Editing Final Report/Thesis 2016 (section)

==== Preparation Test ====
It is always necessary to check if the method for tests is effective before starting any tests. Hence the purpose of this section is to prove that the Levenshtein distance algorithm has the ability to revealing the differences between different languages.  
Units of a fixed length extracted from English version and eight different language versions of the War and Peace were compared. To make it comprehensive, there are six groups of tests with different length varies from 50 letters/unit to 800 letters/unit and in each length group there are 100 times of comparison (10 units of one language compared with 10 units of another language one by one using a double ‘for loop’ ). Each unit was uniquely selected from texts without any overlapping. Results of these tests are normalized with the unit of length = 50. 

The result of the tests was presented in boxplots in the figure below (Language names were abbreviated, En stands for English, It-Italian, Fr-French, Ge-German, Pq-Portuguese, La-Latin, Sp-Spanish, Tr-Turkish and Po-Polish). Each box is a set of the output Levenshtein Distances between two texts. For example, the leftmost box represents the test results of 10 English units versus another 10 English units; same rule applies for the others. 

[[File:Group1.jpg|thumb|600px|center|Levenshtein Test Result]]

By analyzing the five box plots above in the Figure Group 1, the following conclusions can be inferred:
1. In all the five figures, the leftmost boxes are significantly lower than the others, which mean that the Levenshtein distances between English strings are much lower than those between English strings and strings of other languages.  Hence, the Levenshtein Distance is able to manifest the difference between different languages.

2. As the unit length grows the boxes become lower and more compact (median value and standard deviation shrink when unit length goes up). Some of them even converged into a specific value.  In addition, the difference between the last two plots (unit length = 400 and unit length = 800) is trivial. It means that the Levenshtein distances tend to be stable as the length of the unit increases.  

3.  When increasing the unit size, the trends of the nine language groups are highly similar: median values of the Levenshtein Distances decrease as the unit size increases. This implies that the performance of the Levenshtein Distance algorithm is independent with different languages.