If I have a sentence, ex: “get out of here”
And I want to use word2vec Embed. to represent it .. I found three different ways to do that:
1- for each word, we compute the AVG of its embedding vector, so each word replaced by a single value.
2- as in 1, but with using the standard deviation of the embedding vector values.
3- or by adding the Embed. vector as it is. So if I use 300 length embedding vector .. for the above example, I will have in the final a vector of (300 * 4 words) 1200 length as a final vector to represent the sentence.
Which one of them is most suitable .. ? specifically, for the sentence similarity applications ..
The way you describe option (1) makes it sound like each word becomes a single number. That wouldn't work.
The simple approach that's often used is to average all word-vectors for words in the sentence together - so with 300-dimensional word-vectors, you still wind up with a 300-dimensional sentence-average vector. Perhaps that's what you mean by your option (1).
(Sometimes, all vectors are normalized to unit-length before this operation, but sometimes not - because the non-normalized vector lengths can sometimes indicate the strength of a word's meaning. Sometimes, word-vectors are weighted by some other frequency-based indicator of their relative importance, such as TF/IDF.)
I've never seen your option (2) used and don't quite understand what you mean or how it could possibly work.
Your option (3) would be better described as "concatenating the word-vectors". It gives different-sized vectors depending on the number of words in the sentence. Slight differences in word placement, such as comparing "get out of here" and "of here get out", would result in very different vectors, that usual methods of comparing vectors (like cosine-similarity) would not detect as being 'close' at all. So it doesn't make sense, and I've not seen it used.
So, only your option (1), as properly implemented to (weighted-)average word-vectors, is a good baseline for sentence-similarities.
But, it's still fairly basic and there are many other ways to compare sentences using text-vectors. Here are just a few:
One algorithm closely related to word2vec itself is called 'Paragraph Vectors', and is often called Doc2Vec. It uses a very word2vec-like process to train vectors for full ranges of text (whether they're phrases, sentences, paragraphs, or documents) that work kind of like 'floating document-ID words' over the full text. It sometimes offers a benefit over just averaging word-vectors, and in some modes can produce both doc-vectors and word-vectors that are also comparable to each other.
If your interest isn't just pairwise sentence similarities, but some sort of downstream classification task, then Facebook's 'FastText' refinement of word2vec has a classification mode, where the word-vectors are trained not just to predict neighboring words, but to be good at predicting known text classes, when simply added/averaged together. (Text-vectors constructed from such classification vectors might be good at similarities too, depending on how well the training-classes capture salient contrasts between texts.)
Another way to compute pairwise similarities, using just word-vectors, is "Word Mover's Distance". Rather than averaging all the word-vectors for a text together into a single text-vector, it considers each word-vector as a sort of "pile of meaning". Compared to another sentence, it calculates the minimum routing work (distance along lots of potential word-to-word paths) to move all the "piles" from one sentence into the configuration of another sentence. It can be expensive to calculate, but usually represents sentence-contrasts better than the simple single-vector-summary that naive word-vector averaging achieves.
`
model = Word2Vec(sentences,vector_size=100, min_count=1)
def sent_vectorizer(sent, model):
sent_vec =[]
numw = 0
for w in sent:
try:
if numw == 0:
sent_vec = model[w]
else:
sent_vec = np.add(sent_vec, model[w])
numw+=1
except:
pass
return np.asarray(sent_vec) / numw
X=[]
for sentence in sentences:
X.append(sent_vectorizer(sentence, model))
print ("========================")
print (X)
`
Related
Levenshtein seems to be very.. agnostic..in terms of how it scores distance/similarity in terms.
For instance:
Olive Garden vs Olden Garden = 3
whereas
Olive Garden vs Olive Garden Restaurant = 11
In the real world (as I see it or at least for some applications) the latter should be weighted much more heavily.
Is there a modification or another 'distance' comparison tool that doesn't try to account as much for misspelling and transposition that would weight the second example higher because of the sheer # of 100% matches on the first part of the phrase?
