W. H. Wolberg and O. L. Mangarasian. Multisurface method of pattern separation for medical diagnosis applied to breast cytology. Proceedings of the National Academy of Sciences of the USA, 87:9193--9196, 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....exhibit some over fitting. Another data set which was tested was the Breast Cancer Wisconsin data where the two classes (malignant or benign) have to be computed from 9 numerical attributes from the patients tumors (200 training cases and 169 test cases) The data was first presented by Wolberg [206]. We compare our results to those produced by Zhang [211] who used a nearest neighbor algorithm to achieve 93:7 accuracy. As can be seen from Table 3.3, over fitting prevents good performance from the kernel based SVMs and the top performer here is the maximum entropy discriminator with an ....

W. Wolberg and O. Mangasarian. Multisurface method of pattern separation for medical diagnosis applied to breast cytology. In Proceedings of the National Academy of Sciences, volume 87, U.S.A., 1990.

....Keywords Pareto optimization, di#erential evolution, artificial neural networks, breast cancer. 1 Introduction The economic and social values of Breast Cancer Diagnosis (BCD) are very high. As a result, the problem has attracted many researchers in the area of computational intelligence recently [6, 8, 10, 22, 26, 32, 33, 34]. Because of the importance of achieving highly accurate classification, Artificial Neural Networks (ANNs) are among the most common methods for BCD. Research in the area of using ANNs for medical purposes more specifically BCD [6, 8, 10, 22, 26, 32, 34] has been at the center of attention ....

....clump thickness, uniformity of cell size, uniformity of cell shape, marginal adhesion, single epithelial cell size, bare nuclei, bland chromatin, normal nucleoli, and mitoses. The class output includes 2 classes, benign and malignant. The original dataset was obtained by Wolberg and Mangasarian [33]. 15 4.2 Experimental Setup To be consistent with the literature [8] we removed the sixteen instances with missing values from the dataset to construct a new dataset with 683 instances. The first 400 instances in the new dataset are chosen as the training set and the remaining 283 as the test ....

W. H. Wolberg and O. L. Mangasarian. Multisurface method of pattern separation for medical diagnosis applied to breast cytology. Proceedings of the National Academy of Sciences, National Academy of Sciences, Washington, DC, 87:9193--9196, 1990.

.... and SVM linear models (dotted line) Another data set whichwas tested was the Breast Cancer Wisconsin data where the two classes (malignant or benign) have to be computed from 9 numerical attributes from the patients (200 training cases and 169 test cases) The data was rst presented byWolberg [24]. We compare our results to those produced by Zhang [25] who used a nearest neighbour algorithm to achieve93:7 accuracy. As can be seen from Table 2, over tting seems to prevent good performance for kernel based SVMs. The maximum entropy discriminator achieves 95:3 accuracy. In Figure 4 we ....

Wolberg W. and Mangasarian O (1990). Multisurface method of pattern separation for medical diagnosis applied to breast cytology, Proceedings of the National Academy of Sciences, U.S.A., Vol. 87.

.... and SVM linear models (dotted line) Another data set which was tested was the Breast Cancer Wisconsin data where the two classes (malignant or benign) have to be computed from 9 numerical attributes from the patients (200 training cases and 169 test cases) The data was rst presented by Wolberg [24]. We compare our results to those produced by Zhang [25] who used a nearest neighbour algorithm to achieve 93:7 accuracy. As can be seen from Table 2, over tting seems to prevent good performance for kernel based SVMs. The maximum entropy discriminator achieves 95:3 accuracy. In Figure 4 we ....

Wolberg W. and Mangasarian O (1990). Multisurface method of pattern separation for medical diagnosis applied to breast cytology, Proceedings of the National Academy of Sciences, U.S.A., Vol. 87.

....discrimination problem. The first is the linear programming (LP) methods stemming from the Multisurface Method of Mangasarian [12, 13] This method and it s later extension the Robust Linear Programming (RLP) approach [6] have been used in a highly successfully breast cancer diagnosis system [26]. The second direction is the quadratic programming (QP) methods based on Vapnik s Statistical Learning Theory [24, 25] Statistical Learning Theory addresses mathematically the problem of how to best construct functions that generalize well on future points. The problem of constructing the best ....

