When does a grid search end?

Sasch

Hello everyone,
I got a quick question and I think you guys can help me out:

When I do a grid search for optimal parameters C (11 different values) and Gamma (10 different values) for my SVM, when will the search stop?
Does it stop immediately the first time it hits a 100% accuracy with an "optimal pair" and then disregards the other untested pairs (assuming there will be an 100% accuracy)?

I also ask this question against the background of time-intense calculations..

Thanx a lot in advance,
Sasch

land

Hi Sasch,

no, Grid Search will test ALL combinations. You might be surprised, but I NEVER saw any 100% accuracy if validated correctly on a real world data set. If you receive a 100% accuracy you rather should double check your process setup than searching for a way to abort calculations...

Greetings,
  Sebastian

Sasch

Oh oh, then I might have a problem as I have several data sets where I hit a 100% accuracy...

Ok from the start:
I have 54 example sets of EEG data (all filtered and baseline corrected), each containing ~180 attributes + 1 label.
I have 3 different labels (=classes) that means 18 example sets for each class. The labels are numbers but "transformed" into text with the import wizard.

So when I now import the whole dataset and do a grid search for best SVM params and cross-validations and so on, I get a 100% accuracy (?).
Can't that be? Or is it in the nature of the SVM that it can find a optimal 100% solution when the number of example sets are much less than the number of attributes (=> "curse of dimensionality"?) ?

Perhaps my process setup is also wrong. I'd appreciate it if you would be so kind to check it. I put the code below:

Sorry I have to cut it into 2 pieces. Hope you don't mind.
So here's part 1:

<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<process version="5.1.001">
  <context>
    <input/>
    <output/>
    <macros/>
  </context>
  <operator activated="true" class="process" compatibility="5.1.001" expanded="true" name="Process">
    <process expanded="true" height="555" width="748">
      <operator activated="true" class="read_csv" compatibility="5.1.001" expanded="true" height="60" name="Read CSV_Data (2)" width="90" x="45" y="30">
        <parameter key="csv_file" value="C:\experiments\realtime-classification\RapidMStorage\david_epoches.csv"/>
        <parameter key="column_separators" value=","/>
        <parameter key="use_quotes" value="false"/>
        <parameter key="first_row_as_names" value="false"/>
        <list key="annotations"/>
        <list key="data_set_meta_data_information">
          <parameter key="0" value="att1.true.real.attribute"/>
          <parameter key="1" value="att2.true.real.attribute"/>
          <parameter key="2" value="att3.true.real.attribute"/>
          <parameter key="3" value="att4.true.real.attribute"/>
          <parameter key="4" value="att5.true.real.attribute"/>
          <parameter key="5" value="att6.true.real.attribute"/>
          <parameter key="6" value="att7.true.real.attribute"/>
          <parameter key="7" value="att8.true.real.attribute"/>
          <parameter key="8" value="att9.true.real.attribute"/>
          <parameter key="9" value="att10.true.real.attribute"/>
          <parameter key="10" value="att11.true.real.attribute"/>
          <parameter key="11" value="att12.true.real.attribute"/>
          <parameter key="12" value="att13.true.real.attribute"/>
          <parameter key="13" value="att14.true.real.attribute"/>
          <parameter key="14" value="att15.true.real.attribute"/>
          <parameter key="15" value="att16.true.real.attribute"/>
          <parameter key="16" value="att17.true.real.attribute"/>
          <parameter key="17" value="att18.true.real.attribute"/>
          <parameter key="18" value="att19.true.real.attribute"/>
          <parameter key="19" value="att20.true.real.attribute"/>