This is a difficult question to answer and I am by no means an expert on the subject, however, I have at least a partial answer to some of your questions. Additionally, you didn't specify a language, so all my examples will use PHP.
To the best of my knowledge there is no single comparison tool or function that is able to determine the relevance, rather than similarity of two strings. However, there are different comparison tools out there that would probably give you better results. The similar_text function in PHP, for example, returns the percent similarity between two strings and would be more accurate in what you're trying to do.
Additionally, you can account for misspellings when comparing the similarity of two strings by first calculating the phonetic "keys" of each string, and then calculating the Levenshtein distance between the phonetic keys. The best phonetic algorithm I know of for calculating the phonetic keys of strings is metaphone. In PHP, the metaphone is built in and can be used like this:
echo metaphone("carrot"); // prints KRT
The cool part about this is that if a user were to misspell carrot and instead type "carrrot," the same phonetic key would be generated (as "carrot" and "carrrot"), sound the same
echo metaphone("carrot"); // prints KRT
echo metaphone("carrrot"); // prints KRT
And obviously the Levenshtein distance between KRT and KRT is 0. The pitfall to this solution is that while metaphone helps with smoothing out spelling errors that don't change how a word sounds, words that are misspelled to the point where they no longer have any phonetic resemblance will not generate similar phonetic keys. In your example, Olive Garden and Olden Garden don't have the same phonetic keys, thus are still seen by Levenshtein as being relatively far apart.
echo levenshtein(metaphone("Olive Garden"), metaphone("Olden Garden")); // prints 2
Conclusion
Even in conjunction with metaphone, using the Levenshtein distance falls short, and is unable to provide the relevance between two strings. The best solution I can give would be to use similar_text in conjunction with metaphone to compare your strings. Something like this:
similar_text(metaphone("Olive Garden Restaurant"), metaphone("Olive Garden"), $sim);
echo $sim; // prints 70%
I have a census list of 150k last names, and trying to use this to validate the spelling of person names in an existing database.
Obviously there are many ethnic names in my database that don't match the census list, but are clearly not misspelled (Italian names like "Petroni", Swedish names like "Magnusdotter").
I would like to create a function (in Perl) to detect slight variations - i.e. likely mis-spellings - between names in the database and other very popular names in the census list (a frequency number is available).
I can imagine the algorithm, but before I dive in - any suggestions to do this in a reliable way - i.e. one that doesn't throw too many false positives?
Thanks!!
Essentially, you're writing a spell checker. You may want to look into an Open Source, multi-lingual spell checker such as Aspell and see what they do. You might even be able to implement what you want as an aspell dictionary.
There are many algorithms for doing approximate string matching. The Levenshtein distance between words is one algorithm, and there are several Perl modules to calculate it, but Text::Fuzzy looks pretty good.
That's great for comparing a few words, but you have to choose between 150k. You could just see if it's fast enough. You could try caching the result. But it remains an O(n) algorithm. Instead (or in addition) you can create an index using a phonetic matching algorithm. Generally, these index words by what they sound like to allow matching on misspelled words. Once you've generated the index for each word, you can match a new word against the index very quickly. Obviously this is subject to cultural ideas of what words sound like which is why there are many algorithms each with different optimizations. You can create several indexes using different algorithms and try them all.
You can even combine the two and do approximate string matching on the phonetic indexes.
I have a scenario where i have retreived information/raw data from the internet and placed them into their respective json or .txt files.
From there on i would like to calculate the frequecies of each term in each document and their cosine similarity by using tf-idf.
For example:
there are 50 different documents/texts files that consists 5000 words/strings each
i would like to take the first word from the first document/text and compare all the total 250000 words find its frequencies then do so for the second word and so on for all 50 documents/texts.
Expected output of each frequecy will be from 0 -1
How am i able to do so. I have been referring to sklear package but most of them only consists of a few strings in each comparisons.
You really should show us your code and explain in more detail which part it is that you are having trouble with.
What you describe is not usually how it's done. What you usually do is vectorize documents, then compare the vectors, which yields the similarity between any two documents under this model. Since you are asking about NLTK, I will proceed on the assumption that you want this regular, traditional method.
