Anderson's Iris Data Research Articles

A Study on DS-SVM-Based Forecast Model from the View of Information Fusion

Dempster-Shafer Theory is specially advantaged in information fusion, while Support Vector Machine (SVM) can well deal with high-dimensional limited sample data. This Article firstly forecasts the data samples by categories with multiple SVMs, and hence based thereon, fuses the resulting information from multiple SVM models by using DS theory. At the end, Anderson's Iris data set is used to simulate the system of the created DS-SVM model, which shows that the approaches proposed in this Article can not only increase the accuracy rate of the SVM forecasting model, but also improve the propensity scores of the SVM forecasting model.

POP-Yager: A novel self-organizing fuzzy neural network based on the Yager inference

A Pseudo-Outer Product based Fuzzy neural network using the Yager Rule of Inference [Keller, J. M., Yager, R. R., & Tahani, H. (1992). Neural network implementation of fuzzy logic. Fuzzy Sets and Systems, 45(1), 1-12.] called the POP-Yager FNN is proposed in this paper. The proposed POP-Yager FNN training consists of two phases; namely: the fuzzy membership derivation phase using the Modified Learning Vector Quantization (MLVQ) method [Ang, K. K. (1998). POPFNN-CRI(S): A Fuzzy neural network based on the compositional rule of inference. M. Phil. Dissertation, Nanyang Technological University.]; and the rule identification phase using the novel one-pass LazyPOP learning algorithm [Quek, C. & Zhou, R. W. (1999). The POP learning algorithms: Reducing work in identifying fuzzy rules. Neural Networks, 14(10), 1431-1445]. The proposed two-phase learning process effectively constructs the membership functions and identifies the fuzzy rules. Inference process in POP-Yager is based on the well-established Yager fuzzy inference rule [Keller, J. M., Yager, R. R. & Tahani, H. (1992). Neural network implementation of fuzzy logic. Fuzzy Sets and Systems, 45(1), 1-12]. Operations in POP-Yager strictly perform the logical processes of the Yager inference rule. This gives the novel network a strong theoretical foundation. Extensive experimental results based on the classification performance of the POP-Yager FNN using the Anderson's Iris data [Duda, R. O. & Hart, P. E. (1973). Pattern classification and scene analysis. Wiley.] are presented for discussion. Results show that the POP-Yager FNN possesses excellent recall and generalization abilities. The performance of the POP-Yager FNN as a general approximation of traffic flow data [Tan, G. K. (1997). Feasibility of predicting congestion states with neural networks. Final Year Project Report, Nanyang Technological University, CSE.] is analysed.

Popfnn-cri(s): pseudo outer product based fuzzy neural network using the compositional rule of inference and singleton fuzzifier

A pseudo-outer product based fuzzy neural network using the compositional rule of inference and singleton fuzzifier [POPFNN-CRI(S)] is proposed in this paper. The correspondence of each layer in the proposed POPFNN-CRI(S) to the compositional rule of inference using standard T-norm and fuzzy relation gives it a strong theoretical foundation. The proposed POPFNN-CRI(S) training consists of two phases; namely: the fuzzy membership derivation phase using the novel fuzzy Kohonen partition (FKP) and pseudo Kohonen partition (PFKP) algorithms, and the rule identification phase using the novel one-pass POP learning algorithm. The proposed two-phase learning process effectively constructs the membership functions and identifies the fuzzy rules. Extensive experimental results based on the classification performance of the POPFNN-CRI(S) using the Anderson's Iris data are presented for discussion. Results show that the POPFNN-CRI(S) has taken only 15 training iterations and misclassify only three out of all the 150 patterns in the Anderson's Iris data.

