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POHow do I calculate the value of information gain in order to reduce the floating-point approximation errors?
 

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  1. POHow do I calculate the value of information gain in order to reduce the floating-point approximation errors?
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    <p>I have a dataset containing some features that belong to two class labels denoted by <em>1</em> and <em>2</em>. This dataset is procedded in order to build a decision tree: during the construction of the tree, I need to calculate the information gain to find the best partitioning of the dataset.</p> <p>Let there be <em>N1</em> features associated to label <em>1</em>, and <em>N2</em> features associated to label <em>2</em>, then the <strong>entropy</strong> can be calculated with the following formula:</p> <p><code>Entropy = - (N1/N)*log2(N1/N) - (N2/N)*log2(N2/N)</code>, where <em>N = N1 + N2</em></p> <p>I need to calculate three values of entropy in order to obtain the information gain:</p> <ul> <li><code>entropyBefore</code>, that is the entropy before the partitioning of the current dataset;</li> <li><code>entropyLeft</code>, that is the entropy of the left split after the partitioning;</li> <li><code>entropyRight</code>, that is the entropy of the right split after the partitioning.</li> </ul> <p>So, the information gain is equal to <code>entropyBefore - (S1/N)*entropyLeft - (S2/N)*entropyRight</code>, where <em>S1</em> is the number of the features of class <em>1</em> belonging to the split 1, and <em>S2</em> is the number of the features of class <em>2</em> belonging to the split 2.</p> <p>How do I calculate the value of information gain in order to reduce the floating-point approximation errors? When I apply the above formulas in those cases in which the information gain must be zero, however the calculated value is equal to a very small negative value.</p> <p><strong>UPDATE</strong> (sample code)</p> <pre><code>double N = static_cast&lt;double&gt;(this-&gt;rows()); // rows count of the dataset double entropyBefore = this-&gt;entropy(); // current entropy (before performing the split) bool firstCheck = true; double bestSplitIg; for each possible split { // ... pair&lt;Dataset,Dataset&gt; splitPair = split(...,...); double S1 = splitPair.first.rows(); double S2 = splitPair.second.rows(); double entropyLeft = splitPair.first.entropy(); double entropyRight = splitPair.second.entropy(); double splitIg = entropyBefore - (S1/N*entropyLeft + S2/N*entropyRight); if (firstCheck || splitIg &gt; bestSplitIg) { bestSplitIg = splitIg; // ... firstCheck = false; } } </code></pre>
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    1. USenzom83
    1. USenzom83
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    1. PO
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      1. POHow do I calculate the value of information gain in order to reduce the floating-point approximation errors?
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      1. VTUpMod
    2. VO
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      1. POHow do I calculate the value of information gain in order to reduce the floating-point approximation errors?
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      1. VTUpMod
    1. COwell not using floating point to do it, was my first thought.
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      1. POHow do I calculate the value of information gain in order to reduce the floating-point approximation errors?
      1. USTony Hopkinson
    2. CO@TonyHopkinson: Please explain what better way you propose to calculate log2 without floating point.
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      1. POHow do I calculate the value of information gain in order to reduce the floating-point approximation errors?
      1. USEric Postpischil
    3. COPlease show a [short, self-contained compilable example](http://sscce.org) with both code and data that demonstrates the problem.
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      1. POHow do I calculate the value of information gain in order to reduce the floating-point approximation errors?
      1. USEric Postpischil
 

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