Anyway, with a traditional word representation, cosine similarity between two words is meaningless -- either two words are identical, or they're not. But there are certainly other ways you could approach term similarity or document similarity.
Copying the code from https://stackoverflow.com/a/23796566/874188 so we have a baseline:
from sklearn.feature_extraction.text import TfidfVectorizer
corpus = ["This is very strange",
"This is very nice"]
vectorizer = TfidfVectorizer(min_df=1)
X = vectorizer.fit_transform(corpus)
idf = vectorizer._tfidf.idf_
print dict(zip(vectorizer.get_feature_names(), idf))
There is nothing here which depends on the length of the input. The number of features in idf will be larger if you have longer documents and there will be more of them in the corpus if you have more documents, but the algorithm as such will not need to change at all to accommodate more or longer documents.
If you don't want to understand why, you can stop reading here.
The vectors are basically an array of counts for each word form. The length of each vector is the number of word forms (i.e. the number of features). So if you have a lexicon with six entries like this:
0: a
1: aardvark
2: banana
3: fruit
4: flies
5: like
then the input document "a fruit flies like a banana" will yield a vector of six elements like this:
[2, 0, 1, 1, 1, 1]
because there are two occurrences of the word at index zero in the lexicon, zero occurrences of the word at index one, one of the one at index two, etc. This is a TF (term frequency) vector. It is already a useful vector; you can compare two of them using cosine distance, and obtain a measurement of their similarity.
The purpose of the IDF factor is to normalize this. The normalization brings three benefits; computationally, you don't need to do any per-document or per-comparison normalization, so it's faster; and the algorithm also normalizes frequent words so that many occurrences of "a" is properly regarded as insignificant if most documents contain many occurrences of this word (so you don't have to do explicit stop word filtering), whereas many occurrences of "aardvark" is immediately obviously significant in the normalized vector. Also, the normalized output can be readily interpreted, whereas with plain TF vectors you have to take document length etc. into account to properly understand the result of the cosine similarity comparison.
So if the DF (document frequency) of "a" is 1000, and the DF of the other words in the lexicon is 1, the scaled vector will be
[0.002, 0, 1, 1, 1, 1]
(because we take the inverse of the document frequency, i.e. TF("a")*IDF("a") = TF("a")/DF("a") = 2/1000).
The cosine similarity basically interprets these vectors in an n-dimensional space (here, n=6) and sees how far from each other their arrows are. Just for simplicity, let's scale this down to three dimensions, and plot the (IDF-scaled) number of "a" on the X axis, the number of "aardvark" occurrences on the Y axis, and the number of "banana" occurrences on the Z axis. The end point [0.002, 0, 1] differs from [0.003, 0, 1] by just a tiny bit, whereas [0, 1, 0] ends up at quite another corner of the cube we are imagining, so the cosine distance is large. (The normalization means 1.0 is the maximum of any element, so we are talking literally a corner.)
Now, returning to the lexicon, if you add a new document and it has words which are not already in the lexicon, they will be added to the lexicon, and so the vectors will need to be longer from now on. (Vectors you already created which are now too short can be trivially extended; the term weight for the hitherto unseen terms will obviously always be zero.) If you add the document to the corpus, there will be one more vector in the corpus to compare against. But the algorithm doesn't need to change; it will always create vectors with one element per lexicon entry, and you can continue to compare these vectors using the same methods as before.
You can of course loop over the terms and for each, synthesize a "document" consisting of just that single term. Comparing it to other single-term "documents" will yield 0.0 similarity to the others (or 1.0 similarity to a document containing the same term and nothing else), so that's not too useful, but a comparison against real-world documents will reveal essentially what proportion of each document consists of the term you are examining.
The raw IDF vector tells you the relative frequency of each term. It usually expresses how many documents each term occurred in (so even if a term occurs more than once in a document, it only adds 1 to the DF for this term), though some implementations also allow you to use the bare term count.
