Data mining with Support Vector Machine
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1 Data mining with Support Vector Machine Ms. Arti Patle IES, IPS Academy Indore (M.P.) Mr. Deepak Singh Chouhan IES, IPS Academy Indore (M.P.) Abstract: Machine Learning is considered as a subfield of Artificial Intelligence and it is concerned with the development of techniques and methods which enable the computer to learn. In this paper introduce SVM. It is techniques and methodologies developed for machine learning tasks Support vector machines (SVMs) are a set of related supervised learning methods used for classification and regression. Support Vector Machine (SVM) is a classification and regression prediction tool that uses machine learning theory to maximize predictive accuracy. Support Vector Machines are state-of-the art data mining techniques which have proven their performance in many applications, such as credit scoring, financial time series prediction, spam categorization and brain tumor classification. The strength of this technique lies with its ability to model nonlinearity, resulting in complex mathematical models. Improvements in databases technology, computing performance and artificial intelligence have contributed to the development of intelligent data analysis.. The classification used in various area one of them is Credit Scoring. The assessment of risk of default on credit is important for financial institutions. Logistic regression and discriminant analysis are techniques traditionally used in credit scoring for determining likelihood to default based on consumer application and credit reference agency data. Test support vector machines against traditional methods on a large credit card database. From that find that they are competitive and can be used as the basis of a feature selection method to discover those features that are most significant in determining risk of default. Keyword: SVM, Credit risk evaluation, feature selection, Data classification, Machine learning Introduction: A Support Vector Machine (SVM) performs classification by constructing an N- dimensional hyperplane that optimally separates the data into two categories. SVM models are closely related to neural networks. In fact, a SVM model using a sigmoid kernel function is equivalent to a two-layer, perceptron neural network. Support Vector Machine (SVM) models are a close cousin to classical multilayer perceptron neural networks. Using a kernel function, SVM s are an alternative training method for polynomial, radial basis function and multi-layer perceptron classifiers in which the weights of the network are found by solving a quadratic programming problem with linear constraints, rather than by solving a non-convex, unconstrained minimization problem as in standard neural network training. In the parlance of SVM literature, a predictor variable is called an attribute, and
2 a transformed attribute that is used to define the hyperplane is called a feature. The task of choosing the most suitable representation is known as feature selection. A set of features that describes one case (i.e., a row of predictor values) is called a vector. So the goal of SVM modeling is to find the optimal hyperplane that separates clusters of vector in such a way that cases with one category of the target variable are on one side of the plane and cases with the other category are on the other size of the plane. The vectors near the hyperplane are the support vectors. The figure below presents an overview of the SVM process. Algorithm : separated. The SVM analysis attempts to find a 1-dimensional hyperplane (i.e. a line) that separates the cases based on their target categories. There are an infinite number of possible lines; two candidate lines are shown above. The question is which line is better, and how do we define the optimal line. The dashed lines drawn parallel to the separating line mark the distance between the dividing line and the closest vectors to the line. The distance between the dashed lines is called the margin. The vectors (points) that constrain the width of the margin are the support vectors. The following figure illustrates this Before considering N-dimensional hyperplanes, let s look at a simple 2- dimensional example. Assume we wish to perform a classification, and our data has a categorical target variable with two categories. Also assume that there are two predictor variables with continuous values. If we plot the data points using the value of one predictor on the X axis and the other on the Y axis we might end up with an image such as shown below. One category of the target variable is represented by rectangles while the other category is represented by ovals. In this idealized example, the cases with one category are in the lower left corner and the cases with the other category are in the upper right corner; the cases are completely Rather than fitting nonlinear curves to the data, SVM handles this by using a kernel function to map the data into a different space where a hyperplane can be used to do the separation. The kernel function may transform the data into a higher dimensional space to make it possible to perform the separation.