A fuzzy neural network for pattern classification and feature selection

A fuzzy neural network with memory connections for classification, and weight connections for selection is introduced, thereby solving simultaneously two major problems in pattern recognition: pattern classification and feature selection. The proposed network attempts to select important features from among the originally given plausible features, while maintaining the maximum recognition rate. The resulting value of weight connection represents the degree of importance of feature. Moreover, the knowledge acquired by the network can be described as a set of interpretable rules. The effectiveness of this new method has been validated by using Anderson's IRIS data. The results are: first, the use of two features selected by our method from among the original four in the proposed network results in virtually identical classifier performance; and second, the constructed classifier is described by three simple rules that are of if–then form.

Discrimination by means of components that are orthogonal in the data space

Krzanowski (J. Chemometrics, 9, 509 (1995)) proposed a method for obtaining so-called orthogonal canonical variates (henceforth called components) for discrimination purposes. In contrast with ordinary discriminant analysis, this method employs components that are orthogonal in the original data space. These components are derived in a successive way, thus optimizing discrimination of a component given the previously extracted components. Two alternative procedures are proposed to extract the desired number of components simultaneously, yielding a better overall discrimination. The simultaneous approaches are applied to the same two data sets as analysed by Krzanowski, as well as to Anderson's Iris data, and a comparison of discriminatory quality of the solutions is presented. © 1997 John Wiley & Sons, Ltd.

MOUNTAIN METHOD-BASED FUZZY CLUSTERING: METHODOLOGICAL CONSIDERATIONS

The mountain method is a grid-based procedure for determining the approximate locations of cluster centers in data sets with clustering tendencies. This paper supplies additional background and detail in two important areas. In the first part of the paper, crucial methodological considerations arc discussed, including the choice of grid size, the choice of parameter values, and the notion of “peak non-reusability.” The paper also introduces the possibility of using the singular value decomposition with mountain method output as a means of estimating the number of clusters in the data. In the second pan of the paper, the mountain method is discussed as part of a general grid-based approach to the location of “objects” in spatial data. An example using Anderson's iris data is included, and an application of the method to a problem in robotics is described in detail.

Fuzzy Kohonen clustering networks

Kohonen networks are well known for cluster analysis (unsupervised learning). This class of algorithms is a set of heuristic procedures that suffers from several major problems (e.g. neither termination or convergence is guaranteed, no model is optimized by the learning strategy, and the output is often dependent on the sequence of data). A fuzzy Kohonen clustering network is proposed which integrates the Fuzzy c-Means (FCM) model into the learning rate and updating strategies of the Kohonen network. This yield an optimization problem related to FCM, and the numerical results show improved convergence as well as reduced labeling errors. It is proved that the proposed scheme is equivalent to the c-Means algorithms. The new method can be viewed as a Kohonen type of FCM, but is “self-organizing” since the “size” of the update neighborhood and learning rate in the competitive layer are automatically adjusted during learning. Anderson's IRIS data is used to illustrate this method; and results are compared with the standard Kohonen approach.

Generalized k-nearest neighbor rules

This paper discusses a suitable framework for generalizing the k-nearest neighbor ( k-NNR) algorithms to cases where the design labels are not necessarily crisp, i.e., not binary-valued. The proposed framework imbeds all crisp k-NNR's into a larger structure of fuzzy k-NNR's. The resultant model enables neighborhood voting to be a continuous function of local labels at a point to be classified. We emphasize that the decision itself may be crisp even when a fuzzy k-NNR is utilized. The usefulness of this extension of the conventional technique is illustrated by comparing the observed error rates of four classifiers (the hard k-NNR, two fuzzy k-NNR's, and a fuzzy 1-nearest prototype rule (1-NPR) on three data sets: Anderson's Iris data, and samples from (synthetic) univariate and bivariate normal mixtures. Our conclusions: all four designs yield comparable (usually within 4%) error rates; the Fuzzy c-Means (FCM) based k-NNR is usually the best design; the FCM/1-NPR is the most efficient and perhaps most useful of the four designs; and finally, that generalized NNR's are an important and useful extension of the conventional ones.