Determine the difficulty of an english word - algorithm

I am working a word based game. My word database contains around 10,000 english words (sorted alphabetically). I am planning to have 5 difficulty levels in the game. Level 1 shows the easiest words and Level 5 shows the most difficult words, relatively speaking.
I need to divide the 10,000 long words list into 5 levels, starting from the easiest words to difficult ones. I am looking for a program to do this for me.
Can someone tell me if there is an algorithm or a method to quantitatively measure the difficulty of an english word?
I have some thoughts revolving around using the "word length" and "word frequency" as factors, and come up with a formula or something that accomplishes this.

Get a large corpus of texts (e.g. from the Gutenberg archives), do a straight frequency analysis, and eyeball the results. If they don't look satisfying, weight each text with its Flesch-Kincaid score and run the analysis again - words that show up frequently, but in "difficult" texts will get a score boost, which is what you want.
If all you have is 10000 words, though, it will probably be quicker to just do the frequency sorting as a first pass and then tweak the results by hand.

I'm not understanding how frequency is being used... if you were to scan a newspaper, I'm sure you would see the word "thoroughly" mentioned much more frequently than the word "bop" or "moo" but that doesn't mean it's an easier word; on the contrary 'thoroughly' is one of the most disgustingly absurd spelling anomalies that gives grade school children nightmares...
Try explaining to a sane human being learning english as a second language the subtle difference between slaughter and laughter.

I agree that frequency of use is the most likely metric; there are studies supporting a high correlation between word frequency and difficulty (correct responses on tests, etc.). Check out the English Lexicon Project at http://elexicon.wustl.edu/ for some 70k(?) frequency-rated words.

Crowd-source the answer.
Create an online 'game' that lists 10 words at random.
Get the player to drag and drop them into easiest - hardest, and tick to indicate if the player has ever heard of the word.
Apply an ranking algorithm (e.g. ELO) on the result of each experiment.
Repeat.
It might even be fun to play, you could get a language proficiency score at the end.

Difficulty is a pretty amorphus concept. If you've no clear idea of what you want, perhaps you could take a look at the Porter Stemming Algorithm (see for example the original paper). That contains a more advanced idea of 'length' by defining words as being of the form [C](VC){m}[V]; C means a block of consonants and V a block of vowels and this definition says a word is an optional C followed by m VC blocks and finally an optional V. The m value is this advanced 'length'.

depending on the type of game the definition of "difficult" will change. If your game involves typing quickly (ztype-style...), "difficult" will have a different meaning than in a game where you need to define a word's meaning.
That said, Scrabble has a way to measure how "difficult" a word is which is also quite easy algoritmically.
Also you may look into defining "difficult" in terms of your game. You could beta test your game and classify words according to how "difficult" players find them in the context of your own game.

There are several factors that relate to word difficulty, including age at acquisition, imageability, concreteness, abstractness, syllables, frequency (spoken and written). There are also psycholinguistic databases that will search for word by at least some of these factors. (just do a search for "psycholinguistic database".

Word frequency is an obvious choice (of course not perfect). You can download Google n-grams V2 here, which is license under the Creative Commons Attribution 3.0 Unported License.
Format: ngram TAB year TAB match_count TAB page_count TAB volume_count NEWLINE
Example:
Corpus used (from Lin, Yuri, et al. "Syntactic annotations for the google books ngram corpus." Proceedings of the ACL 2012 system demonstrations. Association for Computational Linguistics, 2012.):

Word length is a good indicator , for word frequency , you would need data as an algorithm can obviously not determine it by itself.
You could also use some sort of scoring like the scrabble game does : each letter has a value and the final value would be the sum of the values.
It would be imo easier to find frequency data about each letter in your language .

In his article on spell correction Peter Norvig uses a dictionary to count the number of occurrences of each word (and thus determine their frequency).
You could use this as a stepping stone :)
Also, frequency should probably influence the difficulty more than length... you would have to beta-test the game for that.

In addition to metrics such as Flesch-Kincaid, you could try an approach based on the Dale-Chall readability formula, using lists of words that are familiar to readers of a particular level of ability.
Implementations of many of the readability formulae contain code for estimating the number of syllables in a word, which may also be useful.