3 The concept of a kernel mapping function is very powerful. It allows SVM models to perform separations even with very complex boundaries. Model Parameter: four basic concepts: (i) the separating hyper plane, (ii) the maximum-margin hyper plane, (iii)the soft margin (iv) the kernel function The separating hyper plane The human eye is very good at pattern recognition. Even a quick glance at Figure 1a shows that the AML profiles form a cluster in the upper left region of the plot, and the ALL profiles cluster in the lower right. A simple rule might state that a patient has AML if the expression level of MARCKSL1 is twice as high as the expression level of ZYX, and vice versa for ALL. Geometrically, this rule corresponds to drawing a line between the two clusters (Fig. 1b). Subsequently, predicting the label of an unknown expression profile is easy: one simply needs to ask whether the new profile falls on the ALL or the AML side of this separating line. Now, to define the notion of a separating hyper plane, consider a situation in which the microarray does not contain just two genes. For example, if the microarray contains a single gene, then the space in which the corresponding onedimensional expression profiles reside is a one-dimensional line. We can divide this line in half by using a single point (Fig. 1c). In two dimensions (Fig. 1b), a straight line divides the space in half, and in three dimensions, we need a plane to divide the space (Fig. 1d). We can extrapolate this procedure mathematically to higher dimensions. The general term for a straight line in a high-dimensional space is a hyper plane, and so the separating hyperplane is, essentially, the line that separates the ALL and AML samples. The maximum-margin hyperplane The concept of treating the objects to be classified as points in a high-dimensional space and finding a line that separates them is not unique to the SVM. The SVM, however, is different from other hyperplanebased classifiers by virtue of how the hyperplane is selected. Consider again the classification problem portrayed in Figure 1a. We have now established that the goal of the SVM is to identify a line that separates the ALL from the AML expression profiles in this two-dimensional space. However, many such lines exist (Fig. 1e). Which one provides the best classifier? the simple idea of selecting the line that is, roughly speaking, in the middle. In other words, one would select the line that separates the two classes but adopts the maximal distance from any one of the given expression profiles (Fig. 1f). The soft margin where the data set contains an error, the circled gene expression profile. Intuitively, we would like the SVM to be able to deal with errors in the data by allowing a few
4 anomalous expression profiles to fall on the wrong side of the separating hyperplane. To handle cases like these, the SVM algorithm has to be modified by adding a soft margin. Essentially, this allows some data points to push their way through the margin of the separating hyperplane without affecting the final result. Figure 1h shows the soft margin solution to the problem in Figure 1g. The one outlier now resides on the same side of the line with members of the opposite class. The kernel function the kernel function is a mathematical trick that allows the SVM to perform a twodimensional classification of a set of originally one-dimensional data. In general, a kernel function projects data from a lowdimensional space to a space of higher dimension. To understand kernels a bit better, consider the two-dimensional data set shown in Figure 1k. These data cannot be separated using a straight line, but a relatively simple kernel function that projects the data from the two-dimensional space up to four dimensions (corresponding to the products of all pairs of features) allows the data to be linearly separated. We cannot draw the data in a four-dimensional space, but we can project the SVM hyperplane in that space back down to the original two-dimensional space. The result is shown as the curved line in Figure 1k. SVMs to handle nonlinearly separable data sets and to incorporate prior knowledge, the kernel function yield at least two additional benefits. First, kernels can be defined on inputs that are not vectors. This ability to handle nonvector data is critical in biological applications, allowing the SVM to classify DNA and protein sequences, nodes in metabolic, regulatory and protein-protein interaction networks and microscopy images. Second, kernels provide a mathematical formalism for combining different types of data. Support Vector Machine (SVM) classifier SVM separates binary classified data by a hyperplane such that the margin width between the hyperplane and the examples is maximized. Statistical learning theory shows that maximizing the margin width reduces the complexity of the model, consequently reducing the expected general risk of error. For problems where data is not separable by a hyperplane, typical of most real-world classification problems, a soft margin is used. In this case, training examples are allowed some slack to be on the wrong side of the margin. However, they accrue a penalty proportional to how far they are on the wrong side. The sum of the penalties is minimized whilst maximizing the margin width. A parameter C controls the relative cost of each goal in the overall optimization problem. The SVM optimization problem can be expressed algebraically as a dual form quadratic programming problem. Linear and Non Linear Case:
5 even outperform the C4.5 rules that result from the dataset with the actual class labels. These advantages make it appropriate to consider SVMs and their extracted rules for applications where both accuracy and comprehensibility are required. One no longer needs to settle for the traditional comprehensible, yet less accurate classification methods. Comparision : SVM must deal with (a) more than two predictor variables, (b) separating the points with non-linear curves, (c) handling the cases where clusters cannot be completely separated, and (d) handling classifications with more than two categories Conclusion: The support vector machine has been introduced as a robust tool for many aspects of data mining including classification, regression and outlier detection. Rule extraction techniques generate classification models that have clear advantages. First of all, they are comprehensible and therefore easy to incorporate in real-life applications where clarity of the classifications made is needed. Secondly, the extracted rules only lose a small percentage in accuracy of the black box model from which they are generated. Since Support Vector Machines are among the best performing classifiers, rules extracted from SVMs achieve an accuracy that often surpasses that of the classical methods, such as C4.5 and logit. Using the SVM model instead of the original data points eliminates the apparent conflicts and creates a cleaner dataset. In our experiments, the rules generated by C4.5 on the data with labels predicted by the SVM Refrences: 1. Cheng-Lung Huang a, Mu-Chen Chen b, Chieh-Jen Wang c Credit scoring with a data mining approach based on support vector machines Department of Information Management, 2, Juoyue Road, Nantz District, Kaohsiung 811, Taiwan 2. Cristianini, N., & Shawe-Taylor, J. (2000). An introduction to support vector machines. Cambridge: Cambridge University Press 3. Davis, R. H., Edelman, D. B., & Gammerman, A. J. (1992). Machine learning algorithms for credit-card applications. Journal of Mathematics Applied in Business and Industry 4. Brill, J. (1998). The importance of credit scoring models in improving cash flow and collection. Business Credit, 5. Lee, T.-S., Chiu, C.-C., Lu, C.-J., & Chen, I.- F. (2002). Credit scoring using the hybrid neural discriminant technique. Expert Systems with Applications
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