W. H. Wolberg and O. L. Mangasarian. Multisurface method of pattern separation for medical diagnosis applied to breast cytology. Proceedings of the National Academy of Sciences, U.S.A., 87:9193--9196, 1990. 30

....began in 1989 with the collaborative work of W. H. Wolberg (Surgery and Human Oncology) and O. L. Mangasarian (Computer Sciences) The Multisurface Method (MSM) 53, 54] of pattern separation was first applied to a collection of cases represented by nine subjectively evaluated cytological features [57, 58, 92]. The MSM procedure uses a linear programming model to place successive pairs of separating planes in the feature space of the input examples, building a piecewise linear separating surface. The procedure can also be considered a neural network training algorithm [9] While successful [93] the ....

....assumption. 2.3 Extraction of digital nuclear features In order to evaluate the size, shape and texture of the cell nuclei, we arrived at a set of ten features [86, 94] which are computed for each cell. Some of these replicate or approximate features previously evaluated subjectively by Wolberg [92], while others are unique to this work. All of the size and shape features were verified using idealized phantom cells [97] The computed features are as follows. 1. Radius Radius is computed by averaging the length of radial line segments, that is, lines from the center of mass of the snake to ....

W. H. Wolberg and O. L. Mangasarian. Multisurface method of pattern separation for medical diagnosis applied to breast cytology. Proceedings of the National Academy of Sciences, U.S.A., 87:9193--9196, 1990.

....classifying further points. Although we shall discuss only the method of separation by polynomial surfaces in this paper, it should be mentioned that other methods have usefully been applied when the desired classi cation of the data points cannot be achieved by linear separators; see, for example [16, 27]. The representation and approximation of boolean functions by polynomials has useful applications in a number of areas of computer science; a discussion of some of the problems studied and the techniques used may be found in the survey of Saks [23] In addition, polynomial discriminators have ....

W.H. Wolberg and O.L. Mangasarian, Multisurface method of pattern separation for medical diagnosis applied to breast cytology, Proc. Nat. Acad. Sci. USA, 87, 1990: 9193-9196. 15

....Clustering Merging the Standardized Iris Data. Data File No. Clusters K Validity Cluster Sizes k iris150.dta 4 0.5766 50, 40, 29, 31 0.192, 0.174, 0.182, 0.227 3 1.1520 50, 51, 49 0.192, 0.248, 0.215 2 5.8216 B 50, 150 0.192, 0. 323 10Our third data set is taken from Wolberg and Mangasarian [23] at the University of Wisconsin Medical School. We randomly selected 200 of the more than 500 feature vectors. As usual, we standardized each of the 30 features separately to be in [0,1] The vectors are labeled for two classes that we think are benign and malignant. One label is attached to 121 ....

W. H. Wolberg and O. L. Mangasarian, "Multisurface method of pattern separation for medical diagnosis applied to breast cytology," Proc. of the Nat. Academy of Sciences, U.S.A., Volume 87, 9193-9196, December, 1990.

....structure and training procedure. FuNe I also uses a concept of weighted rules. We refrained from using this approach in NEFCLASS, because the semantics of weighted fuzzy rules is not clear [8] As a second test for the NEFCLASS learning algorithms we used the Wisconsin Breast Cancer data set [13]. This data set contains 699 cases distributed into two classes (benign and malign) We used only 683 cases, because 16 cases have missing values. Each pattern has nine features. To show how NEFCLASS performs when prior knowledge is supplied, we used a fuzzy clustering method to obtain fuzzy ....

W.H. Wolberg and O.L. Mangasarian. Multisurface method of pattern separation for medical diagnosis applied to breast cytology. Proc. National Academy of Sciences, 87:9193--9196, December 1990. 6

....borderline (DS) is not obvious, nor is it clear whether certain attributes are more important than others. The obliqueness of the data is reflected in the fact that a summation of attribute values or weight of evidence appears broadly to be decisive. On an earlier (smaller) version of the data, Wolberg and Mangasarian (1990) used a statistical method with multiple hyperplanes to obtain accuracies as high as 95.9 . The UCI Repository states highest reported accuracy on the current dataset to be 94 . 10 XCSI will first be applied to the WBC dataset in a train test experiment using a wellknown procedure for ....

Wolberg, W. H. and O. L. Mangasarian (1990). Multisurface method of pattern separation for medical diagnosis applied to breast cytology. Proceedings of the National Academy of Sciences 87, 9193--9196.

