I need to code a solution for a certain requirement, and I wanted to know if anyone is either familiar with an off-the-shelf library that can achieve it, or can direct me at the best practice. Description:
The user inputs a word that is supposed to be one of several fixed options (I hold the options in a list). I know the input must be in a member in the list, but since it is user input, he/she may have made a mistake. I'm looking for an algorithm that will tell me what is the most probable word the user meant. I don't have any context and I can’t force the user to choose from a list (i.e. he must be able to input the word freely and manually).
For example, say the list contains the words "water", “quarter”, "beer", “beet”, “hell”, “hello” and "aardvark".
The solution must account for different types of "normal" errors:
Speed typos (e.g. doubling characters, dropping characters etc)
Keyboard adjacent-character typos (e.g. "qater" for “water”)
Non-native English typos (e.g. "quater" for “quarter”)
And so on...
The obvious solution is to compare letter-by-letter and give "penalty weights" to each different letter, extra letter and missing letter. But this solution ignores thousands of "standard" errors I'm sure are listed somewhere. I'm sure there are heuristics out there that deal with all the cases, both specific and general, probably using a large database of standard mismatches (I’m open to data-heavy solutions).
I'm coding in Python but I consider this question language-agnostic.
Any recommendations/thoughts?
You want to read how google does this: http://norvig.com/spell-correct.html
Edit: Some people have mentioned algorithms that define a metric between a user given word and a candidate word (levenshtein, soundex). This is however not a complete solution to the problem, since one would also need a datastructure to efficiently perform a non-euclidean nearest neighbour search. This can be done e.g. with the Cover Tree: http://hunch.net/~jl/projects/cover_tree/cover_tree.html
A common solution is to calculate the Levenshtein distance between the input and your fixed texts. The Levenshtein distance of two strings is just the number of simple operations - insertions, deletions, and substitutions of a single character - required to turn one of the string into the other.
Have you considered algorithms that compare by phonetic sounds, such as soundex? It shouldn't be too hard to produce soundex representations of your list of words, store them, and then get a soundex of the user input and find the closest match there.
Look for the Bitap algorithm. It qualifies well for what you want to do, and even comes with a source code example in Wikipedia.
If your data set is really small, simply comparing the Levenshtein distance on all items independently ought to suffice. If it's larger, though, you'll need to use a BK-Tree or similar indexing system. The article I linked to describes how to find matches within a given Levenshtein distance, but it's fairly straightforward to adapt to do nearest-neighbor searches (and left as an exercise to the reader ;).
Though it may not solve the entire problem, you may want to consider using the soundex algorithm as part of the solution. A quick google search of "soundex" and "python" showed some python implementations of the algorithm.
Try searching for "Levenshtein distance" or "edit distance". It counts the number of edit operations (delete, insert, change letter) you need to transform one word into another. It's a common algorithm, but depending on the problem you might need something special with different weights for the different types of typos.
Related
I have a few algorithms that extract and rank keywords [both terms and bigrams] from a paragraph [most are based on the tf-idf model].
I am looking for an experiment to evaluate these algorithms. This experiment should give a grade to each algorithm, indicating "how good was it" [on the evaluation set, of course].
I am looking for an automatic / semi-automatic method to evaluate each algorithm's results, and an automatic / semi-automatic method to create the evaluation set.
Note: These experiments will be ran off-line, so efficiency is not an issue.
The classic way to do this would be to define a set of key words you want the algorithms to find per paragraph, then check how well the algorithms do with respect to this set, e.g. (generated_correct - generated_not_correct)/total_generated (see update, this is nonsense). This is automatic once you have defined this ground truth. I guess constructing that is what you want to automate as well when you talk about constructing the evaluation set? That's a bit more tricky.
Generally, if there was a way to generate key words automatically that's a good way to use as a ground truth - you should use that as your algorithm ;). Sounds cheeky, but it's a common problem. When you evaluate one algorithm using the output of another algorithm, something's probably going wrong (unless you specifically want to benchmark against that algorithm).
So you might start harvesting key words from common sources. For example:
Download scientific papers that have a keyword section. Check if those keywords actually appear in the text, if they do, take the section of text including the keywords, use the keyword section as ground truth.
Get blog posts, check if the terms in the heading appear in the text, then use the words in the title (always minus stop words of course) as ground truth
...
