"Why Matlab and Rapidminer give different results for SVM optimization"

Hi,

I'm using both Matlab and Rapidminer to do SVM classification with optimization for parameters. The data I used have 5000 obs, 36 integer attributes and one binomial label. I'm expecting similar results, yet they turned out to be different. The C statistics from Matlab is 0.672 while that from Rapidminer is 0.598. Also, they gives difference choices of optimal parameters for C and gamma. Rapidminer gives 0.25 and 0.25 respectively, and Matlab gives 4 and 0.25. I would greatly appreciate your help!

Below is the process code:
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<process version="5.3.008">
<context>
<input/>
<output/>
<macros/>
</context>
<operator activated="true" class="process" compatibility="5.3.008" expanded="true" name="Process">
<process expanded="true">
<operator activated="true" class="retrieve" compatibility="5.3.008" expanded="true" height="60" name="Retrieve donation_sarah5" width="90" x="45" y="30">
<parameter key="repository_entry" value="../data/donation_sarah5"/>
</operator>
<operator activated="true" class="normalize" compatibility="5.3.008" expanded="true" height="94" name="Normalize" width="90" x="45" y="120"/>
<operator activated="true" class="split_data" compatibility="5.3.008" expanded="true" height="94" name="Split Data" width="90" x="179" y="255">
<enumeration key="partitions">
<parameter key="ratio" value="0.8"/>
<parameter key="ratio" value="0.2"/>
</enumeration>
<parameter key="sampling_type" value="stratified sampling"/>
</operator>
<operator activated="true" class="optimize_parameters_grid" compatibility="5.3.008" expanded="true" height="112" name="Optimize Parameters (Grid)" width="90" x="246" y="30">
<list key="parameters">
<parameter key="SVM.C" value=".25,1,4"/>
<parameter key="SVM.kernel_gamma" value=".25,1,4"/>
</list>
<process expanded="true">
<operator activated="true" class="x_validation" compatibility="5.3.008" expanded="true" height="112" name="Validation" width="90" x="45" y="30">
<description>A cross-validation evaluating a decision tree model.</description>
<process expanded="true">
<operator activated="true" class="support_vector_machine" compatibility="5.3.008" expanded="true" height="112" name="SVM" width="90" x="112" y="30">
<parameter key="kernel_type" value="radial"/>
<parameter key="kernel_gamma" value="4"/>
<parameter key="C" value="4"/>
<parameter key="scale" value="false"/>
</operator>
<connect from_port="training" to_op="SVM" to_port="training set"/>
<connect from_op="SVM" from_port="model" to_port="model"/>
<portSpacing port="source_training" spacing="0"/>
<portSpacing port="sink_model" spacing="0"/>
<portSpacing port="sink_through 1" spacing="0"/>
</process>
<process expanded="true">
<operator activated="true" class="apply_model" compatibility="5.3.008" expanded="true" height="76" name="Apply Model" width="90" x="45" y="30">
<list key="application_parameters"/>
</operator>
<operator activated="true" class="performance_binominal_classification" compatibility="5.3.008" expanded="true" height="76" name="Performance" width="90" x="226" y="30">
<parameter key="accuracy" value="false"/>
<parameter key="AUC" value="true"/>
</operator>
<connect from_port="model" to_op="Apply Model" to_port="model"/>
<connect from_port="test set" to_op="Apply Model" to_port="unlabelled data"/>
<connect from_op="Apply Model" from_port="labelled data" to_op="Performance" to_port="labelled data"/>
<connect from_op="Performance" from_port="performance" to_port="averagable 1"/>
<portSpacing port="source_model" spacing="0"/>
<portSpacing port="source_test set" spacing="0"/>
<portSpacing port="source_through 1" spacing="0"/>
<portSpacing port="sink_averagable 1" spacing="0"/>
<portSpacing port="sink_averagable 2" spacing="0"/>
</process>
</operator>
<connect from_port="input 1" to_op="Validation" to_port="training"/>
<connect from_op="Validation" from_port="model" to_port="result 1"/>
<connect from_op="Validation" from_port="averagable 1" to_port="performance"/>
<portSpacing port="source_input 1" spacing="0"/>
<portSpacing port="source_input 2" spacing="0"/>
<portSpacing port="sink_performance" spacing="0"/>
<portSpacing port="sink_result 1" spacing="0"/>
<portSpacing port="sink_result 2" spacing="0"/>
</process>
</operator>
<operator activated="true" class="apply_model" compatibility="5.3.008" expanded="true" height="76" name="Apply Model (2)" width="90" x="380" y="165">
<list key="application_parameters"/>
</operator>
<operator activated="true" class="performance_binominal_classification" compatibility="5.3.008" expanded="true" height="76" name="Performance (2)" width="90" x="581" y="255">
<parameter key="accuracy" value="false"/>
<parameter key="AUC" value="true"/>
</operator>
<connect from_op="Retrieve donation_sarah5" from_port="output" to_op="Normalize" to_port="example set input"/>
<connect from_op="Normalize" from_port="example set output" to_op="Split Data" to_port="example set"/>
<connect from_op="Split Data" from_port="partition 1" to_op="Optimize Parameters (Grid)" to_port="input 1"/>
<connect from_op="Split Data" from_port="partition 2" to_op="Apply Model (2)" to_port="unlabelled data"/>
<connect from_op="Optimize Parameters (Grid)" from_port="parameter" to_port="result 4"/>
<connect from_op="Optimize Parameters (Grid)" from_port="result 1" to_op="Apply Model (2)" to_port="model"/>
<connect from_op="Apply Model (2)" from_port="labelled data" to_op="Performance (2)" to_port="labelled data"/>
<connect from_op="Apply Model (2)" from_port="model" to_port="result 1"/>
<connect from_op="Performance (2)" from_port="performance" to_port="result 2"/>
<connect from_op="Performance (2)" from_port="example set" to_port="result 3"/>
<portSpacing port="source_input 1" spacing="0"/>
<portSpacing port="sink_result 1" spacing="0"/>
<portSpacing port="sink_result 2" spacing="0"/>
<portSpacing port="sink_result 3" spacing="0"/>
<portSpacing port="sink_result 4" spacing="0"/>
<portSpacing port="sink_result 5" spacing="0"/>
</process>
</operator>
</process>