....8 Theta 1 2.74 (0.35) Monks2 17 Theta 8 Theta 1 2.48 (0.56) Monks3 17 Theta 8 Theta 1 1.93 (0.09) S junction 240 Theta 8 Theta 3 227.04 (4.37) Mushroom 127 Theta 8 Theta 1 141.35 (15.43) B cancer 90 Theta 8 Theta 1 16.29 (3.52) 4. The Wisconsin breast cancer classification dataset [17]. Each of the 699 patterns in the dataset is described by 9 attributes. The nine measurements taken from fine needle aspirates from human breast tissues correspond to cytological characteristics of a benign or of a malignant sample. These are A 1 . clump thickness, A 2 . uniformity of cell size, A ....

..... bland chromatin, A 8 . normal nucleoli, and A 9 . mitosis. Each of these nine attributes of the fine needle aspirates was graded 1 to 10 at the time of sample collection, with 1 being the closest to benign and 10 the most anaplastic (more detailed description of these attributes can be found in [17]) Since the attributes are integer valued ranging from 1 to 10, we created 10 input units for each attribute. The attribute values are represented by the following encoding scheme: A i = k , 8 : I 10 Theta(i Gamma1) j = 1 8 j = 1; 2; k I 10 Theta(i Gamma1) j = ....

W.H. Wolberg and O.L. Mangasarian, "Multisurface method of pattern separation for medical diagnosis applied to breast cytology," Proceedings of the National Academy of Sciences, vol. 87, pp. 9193--9196, 1990.

....of these data sets, as well as comparative studies between the Proben1 results, individual classifiers and ensembles of classifiers is available in (Tumer and Ghosh, 1995c) CANCER1 is based on breast cancer data, obtained from the University of Wisconsin Hospitals, from Dr. William H. Wolberg (Mangasarian et al. 1990; Wolberg and Mangasarian, 1990) This set has 9 inputs, 2 outputs and 699 patterns, of which 350 are used for training. GENE1 is based on intron exon boundary detection, or the detection of splice junctions in DNA sequences (Noordewier et al. 1991; Towell and Shavlik, 1992) 120 inputs are used ....

....as comparative studies between the Proben1 results, individual classifiers and ensembles of classifiers is available in (Tumer and Ghosh, 1995c) CANCER1 is based on breast cancer data, obtained from the University of Wisconsin Hospitals, from Dr. William H. Wolberg (Mangasarian et al. 1990; Wolberg and Mangasarian, 1990). This set has 9 inputs, 2 outputs and 699 patterns, of which 350 are used for training. GENE1 is based on intron exon boundary detection, or the detection of splice junctions in DNA sequences (Noordewier et al. 1991; Towell and Shavlik, 1992) 120 inputs are used to determine whether a DNA ....

Wolberg, W. H. and Mangasarian, O. (1990). Multisurface method of pattern separation for medical diagnosis applied to breast cytology. In Proceedings of the National Academy of Sciences, volume 87, pages 9193--9196, U.S.A.

....cases, training was stopped when the test set error reached a plateau. We report error percentages on the test set, and the standard deviation on those values based on 20 runs. CANCER1 is based on breast cancer data, obtained from the University of Wisconsin Hospitals, from Dr. William H. Wolberg [28, 47]. This set has 9 inputs, 2 outputs and 699 9 Available at URL ftp: ftp.ira.uka.de pub papers techreports 1994 1994 21.ps.Z. 10 Proben1 results reported here correspond to the pivot and no shortcut architectures, discussed in [34] The large error in the Proben1 no shortcut architecture ....

William H. Wolberg and O.L. Mangasarian. Multisurface method of pattern separation for medical diagnosis applied to breast cytology. In Proceedings of the National Academy of Sciences, volume 87, pages 9193--9196, U.S.A, December 1990.

.... problem The database for the Wisconsin Breast Cancer Diagnosis is available publicly via anonymous ftp from the University of California Irvine repository [12] This data set has been used as the test data for several studies on pattern classification methods using linear programming techniques [3, 9, 20] and statistical techniques [21] Each pattern in the data set has nine attributes. The nine measurements taken from fine needle aspirates from human breast tissues correspond to cytological characteristics of benign or of malignant sample. These are A 1 . clump thickness, A 2 . uniformity of ....

..... bland chromatin, A 8 . normal nucleoli, and A 9 . mitosis. Each of these nine attributes of the fine needle aspirates was graded 1 to 10 at the time of sample collection, with 1 being the closest to benign and 10 the most anaplastic (more detailed description of these attributes can be found in [20]) Since the attributes are integer valued ranging from 1 to 10, we created 10 input units for each attribute. With an additional input for the bias weight at the hidden units, we have a total of 91 input units. Let us denote these inputs as I 1 ; I 2 ; I 91 . For i = 0; 1; 8 the ....

