1. A Support Vector Machine Approach to Sonar Classification
Henry C. Zeringue
ECE 539

2. Abstract
This poster reports research on classification of sonar data using a support vector machine (SVM) approach with a radial basis kernel. Data from mine and rock reflections are used to train and test the SVM. The present research looks at the effect of kernel parameter, p1, on the classification rate. Classification rates of 84% are realized for angle independent data, and 91.5% for angle dependent data. This approach is comparable to previous methods.

3. Signals
The data used is taken from sonar recordings. Each reflection comes from either a metal cylinder or a rock. A 250ms pulse consisting of frequencies from Hz is sent to the target and the subsequent reflection is recorded as data. Each data instance has 60 inputs and a single output (1 for “mine” or -1 for “rock”). The aspect angle for each recording is arbitrary and not supplied.

4. Data Set Representation
There are 208 data instances. The data was represented using the method described by Gorman and Sejnowski [1]. The data order was randomized. The data was broken into 13 sets of 16 instances each. Each of the sets was used as the test data. While a set was use for testing, the other 12 sets were put together for the training data.

5. Data Set Representation Cont.
In this way, each instance was used in testing. Since no aspect angle information was given with the data, this method does not take aspect angle into account. This could cause problems if an angle in the testing set were underrepresented in the training set. This would cause a lower classification rate for that angle. A method for taking the aspect ratio into account was also used.

6. Angle Dependent Representation
Gorman and Sejnowski were able to break the data into two sets “designed to ensure that both sets contained returns from each target aspect angle with representative frequency” [1]. Each of these sets have 104 training samples and 104 testing samples. The present work uses the same sets and determines how the classification rate changes for this data and compares it to previous work [1].

7. Previous Work [1]
The present data was used by others who presented results using classification rates from trained human subjects [2], and a Multi Layer Perceptron (MLP) neural network approach [1]. The MLP approach looks at the effect of the number of hidden neurons on the classification of both the angle dependent and angle independent data.

8. Support Vector Machine
Support Vector Machine (SVM) is a mathematical approach which breaks data spaces into two groups by looking at the distances between data points of those groups [3]. The present data is amenable to this approach, since the data output takes one of two possible outputs.
To classify the data, the SVM must first determine the two classes. To do this, the algorithm looks at the training data and finds the distances between data points of the differing classes. Once the two groups have been separated, it finds a boundary between the two groups. When

9. Support Vector Machine (cont.)
a new input is introduced, SVM determines which group the input belongs to by which side of the boundary it falls. The kernel value (p1) is used is used to help determine the gap, and therefore has an effect on the classification rate.
SVM is a deterministic method. This means that for given training and testing data, it will yield the same classification each time the SVM is run. This classification is independent of the ordering of the training and testing data, unlike some implementations which are dependent on the order in which the data is presented to the network.

10. Implementation
Matlab® [4] was used to implement a SVM using the SVM toolbox [5]. The program ran 13 iterations for 30 p1 values between 0.01 and 1.9. The data was then analyzed and plotted using Excel® (Microsoft Corp.). The present data is also compared with that of Gorman and Sejnowski.

11. Results
The average classification rate for the SVM using the angle independent data is given in Figure 1. This data explores the effect of p1 on the classification rate. The average and standard deviation of the classification rate using the angle dependent data is given in Figure 2. The corresponding data from Gorman and Sejnowski is given in Figure 3.

12. Results
Figure 1. SVM classification rate for different values of p1 using angle independent data.

13. Results (cont.) Figure 2. SVM data for angle dependent data.
Figure 3. MLP data for angle dependent data [1].

14. Conclusion
A SVM neural network implementation is presented. The affect of p1 on the classification rate is seen (Figure 1). The values of p1  0.3 yielded the best rates. Figures 2 and 3 show the SVM implementation compared to previous methods [1]. The standard deviation of 0 in the angle dependent data displays the deterministic nature of SVM. The SVM implementation yielded acceptable classification of the data and is a useful method for sonar classification when the correct parameters are used.

15. References Acknowledgements
[1] Gorman, R.P., T.J. Sejnowski (1988) Analysis of Hidden Units in a Layered Network Trained to Classify Sonar Targets. Neural Networks, v.1 pp
[2] Gorman, R. P., T. Sawatari (1985) The use of multidimensional perceptual models in the selection of sonar echo features. Journal of the Acoustic Society of America, v. 77 n. 3 pp
[3] Neural Networks: A Comprehensive Approach, Prentice Hall, Upper Saddle River, NJ
[4] The Mathworks Inc., Natick, MA
[5] Gunn, S., SVM Toolbox for Matlab
Acknowledgements
The author would like to thank Glenn Walker for his Matlab expertise.