          <parameter key="20" value="att21.true.real.attribute"/>
          <parameter key="21" value="att22.true.real.attribute"/>
          <parameter key="22" value="att23.true.real.attribute"/>
          <parameter key="23" value="att24.true.real.attribute"/>
          <parameter key="24" value="att25.true.real.attribute"/>
          <parameter key="25" value="att26.true.real.attribute"/>
          <parameter key="26" value="att27.true.real.attribute"/>
          <parameter key="27" value="att28.true.real.attribute"/>
          <parameter key="28" value="att29.true.real.attribute"/>
          <parameter key="29" value="att30.true.real.attribute"/>
          <parameter key="30" value="att31.true.real.attribute"/>
          <parameter key="31" value="att32.true.real.attribute"/>
          <parameter key="32" value="att33.true.real.attribute"/>
          <parameter key="33" value="att34.true.real.attribute"/>
          <parameter key="34" value="att35.true.real.attribute"/>
          <parameter key="35" value="att36.true.real.attribute"/>
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          <parameter key="163" value="att164.true.real.attribute"/>
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          <parameter key="174" value="att175.true.real.attribute"/>
          <parameter key="175" value="att176.true.real.attribute"/>
          <parameter key="176" value="att177.true.real.attribute"/>
          <parameter key="177" value="att178.true.real.attribute"/>
          <parameter key="178" value="att179.true.real.attribute"/>
          <parameter key="179" value="att180.true.text.label"/>
        </list>
      </operator>
      <operator activated="true" class="multiply" compatibility="5.1.001" expanded="true" height="94" name="Multiply (2)" width="90" x="179" y="30"/>
      <operator activated="true" class="optimize_parameters_grid" compatibility="5.1.001" expanded="true" height="94" name="Optimize SVM_Parameters (Grid)" width="90" x="313" y="120">
        <list key="parameters">
          <parameter key="SVM.C" value="0.03125,0.125,0.5,2,8,32,128,512,2048,8192,32768"/>
          <parameter key="SVM.gamma" value="0.5,2,8,0.125,0.03125,0.0078125,0.001953125,0.000488281,0.00012207,0.000030517578125"/>
        </list>
        <parameter key="parallelize_optimization_process" value="true"/>
        <process expanded="true" height="487" width="826">
          <operator activated="true" class="x_validation" compatibility="5.1.001" expanded="true" height="112" name="Validation" width="90" x="179" y="30">
            <parameter key="average_performances_only" value="false"/>
            <parameter key="leave_one_out" value="true"/>
            <process expanded="true" height="487" width="165">
              <operator activated="true" class="support_vector_machine_libsvm" compatibility="5.1.001" expanded="true" height="76" name="SVM" width="90" x="45" y="30">
                <parameter key="gamma" value="0.000030517578125"/>
                <parameter key="C" value="32768"/>
                <parameter key="cache_size" value="250"/>
                <list key="class_weights"/>
                <parameter key="calculate_confidences" value="true"/>
              </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" height="487" width="300">
              <operator activated="true" class="apply_model" compatibility="5.1.001" expanded="true" height="76" name="Apply Model" width="90" x="45" y="30">
                <list key="application_parameters"/>
              </operator>
              <operator activated="true" class="performance_classification" compatibility="5.1.001" expanded="true" height="76" name="Performance" width="90" x="180" y="30">
                <list key="class_weights"/>
              </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="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"/>
        </process>
      </operator>