As of right now, I decided to take a dictionary and iterate through the entire thing. Every time I see a newline, I make a string containing from that newline to the next newline, then I do string.find() to see if that English word is somewhere in there. This takes a VERY long time, each word taking about 1/2-1/4 a second to verify.
It is working perfectly, but I need to check thousands of words a second. I can run several windows, which doesn't affect the speed (Multithreading), but it still only checks like 10 a second. (I need thousands)
I'm currently writing code to pre-compile a large array containing every word in the English language, which should speed it up a lot, but still not get the speed I want. There has to be a better way to do this.
The strings I'm checking will look like this:
"hithisisastringthatmustbechecked"
but most of them contained complete garbage, just random letters.
I can't check for impossible compinations of letters, because that string would be thrown out because of the 'tm', in between 'thatmust'.
You can speed up the search by employing the Knuth–Morris–Pratt (KMP) algorithm.
Go through every dictionary word, and build a search table for it. You need to do it only once. Now your search for individual words will proceed at faster pace, because the "false starts" will be eliminated.
There are a lot of strategies for doing this quickly.
Idea 1
Take the string you are searching and make a copy of each possible substring beginning at some column and continuing through the whole string. Then store each one in an array indexed by the letter it begins with. (If a letter is used twice store the longer substring.
So the array looks like this:
a - substr[0] = "astringthatmustbechecked"
b - substr[1] = "bechecked"
c - substr[2] = "checked"
d - substr[3] = "d"
e - substr[4] = "echecked"
f - substr[5] = null // since there is no 'f' in it
... and so forth
Then, for each word in the dictionary, search in the array element indicated by its first letter. This limits the amount of stuff that has to be searched. Plus you can't ever find a word beginning with, say 'r', anywhere before the first 'r' in the string. And some words won't even do a search if the letter isn't in there at all.
Idea 2
Expand upon that idea by noting the longest word in the dictionary and get rid of letters from those strings in the arrays that are longer than that distance away.
So you have this in the array:
a - substr[0] = "astringthatmustbechecked"
But if the longest word in the list is 5 letters, there is no need to keep any more than:
a - substr[0] = "astri"
If the letter is present several times you have to keep more letters. So this one has to keep the whole string because the "e" keeps showing up less than 5 letters apart.
e - substr[4] = "echecked"
You can expand upon this by using the longest words starting with any particular letter when condensing the strings.
Idea 3
This has nothing to do with 1 and 2. Its an idea that you could use instead.
You can turn the dictionary into a sort of regular expression stored in a linked data structure. It is possible to write the regular expression too and then apply it.
Assume these are the words in the dictionary:
arun
bob
bill
billy
body
jose
Build this sort of linked structure. (Its a binary tree, really, represented in such a way that I can explain how to use it.)
a -> r -> u -> n -> *
|
b -> i -> l -> l -> *
| | |
| o -> b -> * y -> *
| |
| d -> y -> *
|
j -> o -> s -> e -> *
The arrows denote a letter that has to follow another letter. So "r" has to be after an "a" or it can't match.
The lines going down denote an option. You have the "a or b or j" possible letters and then the "i or o" possible letters after the "b".
The regular expression looks sort of like: /(arun)|(b(ill(y+))|(o(b|dy)))|(jose)/ (though I might have slipped a paren). This gives the gist of creating it as a regex.
Once you build this structure, you apply it to your string starting at the first column. Try to run the match by checking for the alternatives and if one matches, more forward tentatively and try the letter after the arrow and its alternatives. If you reach the star/asterisk, it matches. If you run out of alternatives, including backtracking, you move to the next column.
This is a lot of work but can, sometimes, be handy.
Side note I built one of these some time back by writing a program that wrote the code that ran the algorithm directly instead of having code looking at the binary tree data structure.
Think of each set of vertical bar options being a switch statement against a particular character column and each arrow turning into a nesting. If there is only one option, you don't need a full switch statement, just an if.
That was some fast character matching and really handy for some reason that eludes me today.
How about a Bloom Filter?
