándola con la metodología de selección de características del algoritmo FOCUS [5]. ...
In this paper the famous neural model, the multilayer perceptron, is extended to a new neural model that is called the additive-Takagi–Sugeno-type multilayer perceptron. The present study proves that this new model can also act as a universal approximator, and thus it can be used in many fields, such as system modeling and identification. The concept of f-duality and the fuzzy operator interactive-or are used to prove that the proposed neural model is functionally equal to a kind of fuzzy inference system. Further, this paper presents another new neuro-fuzzy model that is called the sigmoid-adaptive-network-based fuzzy inference system. Simulation studies show that our proposed models both have stronger approximation capability than multilayer perceptrons.
Spatial and seasonal distribution patterns of suspended particulate matter, particulate organic carbon (POC), particulate nitrogen, chlorophyll a and phytoplankton abundance and biomass were analysed along two transects in the southern Adriatic and northern Ionian Seas. Moreover, 2 years of samples collected by sediment traps at one selected station for each transect are used to assess the variability of fluxes of biogenic (organic carbon, total nitrogen, carbonates, biogenic silica) and lithogenic constituents.
The generalization capability of an artificial neural network (ANN) is the most important performance of it, but to obtain the good generalization capability of an ANN is not an easy thing. During about twenty years rapid development of ANN technology, many methods of improving the generalization capability have been proposed, but the generalization problem related to an ANN is still serious. This paper first narrates the existing methods of improving ANN generalization capability, sorting them in five categories. Second, the existing improving methods are evaluated and tested, their capabilities and shortcomings being pointed out. Finally, the concluding remarks are given and the prospective improving methods are discussed.