I would guess that the grade at wich the word is introduced into normal students vocabulary is a measure of difficulty. Next would be how many standard rule violations it has. Meaning your words that have spellings or pronunciations that seem to violate the normal set off rules. Finally.. the meaning.. can be a tough concept. .. for example ... try explaining abstract to someone who's never heard the word.

Without claiming to know anything about their algorithm, there is an API that returns a 1-10 scale word difficulty: TwinWord API
I have never used it, myself, though.

Related

Algorithm to compare similarity of ideas (as strings)

Consider an arbitrary text box that records the answer to the question, what do you want to do before you die?
Using a collection of response strings (max length 240), I'd like to somehow sort and group them and count them by idea (which may be just string similarity as described in this question).
Is there another or better way to do something like this?
Is this any different than string similarity?
Is this the right question to be asking?
The idea here is to have people write in a text box over and over again, and me to provide a number that describes, generally speaking, that 802 people wrote approximately the same thing
It is much more difficult than string similarity. This is what you need to do at a minimum:
Perform some text formatting/cleaning tasks like removing punctuations characters and common "stop words"
Construct a corpus (collection of words with their usage statistics) from the terms that occur answers.
Calculate a weight for every term.
Construct a document vector from every answer (each term corresponds to a dimension in a very high dimensional Euclidian space)
Run a clustering algorithm on document vectors.
Read a good statistical natural language processing book, or search google for good introductions / tutorials (likely terms: statistical nlp, text categorization, clustering) You can probably find some libraries (weka or nltk comes to mind) depending on the language of your choice but you need to understand the concepts to use the library anyway.
The Latent Semantic Analysis (LSA) might interest you. Here is a nice introduction.
Latent semantic analysis (LSA) is a technique in natural language processing, in particular in vectorial semantics, of analyzing relationships between a set of documents and the terms they contain by producing a set of concepts related to the documents and terms.
[...]
What you want is very much an open problem in NLP. #Ali's answer describes the idea at a high level, but the part "Construct a document vector for every answer" is the really hard one. There are a few obvious ways of building a document vector from a the vectors of the words it contains. Addition, multiplication and averaging are fast, but they affectively ignore the syntax. Man bites dog and Dog bites man will have the same representation, but clearly not the same meaning. Google compositional distributional semantics- as far as I know, there are people at Universities of Texas, Trento, Oxford, Sussex and at Google working in the area.

How do I approximate "Did you mean?" without using Google?

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?

What is the empirically found best value for n in n-gram model?

I am implementing a variation of spell checker. After taking various routes (for improving the time efficiency) I am planning to try out a component which would involve use of n-gram model. So essentially I want to prune the list of likely candidates for further processing. Would you guys happen to know if using one value of n (say 2) will be better over other (say 3)?
According to this website, the average word length in English is 5.10 letters. I would assume that people are more likely to misspell longer words than shorter words, so I'd lean towards going around maybe 3-5 letters forward, if possible, as a gut feeling.
When you say n-grams, I'm going to assume you're talking about letters in a word, rather than words in a sentence (which probably is the most common usage). In this case, I would agree with Mark Rushakoff in that you could prune the candidates list to words including 3-5 characters more or less than the word you're controlling.
Another option would be to implement the Levenshtein algorithm to find the edit distance between two words. This can be done quite efficiently: Firstly, through only checking against your pruned list. Secondly, through ending the distance calculation of a word prematurely once the edit distance exceeds some sort of limit (e.g. 3-5).
As a side note, I disagree with Mark on that you should ignore short words, as they are less frequently misspelt. A large portion of the misspelt words will be short words (such as "and" - "nad", "the" - "teh", "you" - "yuo"), simply because they are much more frequent.
Hope this helps!
If you have sufficient text for training, 3 is a good start. On the other hand, such a model will be quite big and bloat your spell checker.
You could also compare different settings based on perplexity.

