pharmine

SVM is based on the structural risk minimization principle from statistical learning theory (Vapnik 1995; Burges 1998; Evgeniou et al. 2001). A compound is represented by a vector x_i which is its molecular descriptors. In linearly separable cases, SVM constructs a hyperplane which separates two data classes of compounds with a maximum margin. This is accomplished by finding another vector w and a parameter b that minimizes and satisfies the following conditions:

Class 1 (D+)

Class 2 (D–)

where y_i is the data class index of compound i, w is a vector normal to the hyperplane, is the perpendicular distance from the hyperplane to the origin and is the Euclidean norm of w. After the determination of w and b, a given compound with vector x can be classified by:

In non-linearly separable cases, SVM maps the vectors into a higher dimensional feature space using a kernel function K(x_i, x_j). The table below lists three different types of kernel functions which are commonly used. The Gaussian radial basis function kernel has been extensively used in a number of different studies with good results (Burbidge et al. 2001; Czerminski et al. 2001; Trotter et al. 2001).

Commonly used kernel functions

Kernel	Equation
Polynomial
Gaussian radial basis function
Sigmoidal

Linear support vector machine is applied to this feature space and then the decision function is given by:

where l is the number of support vectors and the coefficients alpha_i⁰ and b are determined by maximizing the following Langrangian expression:

under the following conditions:

where C is a penalty for training errors. A positive or negative value from decision function equation indicates that the compound with vector x belongs to the positive or negative data class respectively.

References

• Burbidge R, Trotter M, Buxton B and Holden S (2001). Drug design by machine learning: support vector machines for pharmaceutical data analysis. Computers and Chemistry 26(1): 5-14.
• Burges CJC (1998). A tutorial on support vector machines for pattern recognition. Data Mining and Knowledge Discovery 2(2): 127-167.
• Czerminski R, Yasri A and Hartsough D (2001). Use of support vector machine in pattern classification: Application to QSAR studies. Quantitative Structure-Activity Relationships 20(3): 227-240.
• Evgeniou T and Pontil M (2001). Support vector machines: theory and applications. Machine learning and its applications. Advanced lectures. Paliouras G, Karkaletsis V and Spyropoulos CD. New York, Springer: 249-257.
• Trotter MWB, Buxton BF and Holden SB (2001). Support vector machines in combinatorial chemistry. Measurement and Control 34(8): 235-239.
• Vapnik VN (1995). The nature of statistical learning theory. New York, Springer.
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This entry was posted by Yap Chun Wei on Saturday, June 28th, 2008 at 11:07 pm and is filed under Data mining, Tutorial. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.