## Extracting important snip-its with C# and Log Likelyhood

### How does text summary software pick out the most important ideas to present?

One solution is to use Log Likelyhood to generate a summary of the sentences that contain the important terms and cover the most different topics.

What Log Likelyhood is and why it works can be read here: https://en.wikipedia.org/wiki/Likelihood_function

This article will focus on implementing it in C#. Here's the code I wrote as a translation from the Mahout version. I tried to make it as readable as possible rather than optimizing for performance.

// Log Likelyhood code roughly translated from here: // http://grepcode.com/file/repo1.maven.org/maven2/org.apache.mahout/mahout-math/0.3/org/apache/mahout/math/stats/LogLikelihood.java#LogLikelihood.logLikelihoodRatio%28int%2Cint%2Cint%2Cint%29 static private double ShannonEntropy(List<Int64> elements) { double sum = 0; foreach (Int64 element in elements) { sum += element; } double result = 0.0; foreach (Int64 element in elements) { if(element < 0) { throw new Exception("Should not have negative count for entropy computation (" + element + ")"); } int zeroFlag = (element == 0 ? 1 : 0); result += element * Math.Log((element + zeroFlag) / sum); } return result; } /* Calculate the Raw Log-likelihood ratio for two events, call them A and B. Then we have: Event A Everything but A Event B A and B together (k_11) B, but not A (k_12) Everything but B A without B (k_21) Neither A nor B (k_22) Parameters: k11 The number of times the two events occurred together k12 The number of times the second event occurred WITHOUT the first event k21 The number of times the first event occurred WITHOUT the second event k22 The number of times something else occurred (i.e. was neither of these events */ static public double LogLikelihoodRatio(Int64 k11, Int64 k12, Int64 k21, Int64 k22) { double rowEntropy = ShannonEntropy(new List<Int64>() { k11, k12 }) + ShannonEntropy(new List<Int64>() { k21, k22 }); double columnEntropy = ShannonEntropy(new List<Int64>() { k11, k21 }) + ShannonEntropy(new List<Int64>() { k12, k22 }); double matrixEntropy = ShannonEntropy(new List<Int64>() { k11, k12, k21, k22 }); return 2 * (matrixEntropy - rowEntropy - columnEntropy); }

Now, we have a simple LogLikelihoodRatio function we can call with 4 parameters and get the score result.

Let's say we want to pick out the most important sentences from a particular Wikipedia article in order to summarize it. (See this article for loading Wikipedia in to ElasticSearch: http://blog.novelessay.com/post/loading-wikipedia-in-to-elasticsearch)

Follow these steps:

- Pick a Wikipedia article.
- Get a Term Frequency dictionary for the whole article.
- Parse the article in to sentences.
- For each token in each sentence, calculate the Log Likelyhood score with the above LogLikelihoodRatio function.
- If the result of LogLikelihoodRatio is less than -10, give that sentence +1 to a weight value.
- At the end of each sentence, you have a +X weight value. That can be normalized by the number of words in the sentence.
- After you've obtained the weight score from #6 for all of the sentences in an article, you can sort them and pick the most important ones.

Here's some code with comments about populating the input values passed to the LogLikelihoodRatio function. Be sure to check the result score is less than -10 before adding a +1 weight.

// http://www.cs.columbia.edu/~gmw/candidacy/LinHovy00.pdf - Section 4.1 Int64 k11 = // frequency of current term in this article Int64 k12 = // frequency of current term in all of Wikipedia - k11 Int64 k21 = // total count of all terms in this article - k11 Int64 k22 = // total count of all terms in Wikipedia - k12 double termWeight = LogLikelihoodRatio(k11, k12, k21, k22); if(termWeight < -10) { weightSum++; }

Obviously, in the above you don't want to be calculating Term Frequency across Wikipedia on-the-fly. K11 and K21 will get calculated as you process an article, but K12 and K22 should be calculated in advance and cached in a lookup dictionary.

I use LevelDb as my Term Frequency look up dictionary. You can read about using that here: http://blog.novelessay.com/post/fast-persistent-key-value-pairs-in-c-with-leveldb

In order to build your Term Frequency look up dictionary chace, you could process each documents and create your own term frequency output, or use the ElasticSearch plugin for _termList here: https://github.com/jprante/elasticsearch-index-termlist