Algorithm to determine how positive or negative a statement/text is

I need an algorithm to determine if a sentence, paragraph or article is negative or positive in tone... or better yet, how negative or positive.
For instance:
Jason is the worst SO user I have ever witnessed (-10)
Jason is an SO user (0)
Jason is the best SO user I have ever seen (+10)
Jason is the best at sucking with SO (-10)
While, okay at SO, Jason is the worst at doing bad (+10)
Not easy, huh? :)
I don't expect somebody to explain this algorithm to me, but I assume there is already much work on something like this in academia somewhere. If you can point me to some articles or research, I would love it.
Thanks.
There is a sub-field of natural language processing called sentiment analysis that deals specifically with this problem domain. There is a fair amount of commercial work done in the area because consumer products are so heavily reviewed in online user forums (ugc or user-generated-content). There is also a prototype platform for text analytics called GATE from the university of sheffield, and a python project called nltk. Both are considered flexible, but not very high performance. One or the other might be good for working out your own ideas.
In my company we have a product which does this and also performs well. I did most of the work on it. I can give a brief idea:
You need to split the paragraph into sentences and then split each sentence into smaller sub sentences - splitting based on commas, hyphen, semi colon, colon, 'and', 'or', etc.
Each sub sentence will be exhibiting a totally seperate sentiment in some cases.
Some sentences even if it is split, will have to be joined together.
Eg: The product is amazing, excellent and fantastic.
We have developed a comprehensive set of rules on the type of sentences which need to be split and which shouldn't be (based on the POS tags of the words)
On the first level, you can use a bag of words approach, meaning - have a list of positive and negative words/phrases and check in every sub sentence. While doing this, also look at the negation words like 'not', 'no', etc which will change the polarity of the sentence.
Even then if you can't find the sentiment, you can go for a naive bayes approach. This approach is not very accurate (about 60%). But if you apply this to only sentence which fail to pass through the first set of rules - you can easily get to 80-85% accuracy.
The important part is the positive/negative word list and the way you split things up. If you want, you can go even a level higher by implementing HMM (Hidden Markov Model) or CRF (Conditional Random Fields). But I am not a pro in NLP and someone else may fill you in that part.
For the curious people, we implemented all of this is python with NLTK and the Reverend Bayes module.
Pretty simple and handles most of the sentences. You may however face problems when trying to tag content from the web. Most people don't write proper sentences on the web. Also handling sarcasm is very hard.
This falls under the umbrella of Natural Language Processing, and so reading about that is probably a good place to start.
If you don't want to get in to a very complicated problem, you can just create lists of "positive" and "negative" words (and weight them if you want) and do word counts on sections of text. Obviously this isn't a "smart" solution, but it gets you some information with very little work, where doing serious NLP would be very time consuming.
One of your examples would potentially be marked positive when it was in fact negative using this approach ("Jason is the best at sucking with SO") unless you happen to weight "sucking" more than "best".... But also this is a small text sample, if you're looking at paragraphs or more of text, then weighting becomes more reliable unless you have someone purposefully trying to fool your algorithm.
As pointed out, this comes under sentiment analysis under natural language processing. Afaik GATE doesn't have any component that does sentiment analysis.
In my experience, I have implemented an algorithm which is an adaptation of the one in the paper 'Recognizing Contextual Polarity in Phrase-Level Sentiment Analysis' by Theresa Wilson, Janyce Wiebe, Paul Hoffmann (this) as a GATE plugin, which gives reasonable good results. It could help you if you want to bootstrap the implementation.