A Bloom filter, conceived by Burton Howard Bloom in 1970 is a
space-efficient probabilistic data structure that is used to test
whether an element is a member of a set. False positive matches are
possible, but false negatives are not; i.e. a query returns either
"inside set (may be wrong)" or "definitely not in set". Elements can
be added to the set, but not removed (though this can be addressed
with a "counting" filter). The more elements that are added to the
set, the larger the probability of false positives.
The approach could work as follows: you create the set of words that you want to check against (this is done only once), and then you can quickly run the "in/not-in" check for every sub-string. If the outcome is "not-in", you are safe to continue (Bloom filters do not give false negatives). If the outcome is "in", you then run your more sophisticated check to confirm (Bloom filters can give false positives).
It is my understanding that some spell-checkers rely on bloom filters to quickly test whether your latest word belongs to the dictionary of known words.
This code was modified from How to split text without spaces into list of words?:
from math import log
words = open("english125k.txt").read().split()
wordcost = dict((k, log((i+1)*log(len(words)))) for i,k in enumerate(words))
maxword = max(len(x) for x in words)
def infer_spaces(s):
"""Uses dynamic programming to infer the location of spaces in a string
without spaces."""
# Find the best match for the i first characters, assuming cost has
# been built for the i-1 first characters.
# Returns a pair (match_cost, match_length).
def best_match(i):
candidates = enumerate(reversed(cost[max(0, i-maxword):i]))
return min((c + wordcost.get(s[i-k-1:i], 9e999), k+1) for k,c in candidates)
# Build the cost array.
cost = [0]
for i in range(1,len(s)+1):
c,k = best_match(i)
cost.append(c)
# Backtrack to recover the minimal-cost string.
costsum = 0
i = len(s)
while i>0:
c,k = best_match(i)
assert c == cost[i]
costsum += c
i -= k
return costsum
Using the same dictionary of that answer and testing your string outputs
>>> infer_spaces("hithisisastringthatmustbechecked")
294.99768817854056
The trick here is finding out what threshold you can use, keeping in mind that using smaller words makes the cost higher (if the algorithm can't find any usable word, it returns inf, since it would split everything to single-letter words).
In theory, I think you should be able to train a Markov model and use that to decide if a string is probably a sentence or probably garbage. There's another question about doing this to recognize words, not sentences: How do I determine if a random string sounds like English?
The only difference for training on sentences is that your probability tables will be a bit larger. In my experience, though, a modern desktop computer has more than enough RAM to handle Markov matrices unless you are training on the entire Library of Congress (which is unnecessary- even 5 or so books by different authors should be enough for very accurate classification).
Since your sentences are mashed together without clear word boundaries, it's a bit tricky, but the good news is that the Markov model doesn't care about words, just about what follows what. So, you can make it ignore spaces, by first stripping all spaces from your training data. If you were going to use Alice in Wonderland as your training text, the first paragraph would, perhaps, look like so:
alicewasbeginningtogetverytiredofsittingbyhersisteronthebankandofhavingnothingtodoonceortwiceshehadpeepedintothebookhersisterwasreadingbutithadnopicturesorconversationsinitandwhatistheuseofabookthoughtalicewithoutpicturesorconversation
It looks weird, but as far as a Markov model is concerned, it's a trivial difference from the classical implementation.
I see that you are concerned about time: Training may take a few minutes (assuming you have already compiled gold standard "sentences" and "random scrambled strings" texts). You only need to train once, you can easily save the "trained" model to disk and reuse it for subsequent runs by loading from disk, which may take a few seconds. Making a call on a string would take a trivially small number of floating point multiplications to get a probability, so after you finish training it, it should be very fast.
I'm looking for an algorithm, or at least theory of operation on how you would find similar text in two or more different strings...
Much like the question posed here: Algorithm to find articles with similar text, the difference being that my text strings will only ever be a handful of words.
Like say I have a string:
"Into the clear blue sky"
and I'm doing a compare with the following two strings:
"The color is sky blue" and
"In the blue clear sky"
I'm looking for an algorithm that can be used to match the text in the two, and decide on how close they match. In my case, spelling, and punctuation are going to be important. I don't want them to affect the ability to discover the real text. In the above example, if the color reference is stored as "'sky-blue'", I want it to still be able to match. However, the 3rd string listed should be a BETTER match over the second, etc.