You get the idea. Unless you want to employ people to manually generate keywords, I guess you'll have to make do with something like the above.
Update
The evaluation function mentioned above is stupid. It does not incorporate how many of the available key words have been found. Instead, the way to judge a ranked list of relevant and irrelevant results is to use precision and recall. Precision rewards the absence of irrelevant results, Recall rewards the presence of relevant results. This again gives you two measures. In order to combine these two into a single measure, either use the F-measure, which combines those two measures into a single measure, with an optional weighting. Alternatively, use Precision#X, where X is the number of results you want to consider. Precision#X interestingly is equivalent to Recall#X. However, you need a sensible X here, ie if you have less than X keywords in some cases, those results will be punished for never providing an Xth keyword. In the literature on tag recommendation for example, which is very similar to your case, F-measure and P#5 are often used.
http://en.wikipedia.org/wiki/F1_score
http://en.wikipedia.org/wiki/Precision_and_recall
I need to write a script, probably in Ruby, that will take one block of text and compare a number of transcriptions of recordings of that text to the original to check for accuracy. If that's just completely confusing, I'll try explaining another way...
I have recordings of several different people reading a script that is a few sentences long. These recordings have all been transcribed back to text a number of times by other people. I need to take all of the transcriptions (hundreds) and compare them against the original script for accuracy.
I'm having trouble even conceptualising the pseudocode, and wondering if someone can point me in the right direction. Is there an established algorithm I should be considering? The Levenshtein distance has been suggested to me, but this seems like it wouldn't cope well with longer strings, considering differences in punctuation choices, whitespace, etc.--missing the first word would wreck the entire algorithm, even if every other word were perfect. I'm open to anything--thank you!
Edit:
Thanks for the tips, psyho. One of my biggest concerns, however, is a situation like this:
Original Text:
I would've taken that course if I'd known it was available!
Transcription
I would have taken that course if I'd known it was available!
Even with a word-wise comparison of tokens, this transcription will be marked as quite errant, even though it's almost perfect, and this is hardly an edge-case! "would've" and "would have" are commonly pronounced extremely similarly, especially in this part of the world. Is there a way to make the approach you suggest robust enough to deal with this? I've thought about running a word-wise comparison both forward and backward and building a sort of composite score, but this would fall apart with a transcription like this:
I would have taken that course if I had known it was available!
Any ideas?
Simple version:
Tokenize your input into words (convert a string containing words, punctuation, etc. into an array of lowercase words, without punctuation).
Use the Levenshtein distance (wordwise) to compare the original array with the transcription arrays.
Possible improvements:
You could introduce tokens for punctuation (or replace them all with a simple token like '.').
Levenshtein distance algorithm can be modified so that misspelling a character that with a character that is close on the keyboard generates a smaller distance. You could potentialy apply this, so that when comparing individual words, you would use Levenshtein distance (normalized, so that it's value ranges from 0 to 1, for example by dividing it by the length of the longer of the two words), and then use that value in the "outer" distance calculation.
It's hard to say what algorithm will work best with your data. My tip is: make sure you have some automated way of visualizing or testing your solution. This way you can quickly iterate and experiment with your solution and see how your changes affect the end result.
EDIT:
In response to your concerns:
The easiest way would be to start with normalizing the shorter forms (using gsub):
str.gsub("n't", ' not').gsub("'d", " had").gsub("'re", " are")
Note, that you can even expand "'s" to " is", even if it's not grammatically correct, because if John's means "John is", then you will get it right, and if it means "owned by John", then most likely both texts will contain the same form, so you will not further the distance by expanding both "incorrectly". The other case is when it should mean "John has", but then after "'s" there probably will be "got", so you can handle that easily as well.
You will probably also want to deal with numeric values (1st = first, etc.). Generally you can probably improve the result by doing some preprocessing. Don't worry if it's not always 100% correct, it should just be correct enough:)
Since you're ultimately trying to compare how different transcribers have dealt with the way the passage sounds, you might try comparing using a phonetic algorithm such as Metaphone.
After experimenting with the issues I noted in this question, I found that the Levenshtein Distance actually takes these problems into account. I don't fully understand how or why, but can see after experimentation that this is the case.