Depending on your application you could do it via a Bayesian Filtering algorithm (which is often used in spam filters).
One way to do it would be to have two filters. One for positive documents and another for negative documents. You would seed the positive filter with positive documents (whatever criteria you use) and the negative filter with negative documents. The trick would be to find these documents. Maybe your could set it up so your users effectively rate documents.
The positive filter (once seeded) would look for positive words. Maybe it would end up with words like love, peace, etc. The negative filter would be seeded appropriately as well.
Once your filters are setup, then you run the test text through them to come up with positive and negative scores. Based on these scores and some weighting, you could come up with your numeric score.
Bayesian Filters, though simple, are surprisingly effective.
You can do like this:
Jason is the worst SO user I have ever witnessed (-10)
worst (-), the rest is (+). so, that would be (-) + (+) = (-)
Jason is an SO user (0)
( ) + ( ) = ( )
Jason is the best SO user I have ever seen (+10)
best (+) , the rest is ( ). so, that would be (+) + ( ) = (+)
Jason is the best at sucking with SO (-10)
best (+), sucking (-). so, (+) + (-) = (-)
While, okay at SO, Jason is the worst at doing bad (+10)
worst (-), doing bad (-). so, (-) + (-) = (+)
There are many machine learning approaches for this kind of Sentiment Analysis. I used most of the machine learning algorithms, which are already implemented. my case I have used
weka classification algorithms
SVM
naive basian
J48
Only you have to do this train the model to your context , add featured vector and rule based tune up. In my case I got some (61% accuracy). So We move into stanford core nlp ( they trained their model for movie reviews) and we used their training set and add our training set. we could achieved 80-90% accuracy.
This is an old question, but I happened upon it looking for a tool that could analyze article tone and found Watson Tone Analyzer by IBM. It allows 1000 api calls monthly for free.
It's all about context, I think. If you're looking for the people who are best at sucking with SO. Sucking the best can be a positive thing. For determination what is bad or good and how much I could recommend looking into Fuzzy Logic.
It's a bit like being tall. Someone who's 1.95m can considered to be tall. If you place that person in a group with people all over 2.10m, he looks short.
Maybe essay grading software could be used to estimate tone? WIRED article.
Possible reference. (I couldn't read it.)
This report compares writing skill to the Flesch-Kincaid Grade Level needed to read it!
Page 4 of e-rator says that they look at mispelling and such. (Maybe bad post are misspelled too!)
Slashdot article.
You could also use an email filter of some sort for negativity instead of spam-ness.
How about sarcasm:
Jason is the best SO user I have ever seen, NOT
Jason is the best SO user I have ever seen, right
Ah, I remember one java library for this called LingPipe (commercial license) that we evaluated. It would work fine for the example corpus that is available at the site, but for real data it sucks pretty bad.
Most of the sentiment analysis tools are lexicon based and none of them is perfect. Also, sentiment analysis can be described as a trinary sentiment classification or binary sentiment classification. Moreover, it is a domain specific task. Meaning that tools which work well on news dataset may not do a good job on informal and unstructured tweets.
I would suggest using several tools and have an aggregation or vote based mechanism to decide the intensity of the sentiment. The best survey study on sentiment analysis tools that I have come across is SentiBench. You will find it helpful.
use Algorithm::NaiveBayes;
my $nb = Algorithm::NaiveBayes->new;
$nb->add_instance
(attributes => {foo => 1, bar => 1, baz => 3},
label => 'sports');
$nb->add_instance
(attributes => {foo => 2, blurp => 1},
label => ['sports', 'finance']);
... repeat for several more instances, then:
$nb->train;
# Find results for unseen instances
my $result = $nb->predict
(attributes => {bar => 3, blurp => 2});