And here is my Matlab code:
clear all;
load donation;

Y = donation(:,40);
X = donation(:,2:36);
B = donation(:,40)> prctile(Y,80);
a_logical = logical( B );
B1 = a_logical + 0;

%check what percentage of donation are from the 20% people
ptg = sum(Y.*B1)/sum(Y)*100;
disp('percentage of donation that are from the top 20% people');
disp(ptg);
%randomly split the data into 80% and 20%
A = [X B1];
numA = size(A, 1);
trainsize = floor(0.8 * numA);
testsize = numA - trainsize;
ridx = randperm(numA);
traindata = A(ridx(1:trainsize),:);
testdata = A(ridx(trainsize + 1 : end),:);
Xtestdata = testdata(:,1:35);
B1testdata = testdata(:,36);
Xtraindata = traindata(:,1:35);
B1traindata = traindata(:,36);
n = size(B1traindata,1);
%cross-validation
%Gaussian Radial Basis Function kernel
L = [1/4 1 4];
AUCtrain = [];
for j = L(1:1:3)
for m = L(1:1:3)
indices = crossvalind('Kfold', n, 10);
Bp = [];
Br = [];
for i = 1:10
test = (indices == i); train = ~test;
xtst = Xtraindata(test,:);
ytst = B1traindata(test,:);
xtr = Xtraindata(train,:);
ytr = B1traindata(train,:);
SVMStruct = svmtrain(xtr,ytr,'kernel_function','rbf','RBF_Sigma', j ,'BoxConstraint', m);
Group = svmclassify(SVMStruct,xtst);
Bp = [Bp; Group];
Br = [Br; ytst];
end
[X1,Y1,T,AUCij] = perfcurve(Br,Bp,1);
AUCtrain = [AUCtrain;AUCij];
end
end
disp ('SVM_C statistics on the training data with ten-fold cross validation');
disp (AUCtrain');
%use the optimal parameter for the testdata
SVMStruct = svmtrain(Xtraindata,B1traindata,'kernel_function','rbf','RBF_Sigma', 4 ,'BoxConstraint', 1/4);
Group = svmclassify(SVMStruct,Xtestdata);
[X1,Y1,T,AUCtest] = perfcurve(B1testdata,Group,1);
disp ('SVM_C statistics on the test data after ten-fold cross validation');
disp (AUCtest);