W.H. Wolberg and O.L. Mangasarian, Multisurface method of pattern separation for medical diagnosis applied to breast cytology, Proceedings of the National Academy of Sciences 87 (1990) 9193-9196.

....Breast Cancer Diagnosis Dataset. The Wisconsin Breast Cancer Data (WBCD) is a large data set that consists of 699 patterns of which 458 are benign samples and 241 are malignant samples. Each of these patterns consists of nine measurements taken from fine needle aspirates from a patient s breast [15]. The measurements were graded 1 to 10 at the time of sample collection, with 1 being the closest to benign and 10 the most anaplastic. A linear programming based method for pattern separation called the Multisurface Method has been proposed by Mangasarian [16] A computer program that implements ....

W.H. Wolberg and O.L. Mangasarian, "Multisurface method of pattern separation for medical diagnosis applied to breast cytology," Proc. of the National Academy of Sciences, vol. 87, pp. 9193-9196, 1990.

....format. Rules that cannot be merged, but nevertheless describe adjacent regions, should be grouped in output. In this way the user is guided in interpreting the classification. 3 Experimental Evaluation As an example for our extensions to NEFCLASS we use the Wisconsin Breast Cancer data set [13]. This data set contains 699 cases distributed into two classes (benign and malign) We excluded 16 cases with missing values, and split the dataset into training and test data. Initial rule creation using 5 fuzzy sets per variable creates 166 rules. To demonstrate the pruning strategies the ....

W.H. Wolberg and O.L. Mangasarian. Multisurface method of pattern separation for medical diagnosis applied to breast cytology. Proc. National Academy of Sciences, 87:9193--9196, December 1990.

....some results have even been improved. cancer is a breast cancer diagnosis problem with 9 inputs and two possible outputs: sick or healthy. The file cancer contains 699 examples, from which 3 partitions have been made: cancer1, 2 and 3. This data set was originally obtained from Dr. W. H. Wolberg [27]. Results have been compared to a baseline neural classifier, rprop, which uses a multi layer perceptron with two hidden layers; the two figures shown in table 3 are the number of neurons in the first and second layer; parameters used in rprop are shown in [26] In order to test the performance of ....

William H. Wolberg and O.L. Mangasarian. Multisurface method of pattern separation for medical diagnosis applied to breast cytology. Proceedings of the National Academy of Sciences, U.S.A., 87:9193-- 9196, December 1990.

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W. H. Wolberg and O. L. Mangarasian. Multisurface method of pattern separation for medical diagnosis applied to breast cytology. Proceedings of the National Academy of Sciences of the USA, 87:9193--9196, 1990.

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Wolberg, W.H. & Mangasarian, O.L. Multisurface Method of Pattern Separation for Medical Diagnosis Applied to Breast Cytology. Proceedings of the National Academy of Sciences, USA, vol. 87(23), pp. 9193-9196, 1990.

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Wolberg, W. H. and O. Mangasarian: 1990, `Multisurface method of pattern separation for medical diagnosis applied to breast cytology'. Proceedings of the National Academy of Sciences, U.S.A. 87, 9193--9196.

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William H. Wolberg and O.L. Mangasarian. Multisurface method of pattern separation for medical diagnosis applied to breast cytology. In Proceedings of the National Academy of Sciences, volume 87, pages 9193--9196, U.S.A, December 1990.

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W. H. Wolberg and O. L. Mangasarian. Multisurface method of pattern separation for medical diagnosis applied to breast cytology. Proc. Natl. Acad. Sci. USA, 87:9188--9192, 1990.

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W. Wolberg and O. Mangasarian. Multisurface method of pattern separation for medical diagnosis applied to breast cytology. In Proceedings of the National Academy of Sciences, volume 87, U.S.A., 1990.

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Wolberg, W. H. & Mangasarian, O. L. (1990). Multisurface method of pattern separation for medical diagnosis applied to breast cytology. Proceedings of the National Academy of Sciences, U.S.A., vol. 87, 9193-9196. 39 Dechang Chen Department of Natural and Applied Sciences

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Wolberg, W. H. and Mangasarian, O. L.; "Multisurface method of pattern separation for medical diagnosis applied to breast cytology", Proceedings of the National Academy of Sciences, U.S.A., Volume 87, December 1990, pp 9193-9196.

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