Is there an algorithm that tells the semantic similarity of two phrases

input: phrase 1, phrase 2
output: semantic similarity value (between 0 and 1), or the probability these two phrases are talking about the same thing
You might want to check out this paper:
Sentence similarity based on semantic nets and corpus statistics (PDF)
I've implemented the algorithm described. Our context was very general (effectively any two English sentences) and we found the approach taken was too slow and the results, while promising, not good enough (or likely to be so without considerable, extra, effort).
You don't give a lot of context so I can't necessarily recommend this but reading the paper could be useful for you in understanding how to tackle the problem.
Regards,
Matt.
There's a short and a long answer to this.
The short answer:
Use the WordNet::Similarity Perl package. If Perl is not your language of choice, check the WordNet project page at Princeton, or google for a wrapper library.
The long answer:
Determining word similarity is a complicated issue, and research is still very hot in this area. To compute similarity, you need an appropriate represenation of the meaning of a word. But what would be a representation of the meaning of, say, 'chair'? In fact, what is the exact meaning of 'chair'? If you think long and hard about this, it will twist your mind, you will go slightly mad, and finally take up a research career in Philosophy or Computational Linguistics to find the truth™. Both philosophers and linguists have tried to come up with an answer for literally thousands of years, and there's no end in sight.
So, if you're interested in exploring this problem a little more in-depth, I highly recommend reading Chapter 20.7 in Speech and Language Processing by Jurafsky and Martin, some of which is available through Google Books. It gives a very good overview of the state-of-the-art of distributional methods, which use word co-occurrence statistics to define a measure for word similarity. You are not likely to find libraries implementing these, however.
For anyone just coming at this, i would suggest taking a look at SEMILAR - http://www.semanticsimilarity.org/ . They implement a lot of the modern research methods for calculating word and sentence similarity. It is written in Java.
SEMILAR API comes with various similarity methods based on Wordnet, Latent Semantic Analysis (LSA), Latent Dirichlet Allocation (LDA), BLEU, Meteor, Pointwise Mutual Information (PMI), Dependency based methods, optimized methods based on Quadratic Assignment, etc. And the similarity methods work in different granularities - word to word, sentence to sentence, or bigger texts.
You might want to check into the WordNet project at Princeton University. One possible approach to this would be to first run each phrase through a stop-word list (to remove "common" words such as "a", "to", "the", etc.) Then for each of the remaining words in each phrase, you could compute the semantic "similarity" between each of the words in the other phrase using a distance measure based on WordNet. The distance measure could be something like: the number of arcs you have to pass through in WordNet to get from word1 to word2.
Sorry this is pretty high-level. I've obviously never tried this. Just a quick thought.
I would look into latent semantic indexing for this. I believe you can create something similar to a vector space search index but with semantically related terms being closer together i.e. having a smaller angle between them. If I learn more I will post here.
Sorry to dig up a 6 year old question, but as I just came across this post today, I'll throw in an answer in case anyone else is looking for something similar.
cortical.io has developed a process for calculating the semantic similarity of two expressions and they have a demo of it up on their website. They offer a free API providing access to the functionality, so you can use it in your own application without having to implement the algorithm yourself.
One simple solution is to use the dot product of character n-gram vectors. This is robust over ordering changes (which many edit distance metrics are not) and captures many issues around stemming. It also prevents the AI-complete problem of full semantic understanding.
To compute the n-gram vector, just pick a value of n (say, 3), and hash every 3-word sequence in the phrase into a vector. Normalize the vector to unit length, then take the dot product of different vectors to detect similarity.
This approach has been described in
J. Mitchell and M. Lapata, “Composition in Distributional Models of Semantics,” Cognitive Science, vol. 34, no. 8, pp. 1388–1429, Nov. 2010., DOI 10.1111/j.1551-6709.2010.01106.x
I would have a look at statistical techniques that take into consideration the probability of each word to appear within a sentence. This will allow you to give less importance to popular words such as 'and', 'or', 'the' and give more importance to words that appear less regurarly, and that are therefore a better discriminating factor. For example, if you have two sentences:
1) The smith-waterman algorithm gives you a similarity measure between two strings.
2) We have reviewed the smith-waterman algorithm and we found it to be good enough for our project.
The fact that the two sentences share the words "smith-waterman" and the words "algorithms" (which are not as common as 'and', 'or', etc.), will allow you to say that the two sentences might indeed be talking about the same topic.
Summarizing, I would suggest you have a look at:
1) String similarity measures;
2) Statistic methods;
Hope this helps.
Try SimService, which provides a service for computing top-n similar words and phrase similarity.
This requires your algorithm actually knows what your talking about. It can be done in some rudimentary form by just comparing words and looking for synonyms etc, but any sort of accurate result would require some form of intelligence.
Take a look at http://mkusner.github.io/publications/WMD.pdf This paper describes an algorithm called Word Mover distance that tries to uncover semantic similarity. It relies on the similarity scores as dictated by word2vec. Integrating this with GoogleNews-vectors-negative300 yields desirable results.

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