2 Consider three string precision prediction and precise 30

2. Consider three string \"precision\", \"prediction\" and \"precise\". [30 points] 1) List bi-grams and unique bi-grams for each string. 2) Use Dice Coefficient to computer similarity of any pair of strings 3) will clstex siings wnveir similan, usi any ol strings? Why?

Solution

Hi,
First, Bigram means the sequence of 2 adjacent elements from a string, therefore the given strings they are
precision- {pr,re,ec,ci,is,si,io,on}
prediction-  {pr,re,ed,di,ic,ct,ti,io,on}
precise- {pr,re,ec,ci,is,se}
2. Dice coefficient is given by
s= 2. n_t /(n_x+n_y)
where n_t - is number of bigrams found in both strings
n_x- is number of bigrams found in first string
n_y- is number of bigrams found in second string,
lets take the example of
precision and precise
n_x=  {pr,re,ec,ci,is,si,io,on} = 8
n_y= {pr,re,ec,ci,is,se} = 6
n_t = interesction of above two sets= {pr,re,ec,ci,is}=5,
therefore similarity is s=2*5/(8+6)= 0.71

for precision and prediction
n_x=  {pr,re,ec,ci,is,si,io,on} = 8
n_y= {pr,re,ed,di,ic,ct,ti,io,on} = 9
n_t = interesction of above two sets= {pr,re,io,on}=4
therefore similarity is s=2*4/(8+9)= 0.47

for precise and prediction
n_x=   {pr,re,ec,ci,is,se} = 6
n_y= {pr,re,ed,di,ic,ct,ti,io,on}  = 9
n_t = interesction of above two sets= {pr,re}=2
therefore similarity is s=2*2/(6+9)= 0.26
3. Now, if we are taking cluster of similar strings if their similarity>0.5, then precision and precise will fall under same cluster, because only those pair has s>0.5

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