Sasch

Here's part 2:

<operator activated="true" class="write_parameters" compatibility="5.1.001" expanded="true" height="60" name="Write Parameters" width="90" x="380" y="255">
        <parameter key="parameter_file" value="C:\experiments\realtime-classification\RapidMStorage\Logs\opt_params.par"/>
      </operator>
      <operator activated="true" class="multiply" compatibility="5.1.001" expanded="true" height="94" name="Multiply" width="90" x="447" y="345"/>
      <operator activated="true" class="subprocess" compatibility="5.1.001" expanded="true" height="76" name="Subprocess [ApplyOptimalParas]" width="90" x="581" y="390">
        <process expanded="true" height="555" width="748">
          <operator activated="true" class="set_parameters" compatibility="5.1.001" expanded="true" height="60" name="Set Parameters" width="90" x="45" y="30">
            <list key="name_map">
              <parameter key="SVM" value="SVM_OPT"/>
            </list>
          </operator>
          <operator activated="true" class="read_csv" compatibility="5.1.001" expanded="true" height="60" name="Read CSV_Data (4)" width="90" x="45" y="120">
            <parameter key="csv_file" value="C:\experiments\realtime-classification\RapidMStorage\david_epoches.csv"/>
            <parameter key="column_separators" value=","/>
            <parameter key="use_quotes" value="false"/>
            <parameter key="first_row_as_names" value="false"/>
            <list key="annotations"/>
            <list key="data_set_meta_data_information">
              <parameter key="0" value="att1.true.real.attribute"/>
              <parameter key="1" value="att2.true.real.attribute"/>
              <parameter key="2" value="att3.true.real.attribute"/>
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              <parameter key="5" value="att6.true.real.attribute"/>
              <parameter key="6" value="att7.true.real.attribute"/>
              <parameter key="7" value="att8.true.real.attribute"/>
              <parameter key="8" value="att9.true.real.attribute"/>
              <parameter key="9" value="att10.true.real.attribute"/>
              <parameter key="10" value="att11.true.real.attribute"/>
              <parameter key="11" value="att12.true.real.attribute"/>
              <parameter key="12" value="att13.true.real.attribute"/>
              <parameter key="13" value="att14.true.real.attribute"/>
              <parameter key="14" value="att15.true.real.attribute"/>
              <parameter key="15" value="att16.true.real.attribute"/>
              <parameter key="16" value="att17.true.real.attribute"/>
              <parameter key="17" value="att18.true.real.attribute"/>
              <parameter key="18" value="att19.true.real.attribute"/>
              <parameter key="19" value="att20.true.real.attribute"/>
              <parameter key="20" value="att21.true.real.attribute"/>
              <parameter key="21" value="att22.true.real.attribute"/>
              <parameter key="22" value="att23.true.real.attribute"/>
              <parameter key="23" value="att24.true.real.attribute"/>
              <parameter key="24" value="att25.true.real.attribute"/>
              <parameter key="25" value="att26.true.real.attribute"/>
              <parameter key="26" value="att27.true.real.attribute"/>
              <parameter key="27" value="att28.true.real.attribute"/>
              <parameter key="28" value="att29.true.real.attribute"/>
              <parameter key="29" value="att30.true.real.attribute"/>
              <parameter key="30" value="att31.true.real.attribute"/>
              <parameter key="31" value="att32.true.real.attribute"/>
              <parameter key="32" value="att33.true.real.attribute"/>
              <parameter key="33" value="att34.true.real.attribute"/>
              <parameter key="34" value="att35.true.real.attribute"/>
              <parameter key="35" value="att36.true.real.attribute"/>
              <parameter key="36" value="att37.true.real.attribute"/>
              <parameter key="37" value="att38.true.real.attribute"/>
              <parameter key="38" value="att39.true.real.attribute"/>
              <parameter key="39" value="att40.true.real.attribute"/>
              <parameter key="40" value="att41.true.real.attribute"/>
              <parameter key="41" value="att42.true.real.attribute"/>
              <parameter key="42" value="att43.true.real.attribute"/>
              <parameter key="43" value="att44.true.real.attribute"/>
              <parameter key="44" value="att45.true.real.attribute"/>
              <parameter key="45" value="att46.true.real.attribute"/>
              <parameter key="46" value="att47.true.real.attribute"/>
              <parameter key="47" value="att48.true.real.attribute"/>
              <parameter key="48" value="att49.true.real.attribute"/>
              <parameter key="49" value="att50.true.real.attribute"/>
              <parameter key="50" value="att51.true.real.attribute"/>
              <parameter key="51" value="att52.true.real.attribute"/>
              <parameter key="52" value="att53.true.real.attribute"/>
              <parameter key="53" value="att54.true.real.attribute"/>
              <parameter key="54" value="att55.true.real.attribute"/>
              <parameter key="55" value="att56.true.real.attribute"/>
              <parameter key="56" value="att57.true.real.attribute"/>
              <parameter key="57" value="att58.true.real.attribute"/>
              <parameter key="58" value="att59.true.real.attribute"/>