A coworker was recently asked this when trying to land a (different) research job:
Given 10 128-character strings which have been permutated in exactly the same way, decode the strings. The original strings are English text with spaces, numbers, punctuation and other non-alpha characters removed.
He was given a few days to think about it before an answer was expected. How would you do this? You can use any computer resource, including character/word level language models.
This is a basic transposition cipher. My question above was simply to determine if it was a transposition cipher or a substitution cipher. Cryptanalysis of such systems is fairly straightforward. Others have already alluded to basic methods. Optimal approaches will attempt to place the hardest and rarest letters first, as these will tend to uniquely identify the letters around them, which greatly reduces the subsequent search space. Simply finding a place to place an "a" (no pun intended) is not hard, but finding a location for a "q", "z", or "x" is a bit more work.
The overarching goal for an algorithm's quality isn't to decipher the text, as it can be done by better than brute force methods, nor is it simply to be fast, but it should eliminate possibilities absolutely as fast as possible.
Since you can use multiple strings simultaneously, attempting to create words from the rarest characters is going to allow you to test dictionary attacks in parallel. Finding the correct placement of the rarest terms in each string as quickly as possible will decipher that ciphertext PLUS all of the others at the same time.
If you search for cryptanalysis of transposition ciphers, you'll find a bunch with genetic algorithms. These are meant to advance the research cred of people working in GA, as these are not really optimal in practice. Instead, you should look at some basic optimizatin methods, such as branch and bound, A*, and a variety of statistical methods. (How deep you should go depends on your level of expertise in algorithms and statistics. :) I would switch between deterministic methods and statistical optimization methods several times.)
In any case, the calculations should be dirt cheap and fast, because the scale of initial guesses could be quite large. It's best to have a cheap way to filter out a LOT of possible placements first, then spend more CPU time on sifting through the better candidates. To that end, it's good to have a way of describing the stages of processing and the computational effort for each stage. (At least that's what I would expect if I gave this as an interview question.)
You can even buy a fairly credible reference book on deciphering double transposition ciphers.
Update 1: Take a look at these slides for more ideas on iterative improvements. It's not a great reference set of slides, but it's readily accessible. What's more, although the slides are about GA and simulated annealing (methods that come up a lot in search results for transposition cipher cryptanalysis), the author advocates against such methods when you can use A* or other methods. :)
first, you'd need a test for the correct ordering. something fairly simple like being able to break the majority of texts into words using a dictionary ordered by frequency of use without backtracking.
one you have that, you can play with various approaches. two i would try are:
using a genetic algorithm, with scoring based on 2 and 3-letter tuples (which you can either get from somewhere or generate yourself). the hard part of genetic algorithms is finding a good description of the process that can be fragmented and recomposed. i would guess that something like "move fragment x to after fragment y" would be a good approach, where the indices are positions in the original text (and so change as the "dna" is read). also, you might need to extend the scoring with something that gets you closer to "real" text near the end - something like the length over which the verification algorithm runs, or complete words found.
using a graph approach. you would need to find a consistent path through the graph of letter positions, perhaps with a beam-width search, using the weights obtained from the pair frequencies. i'm not sure how you'd handle reaching the end of the string and restarting, though. perhaps 10 sentences is sufficient to identify with strong probability good starting candidates (from letter frequency) - wouldn't surprise me.
this is a nice problem :o) i suspect 10 sentences is a strong constraint (for every step you have a good chance of common letter pairs in several strings - you probably want to combine probabilities by discarding the most unlikely, unless you include word start/end pairs) so i think the graph approach would be most efficient.
Frequency analysis would drastically prune the search space. The most-common letters in English prose are well-known.
Count the letters in your encrypted input, and put them in most-common order. Matching most-counted to most-counted, translated the cypher text back into an attempted plain text. It will be close to right, but likely not exactly. By hand, iteratively tune your permutation until plain text emerges (typically few iterations are needed.)
If you find checking by hand odious, run attempted plain texts through a spell checker and minimize violation counts.
First you need a scoring function that increases as the likelihood of a correct permutation increases. One approach is to precalculate the frequencies of triplets in standard English (get some data from Project Gutenburg) and add up the frequencies of all the triplets in all ten strings. You may find that quadruplets give a better outcome than triplets.