I'm sure places like Google probably use something similar with the "Did you mean:" feature...
* EDIT *
In talking with a friend, he worked with a guy who wrote a paper on this topic. I thought I might share it with everyone reading this, as there are some really good methods and processes described in it...
Here's the link to his paper, I hope it is helpful to those reading this question, and on the topic of similar string algorithms.
Levenshtein distance will not completely work, because you want to allow rearrangements. I think your best bet is going to be to find best rearrangement with levenstein distance as cost for each word.
To find the cost of rearrangement, kinda like the pancake sorting problem. So, you can permute every combination of words (filtering out exact matches), with every combination of other string, trying to minimize a combination of permute distance and Levenshtein distance on each word pair.
edit:
Now that I have a second I can post a quick example (all 'best' guesses are on inspection and not actually running the algorithms):
original strings | best rearrangement w/ lev distance per word
Into the clear blue sky | Into the c_lear blue sky
The color is sky blue | is__ the colo_r blue sky
R_dist = dist( 3 1 2 5 4 ) --> 3 1 2 *4 5* --> *2 1 3* 4 5 --> *1 2* 3 4 5 = 3
L_dist = (2D+S) + (I+D+S) (Total Subsitutions: 2, deletions: 3, insertion: 1)
(notice all the flips include all elements in the range, and I use ranges where Xi - Xj = +/- 1)
Other example
original strings | best rearrangement w/ lev distance per word
Into the clear blue sky | Into the clear blue sky
In the blue clear sky | In__ the clear blue sky
R_dist = dist( 1 2 4 3 5 ) --> 1 2 *3 4* 5 = 1
L_dist = (2D) (Total Subsitutions: 0, deletions: 2, insertion: 0)
And to show all possible combinations of the three...
The color is sky blue | The colo_r is sky blue
In the blue clear sky | the c_lear in sky blue
R_dist = dist( 2 4 1 3 5 ) --> *2 3 1 4* 5 --> *1 3 2* 4 5 --> 1 *2 3* 4 5 = 3
L_dist = (D+I+S) + (S) (Total Subsitutions: 2, deletions: 1, insertion: 1)
Anyway you make the cost function the second choice will be lowest cost, which is what you expected!
One way to determine a measure of "overall similarity without respect to order" is to use some kind of compression-based distance. Basically, the way most compression algorithms (e.g. gzip) work is to scan along a string looking for string segments that have appeared earlier -- any time such a segment is found, it is replaced with an (offset, length) pair identifying the earlier segment to use. You can use measures of how well two strings compress to detect similarities between them.
Suppose you have a function string comp(string s) that returns a compressed version of s. You can then use the following expression as a "similarity score" between two strings s and t:
len(comp(s)) + len(comp(t)) - len(comp(s . t))
where . is taken to be concatenation. The idea is that you are measuring how much further you can compress t by looking at s first. If s == t, then len(comp(s . t)) will be barely any larger than len(comp(s)) and you'll get a high score, while if they are completely different, len(comp(s . t)) will be very near len(comp(s) + comp(t)) and you'll get a score near zero. Intermediate levels of similarity produce intermediate scores.
Actually the following formula is even better as it is symmetric (i.e. the score doesn't change depending on which string is s and which is t):
2 * (len(comp(s)) + len(comp(t))) - len(comp(s . t)) - len(comp(t . s))
This technique has its roots in information theory.
Advantages: good compression algorithms are already available, so you don't need to do much coding, and they run in linear time (or nearly so) so they're fast. By contrast, solutions involving all permutations of words grow super-exponentially in the number of words (although admittedly that may not be a problem in your case as you say you know there will only be a handful of words).