              <parameter key="59" value="att60.true.real.attribute"/>
              <parameter key="60" value="att61.true.real.attribute"/>
              <parameter key="61" value="att62.true.real.attribute"/>
              <parameter key="62" value="att63.true.real.attribute"/>
              <parameter key="63" value="att64.true.real.attribute"/>
              <parameter key="64" value="att65.true.real.attribute"/>
              <parameter key="65" value="att66.true.real.attribute"/>
              <parameter key="66" value="att67.true.real.attribute"/>
              <parameter key="67" value="att68.true.real.attribute"/>
              <parameter key="68" value="att69.true.real.attribute"/>
              <parameter key="69" value="att70.true.real.attribute"/>
              <parameter key="70" value="att71.true.real.attribute"/>
              <parameter key="71" value="att72.true.real.attribute"/>
              <parameter key="72" value="att73.true.real.attribute"/>
              <parameter key="73" value="att74.true.real.attribute"/>
              <parameter key="74" value="att75.true.real.attribute"/>
              <parameter key="75" value="att76.true.real.attribute"/>
              <parameter key="76" value="att77.true.real.attribute"/>
              <parameter key="77" value="att78.true.real.attribute"/>
              <parameter key="78" value="att79.true.real.attribute"/>
              <parameter key="79" value="att80.true.real.attribute"/>
              <parameter key="80" value="att81.true.real.attribute"/>
              <parameter key="81" value="att82.true.real.attribute"/>
              <parameter key="82" value="att83.true.real.attribute"/>
              <parameter key="83" value="att84.true.real.attribute"/>
              <parameter key="84" value="att85.true.real.attribute"/>
              <parameter key="85" value="att86.true.real.attribute"/>
              <parameter key="86" value="att87.true.real.attribute"/>
              <parameter key="87" value="att88.true.real.attribute"/>
              <parameter key="88" value="att89.true.real.attribute"/>
              <parameter key="89" value="att90.true.real.attribute"/>
              <parameter key="90" value="att91.true.real.attribute"/>
              <parameter key="91" value="att92.true.real.attribute"/>
              <parameter key="92" value="att93.true.real.attribute"/>
              <parameter key="93" value="att94.true.real.attribute"/>
              <parameter key="94" value="att95.true.real.attribute"/>
              <parameter key="95" value="att96.true.real.attribute"/>
              <parameter key="96" value="att97.true.real.attribute"/>
              <parameter key="97" value="att98.true.real.attribute"/>
              <parameter key="98" value="att99.true.real.attribute"/>
              <parameter key="99" value="att100.true.real.attribute"/>
              <parameter key="100" value="att101.true.real.attribute"/>
              <parameter key="101" value="att102.true.real.attribute"/>
              <parameter key="102" value="att103.true.real.attribute"/>
              <parameter key="103" value="att104.true.real.attribute"/>
              <parameter key="104" value="att105.true.real.attribute"/>
              <parameter key="105" value="att106.true.real.attribute"/>
              <parameter key="106" value="att107.true.real.attribute"/>
              <parameter key="107" value="att108.true.real.attribute"/>
              <parameter key="108" value="att109.true.real.attribute"/>
              <parameter key="109" value="att110.true.real.attribute"/>
              <parameter key="110" value="att111.true.real.attribute"/>
              <parameter key="111" value="att112.true.real.attribute"/>
              <parameter key="112" value="att113.true.real.attribute"/>
              <parameter key="113" value="att114.true.real.attribute"/>
              <parameter key="114" value="att115.true.real.attribute"/>
              <parameter key="115" value="att116.true.real.attribute"/>
              <parameter key="116" value="att117.true.real.attribute"/>
              <parameter key="117" value="att118.true.real.attribute"/>
              <parameter key="118" value="att119.true.real.attribute"/>
              <parameter key="119" value="att120.true.real.attribute"/>
              <parameter key="120" value="att121.true.real.attribute"/>
              <parameter key="121" value="att122.true.real.attribute"/>
              <parameter key="122" value="att123.true.real.attribute"/>
              <parameter key="123" value="att124.true.real.attribute"/>
              <parameter key="124" value="att125.true.real.attribute"/>
              <parameter key="125" value="att126.true.real.attribute"/>
              <parameter key="126" value="att127.true.real.attribute"/>
              <parameter key="127" value="att128.true.real.attribute"/>
              <parameter key="128" value="att129.true.real.attribute"/>
              <parameter key="129" value="att130.true.real.attribute"/>
              <parameter key="130" value="att131.true.real.attribute"/>
              <parameter key="131" value="att132.true.real.attribute"/>
              <parameter key="132" value="att133.true.real.attribute"/>
              <parameter key="133" value="att134.true.real.attribute"/>
              <parameter key="134" value="att135.true.real.attribute"/>
              <parameter key="135" value="att136.true.real.attribute"/>
              <parameter key="136" value="att137.true.real.attribute"/>