Second you need a way to produce permutations. One approach, known as hill-climbing, takes the ten strings and enters a loop. Pick two random integers from 1 to 128 and swap the associated letters in all ten strings. Compute the score of the new permutation and compare it to the old permutation. If the new permutation is an improvement, keep it and loop, otherwise keep the old permutation and loop. Stop when the number of improvements slows below some predetermined threshold. Present the outcome to the user, who may accept it as given, accept it and make changes manually, or reject it, in which case you start again from the original set of strings at a different point in the random number generator.
Instead of hill-climbing, you might try simulated annealing. I'll refer you to Google for details, but the idea is that instead of always keeping the better of the two permutations, sometimes you keep the lesser of the two permutations, in the hope that it leads to a better overall outcome. This is done to defeat the tendency of hill-climbing to get stuck at a local maximum in the search space.
By the way, it's "permuted" rather than "permutated."
I am aware of the duplicates of this question:
How does the Google “Did you mean?” Algorithm work?
How do you implement a “Did you mean”?
... and many others.
These questions are interested in how the algorithm actually works. My question is more like: Let's assume Google did not exist or maybe this feature did not exist and we don't have user input. How does one go about implementing an approximate version of this algorithm?
Why is this interesting?
Ok. Try typing "qualfy" into Google and it tells you:
Did you mean: qualify
Fair enough. It uses Statistical Machine Learning on data collected from billions of users to do this. But now try typing this: "Trytoreconnectyou" into Google and it tells you:
Did you mean: Try To Reconnect You
Now this is the more interesting part. How does Google determine this? Have a dictionary handy and guess the most probably words again using user input? And how does it differentiate between a misspelled word and a sentence?
Now considering that most programmers do not have access to input from billions of users, I am looking for the best approximate way to implement this algorithm and what resources are available (datasets, libraries etc.). Any suggestions?
Assuming you have a dictionary of words (all the words that appear in the dictionary in the worst case, all the phrases that appear in the data in your system in the best case) and that you know the relative frequency of the various words, you should be able to reasonably guess at what the user meant via some combination of the similarity of the word and the number of hits for the similar word. The weights obviously require a bit of trial and error, but generally the user will be more interested in a popular result that is a bit linguistically further away from the string they entered than in a valid word that is linguistically closer but only has one or two hits in your system.
The second case should be a bit more straightforward. You find all the valid words that begin the string ("T" is invalid, "Tr" is invalid, "Try" is a word, "Tryt" is not a word, etc.) and for each valid word, you repeat the algorithm for the remaining string. This should be pretty quick assuming your dictionary is indexed. If you find a result where you are able to decompose the long string into a set of valid words with no remaining characters, that's what you recommend. Of course, if you're Google, you probably modify the algorithm to look for substrings that are reasonably close typos to actual words and you have some logic to handle cases where a string can be read multiple ways with a loose enough spellcheck (possibly using the number of results to break the tie).
From the horse's mouth: How to Write a Spelling Corrector
The interesting thing here is how you don't need a bunch of query logs to approximate the algorithm. You can use a corpus of mostly-correct text (like a bunch of books from Project Gutenberg).
I think this can be done using a spellchecker along with N-grams.
For Trytoreconnectyou, we first check with all 1-grams (all dictionary words) and find a closest match that's pretty terrible. So we try 2-grams (which can be built by removing spaces from phrases of length 2), and then 3-grams and so on. When we try a 4-gram, we find that there is a phrase that is at 0 distance from our search term. Since we can't do better than that, we return that answer as the suggestion.
I know this is very inefficient, but Peter Norvig's post here suggests clearly that Google uses spell correcters to generate it's suggestions. Since Google has massive paralellization capabilities, they can accomplish this task very quickly.
Impressive tutroail one how its work you can found here http://alias-i.com/lingpipe-3.9.3/demos/tutorial/querySpellChecker/read-me.html.
In few word it is trade off of query modification(on character or word level) to increasing coverage in search documents. For example "aple" lead to 2mln documents, but "apple" lead to 60mln and modification is only one character, therefore it is obvious that you mean apple.
Datasets/tools that might be useful:
WordNet
Corpora such as the ukWaC corpus
You can use WordNet as a simple dictionary of terms, and you can boost that with frequent terms extracted from a corpus.
You can use the Peter Norvig link mentioned before as a first attempt, but with a large dictionary, this won't be a good solution.