Best,
Sarah

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dara

Hello Sarah

I like your question and probably myself will ask a ton of such questions soon.

However I program in Mathematica and I think for these sorts of classes of algorithm you CANNOT get the same results from different implementations.

CORRECT ME IF I AM WRONG: At the heart of simplest SVM there is a quadratic linear inequality which might have multiple solutions! One implementation hits one and another implementation hits the other one.

If you have a very symmetric separable data i.e. they can be separated using the linear forms, there will be several such separations. Take any crystal form like data that is symmetric and same in multiple views.

Dara

Sarah

Thanks for your thoughts, Dara! I totally agree with you on the existence of multiple solutions.

However, I still couldn't convince myself that the classification performance, which is measured in C statistics in this case, can differ that much between these two software. I'm wondering if anyone knows how I can modify process in Rapidminer to make the results/algorithm comparable to those in Matlab.

It concerns me a lot 'cause I'm using SVM for a research project, and I would like to know if the different results are due to the wrong set-up I have in Rapidminer.

Thanks,
Sarah

dara

Understood Sarah.

I will be watching this thread carefully, because it is also an important issue for us in future. For example, I use Mathematica to do the research end of our work and do not like to see mismatch results as such.

But I fooled myself a couple of times thinking the results should be the same and time and time there was a subtle difference between the two usages of the same algorithm which made a huge difference.

D

dara

Sarah

In Mathematica for the solvers of the equations and inequalities there are some cases that used a random seed to start the looping towards the solutions.

The problem is if you change the seed the solutions vary!

I just did that to solve large system of equations. I am sure Matlab is similar.

So in the algorithm if there is a SOLVE procedure of some kind different software might use exactly the same code, but the rand seed is different, thus you get another solution.

D

MariusHelf

Concerning the optimization results: the optimal values for C and gamma may vary, and additionally depend on the chosen optimization schema. Especially if you are doing a grid search, the possible solutions to of course depend on the step sizes and the search limits etc.

Best regards,
Marius

Sarah

That's true. Yet even when I provides the same step sizes and search limits, it gives the different results.

I later found out that it could be due to the way how Matlab defines parameter C. In case C is a scalar, it is automatically rescaled by N/(2*N1) for the data points of group one and by N/(2*N2) for the data points of group two, where N1 is the number of elements in group one, N2 is the number of elements in group two, and N = N1 + N2. According to Matlab, this rescaling is done to take into account unbalanced groups.

I'm wondering if I could do the same thing to rescale C in Rapidminer. It appears to me that there's a EqualLabelWeighting process that may work. By any chance, do you know how it can be specifically applied to this situation if it's the right process to look into?

Thanks,
Sarah

MariusHelf

Sarahl in the Support Vector Machine operator there are the parameters L pos and L neg that can be used to use asymmetric C values.

Best regards,
Marius

Sarah

Thanks for the reply, Marius. I didn't quite know how to set up L pos and L neg. In the case of my data, one group has 1000 obs and the other has 4000 obs. To adjust for this unbalance, shall I set up L pos as 1 and L neg as 4?

Thanks,
Sarah