              <parameter key="137" value="att138.true.real.attribute"/>
              <parameter key="138" value="att139.true.real.attribute"/>
              <parameter key="139" value="att140.true.real.attribute"/>
              <parameter key="140" value="att141.true.real.attribute"/>
              <parameter key="141" value="att142.true.real.attribute"/>
              <parameter key="142" value="att143.true.real.attribute"/>
              <parameter key="143" value="att144.true.real.attribute"/>
              <parameter key="144" value="att145.true.real.attribute"/>
              <parameter key="145" value="att146.true.real.attribute"/>
              <parameter key="146" value="att147.true.real.attribute"/>
              <parameter key="147" value="att148.true.real.attribute"/>
              <parameter key="148" value="att149.true.real.attribute"/>
              <parameter key="149" value="att150.true.real.attribute"/>
              <parameter key="150" value="att151.true.real.attribute"/>
              <parameter key="151" value="att152.true.real.attribute"/>
              <parameter key="152" value="att153.true.real.attribute"/>
              <parameter key="153" value="att154.true.real.attribute"/>
              <parameter key="154" value="att155.true.real.attribute"/>
              <parameter key="155" value="att156.true.real.attribute"/>
              <parameter key="156" value="att157.true.real.attribute"/>
              <parameter key="157" value="att158.true.real.attribute"/>
              <parameter key="158" value="att159.true.real.attribute"/>
              <parameter key="159" value="att160.true.real.attribute"/>
              <parameter key="160" value="att161.true.real.attribute"/>
              <parameter key="161" value="att162.true.real.attribute"/>
              <parameter key="162" value="att163.true.real.attribute"/>
              <parameter key="163" value="att164.true.real.attribute"/>
              <parameter key="164" value="att165.true.real.attribute"/>
              <parameter key="165" value="att166.true.real.attribute"/>
              <parameter key="166" value="att167.true.real.attribute"/>
              <parameter key="167" value="att168.true.real.attribute"/>
              <parameter key="168" value="att169.true.real.attribute"/>
              <parameter key="169" value="att170.true.real.attribute"/>
              <parameter key="170" value="att171.true.real.attribute"/>
              <parameter key="171" value="att172.true.real.attribute"/>
              <parameter key="172" value="att173.true.real.attribute"/>
              <parameter key="173" value="att174.true.real.attribute"/>
              <parameter key="174" value="att175.true.real.attribute"/>
              <parameter key="175" value="att176.true.real.attribute"/>
              <parameter key="176" value="att177.true.real.attribute"/>
              <parameter key="177" value="att178.true.real.attribute"/>
              <parameter key="178" value="att179.true.real.attribute"/>
              <parameter key="179" value="att180.true.text.label"/>
            </list>
          </operator>
          <operator activated="true" class="support_vector_machine_libsvm" compatibility="5.1.001" expanded="true" height="76" name="SVM_OPT" width="90" x="246" y="120">
            <parameter key="gamma" value="0.5"/>
            <parameter key="C" value="0.03125"/>
            <parameter key="cache_size" value="250"/>
            <list key="class_weights"/>
            <parameter key="calculate_confidences" value="true"/>
          </operator>
          <operator activated="true" class="write_model" compatibility="5.1.001" expanded="true" height="60" name="Write Model" width="90" x="447" y="120">
            <parameter key="model_file" value="C:\experiments\realtime-classification\RapidMStorage\Logs\c4_svm_model.mod"/>
            <parameter key="output_type" value="XML"/>
          </operator>
          <connect from_port="in 1" to_op="Set Parameters" to_port="parameter set"/>
          <connect from_op="Read CSV_Data (4)" from_port="output" to_op="SVM_OPT" to_port="training set"/>
          <connect from_op="SVM_OPT" from_port="model" to_op="Write Model" to_port="input"/>
          <connect from_op="Write Model" from_port="through" to_port="out 1"/>
          <portSpacing port="source_in 1" spacing="0"/>
          <portSpacing port="source_in 2" spacing="0"/>
          <portSpacing port="sink_out 1" spacing="0"/>
          <portSpacing port="sink_out 2" spacing="0"/>
        </process>
      </operator>
      <connect from_op="Read CSV_Data (2)" from_port="output" to_op="Multiply (2)" to_port="input"/>
      <connect from_op="Multiply (2)" from_port="output 1" to_port="result 3"/>
      <connect from_op="Multiply (2)" from_port="output 2" to_op="Optimize SVM_Parameters (Grid)" to_port="input 1"/>
      <connect from_op="Optimize SVM_Parameters (Grid)" from_port="performance" to_port="result 4"/>
      <connect from_op="Optimize SVM_Parameters (Grid)" from_port="parameter" to_op="Write Parameters" to_port="input"/>
      <connect from_op="Write Parameters" from_port="through" to_op="Multiply" to_port="input"/>
      <connect from_op="Multiply" from_port="output 1" to_port="result 1"/>
      <connect from_op="Multiply" from_port="output 2" to_op="Subprocess [ApplyOptimalParas]" to_port="in 1"/>
      <connect from_op="Subprocess [ApplyOptimalParas]" from_port="out 1" to_port="result 2"/>
      <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>

Thanks so much for your help,
Sasch