Instead, I suggest you use something like locality sensitive hashing (LSH). This is commonly used to detect duplicate documents, but it will work just as well for spelling correction. You will need a list of terms and strings of terms extracted from your data that you think people may search for - you'll have to choose a cut-off length for the strings. Alternatively if you have some data of what people actually search for, you could use that. For each string of terms you generate a vector (probably character bigrams or trigrams would do the trick) and store it in LSH.
Given any query, you can use an approximate nearest neighbour search on the LSH described by Charikar to find the closest neighbour out of your set of possible matches.
Note: links removed as I'm a new user - sorry.
#Legend - Consider using one of the variations of the Soundex algorithm. It has some known flaws, but it works decently well in most applications that need to approximate misspelled words.
Edit (2011-03-16):
I suddenly remembered another Soundex-like algorithm that I had run across a couple of years ago. In this Dr. Dobb's article, Lawrence Philips discusses improvements to his Metaphone algorithm, dubbed Double Metaphone.
You can find a Python implementation of this algorithm here, and more implementations on the same site here.
Again, these algorithms won't be the same as what Google uses, but for English language words they should get you very close. You can also check out the wikipedia page for Phonetic Algorithms for a list of other similar algorithms.
Take a look at this: How does the Google "Did you mean?" Algorithm work?
I am hoping I am wording this correctly to get across what I am looking for.
I need to compare two pieces of text. If the two strings are alike I would like to get scores that are very alike if the strings are very different i need scores that are very different.
If i take a md5 hash of an email and change one character the hash changes dramatically I want something to not change too much. I need to compare how alike two pieces of content are without storing the string.
Update: I am looking now at combining some ideas from the various links people have provided. Ideally I would of liked a single input function to create my score so I am looking at using a reference string to always compare my input to. I am also looking at taking asci characters and suming these up. Still reading all the links provided.
What you're looking for is a LCS algorithm (see also Levenshtein distance). You may also try Soundex or some other phonetic algorithm.
Reading your comments, it sounds like you are actually trying to compare entire documents, each containing many words.
This is done successfully in information retrieval systems by treating documents as N-dimensional points in space. Each word in the language is an axis. The distance along the axis is determined by the number of times that word appears in the document. Similar documents are then "near" each other in space.
This way, the whole document doesn't need to be stored, just its word counts. And usually the most common words in the language are not counted at all.
Check their Levenshtein Distance
In PHP you even have the levenshtein() function that makes exactly that.
I need to compare two pieces of text. If the two strings are alike I would like to get scores that are very alike if the strings are very different i need scores that are very different.
It really depends on what you mean by "same" or "different". For example, if someone replaces "United States of America" with "USA" in your string, is that mostly the same string (because USA is just an abbreviation for something longer), or is it very different (because a lot of characters changed)?
You essentially need to either devise a function that describes how to compute "sameness" or use a pre-existing definition thereof. For example, the aforementioned Levenshtein distance measures total difference based on the number of changes you have to make to get to the original string.
Since the Levenshtein distance needs both input strings to produce a value, you would have to store all strings.
You could, however, use a small number of strings as markers and only store these as strings.
You would then calculate the Levenshtein distance from a new string to each of these marker strings and store these values. You could then guess that two strings that have a similar Levenshtein distance to all markers are also similar to each other. It would likely be sensible to "engineer" these markers in such a way that their mutual Levenshtein distance is as large as possible. I don't know whether there has been some research in this direction.
Many people have suggested looking at distance/metric like approaches, and I think the wording of the question leads that way. (By the way, a hash like md5 is trying to do pretty much the opposite thing that a metric does, so it's hardly surprising that this wouldn't work for you. There are similar ideas that don't change much under small deltas, but I suspect they don't encode enough information for what you want to do)
Particularly given your update in the comments though, I think this type of approach is not very helpful.
What you are looking for is more of a clustering problem, where you want to generate a signature (i.e. feature vector) from each email and later compare it to new inputs. So essentially what you have is a machine learning problem. Deciding what "close" means may be a bit of a challenge. To get started though, assuming it actually is emails you're looking at you may do well to look at the sorts of feature generation done by many spam-filters, this will give you (probably Euclidean, at least to start) a space to measure distances in based on a signature (feature vector).
Without knowing more about your problem it's hard to be more specific.