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# Shingling and Jaccard Similarity

Andre Ross gives a very good description of the shingling process in this blog post: http://digfor.blogspot.com/2013/03/fruity-shingles.html . As discussed in the tip of the night for January 16, 2015 document shingling involves comparing n-grams of overlapping word sequences in two different text files. Ross notes that shingling involves of the calculation of Jaccard Similarity, "the number of items in the intersection of A and B divided by the number of items in the union of A and B" or

Sim(A,B) = |A ∩ B |

______

|A ∪ B |

. . . so we get a figure based the number of n-grams the two have in common divided over the total number of unique n-grams used in both.

Here's an example.

1. In Fig. 1 we see 3 text files, which are edited over the period of several weeks. The August version is almost the same as the July version, but one phrase has been moved around. In the September version while the original first sentence is still present in parts, an entirely new phrase has been added and more changes have been made.

2. In Fig 2., we run the n-gram generator as was discussed in on the night of January 16, 2015 , and copy out the three word overlapping n-grams for each of the three text files to an Excel spreadsheet.

3. In Excel the n-grams from each text file are pasted into columns A, C, and E, and then we run VLOOKUP formulas in column B to check which of n-grams from the July version in column A are the same as those in the August version in column C [18], and which of the n-grams from the August version in column C match those in column E for the September version [8].

4. On a second worksheet, we combined the n-grams from a July and August de-duped set, and an August and September de-duped set to get totals of 36 and 49 respectively.

5. So while the July and August versions of have a Jaccard similarity of 0.5, the August and September versions only have a Jaccard similarity of 0.16.