One way (although this is perhaps better suited a spellcheck-type algorithm) is the "edit distance", ie., calculate how many edits it takes to transform one string to another. A common technique is found here:
http://en.wikipedia.org/wiki/Levenshtein_distance
You might want to look into the algorithms used by biologists to compare DNA sequences, since they have to cope with many of the same things (chunks may be missing, or have been inserted, or just moved to a different position in the string.
The Smith-Waterman algorithm would be one example that'd probably work fairly well, although it might be too slow for your uses. Might give you a starting point, though.
i had a similar problem, i needed to get the percentage of characters in a string that were similar. it needed exact sequences, so for example "hello sir" and "sir hello" when compared needed to give me five characters that are the same, in this case they would be the two "hello"'s. it would then take the length of the longest of the two strings and give me a percentage of how similar they were. this is the code that i came up with
int compare(string a, string b){
return(a.size() > b.size() ? bigger(a,b) : bigger(b,a));
}
int bigger(string a, string b){
int maxcount = 0, currentcount = 0;//used to see which set of concurrent characters were biggest
for(int i = 0; i < a.size(); ++i){
for(int j = 0; j < b.size(); ++j){
if(a[i+j] == b[j]){
++currentcount;
}
else{
if(currentcount > maxcount){
maxcount = currentcount;
}//end if
currentcount = 0;
}//end else
}//end inner for loop
}//end outer for loop
return ((int)(((float)maxcount/((float)a.size()))*100));
}
I can't mark two answers here, so I'm going to answer and mark my own. The Levenshtein distance appears to be the correct method in most cases for this. But, it is worth mentioning j_random_hackers answer as well. I have used an implementation of LZMA to test his theory, and it proves to be a sound solution. In my original question I was looking for a method for short strings (2 to 200 chars), where the Levenshtein Distance algorithm will work. But, not mentioned in the question was the need to compare two (larger) strings (in this case, text files of moderate size) and to perform a quick check to see how similar the two are. I believe that this compression technique will work well but I have yet to study it to find at which point one becomes better than the other, in terms of the size of the sample data and the speed/cost of the operation in question. I think a lot of the answers given to this question are valuable, and worth mentioning, for anyone looking to solve a similar string ordeal like I'm doing here. Thank you all for your great answers, and I hope they can be used to serve others well too.
There's another way. Pattern recognition using convolution. Image A is run thru a Fourier transform. Image B also. Now superimposing F(A) over F(B) then transforming this back gives you a black image with a few white spots. Those spots indicate where A matches B strongly. Total sum of spots would indicate an overall similarity. Not sure how you'd run an FFT on strings but I'm pretty sure it would work.
The difficulty would be to match the strings semantically.
You could generate some kind of value based on the lexical properties of the string. e.g. They bot have blue, and sky, and they're in the same sentence, etc etc... But it won't handle cases where "Sky's jean is blue", or some other odd ball English construction that uses same words, but you'd need to parse the English grammar...
To do anything beyond lexical similarity, you'd need to look at natural language processing, and there isn't going to be one single algorith that would solve your problem.
Possible approach:
Construct a Dictionary with a string key of "word1|word2" for all combinations of words in the reference string. A single combination may happen multiple times, so the value of the Dictionary should be a list of numbers, each representing the distance between the words in the reference string.
When you do this, there will be duplication here: for every "word1|word2" dictionary entry, there will be a "word2|word1" entry with the same list of distance values, but negated.
For each combination of words in the comparison string (words 1 and 2, words 1 and 3, words 2 and 3, etc.), check the two keys (word1|word2 and word2|word1) in the reference string and find the closest value to the distance in the current string. Add the absolute value of the difference between the current distance and the closest distance to a counter.
If the closest reference distance between the words is in the opposite direction (word2|word1) as the comparison string, you may want to weight it smaller than if the closest value was in the same direction in both strings.
When you are finished, divide the sum by the square of the number of words in the comparison string.
This should provide some decimal value representing how closely each word/phrase matches some word/phrase in the original string.
Of course, if the original string is longer, it won't account for that, so it may be necessary to compute this both directions (using one as the reference, then the other) and average them.
I have absolutely no code for this, and I probably just re-invented a very crude wheel. YMMV.