Spell checker with fused spelling error correction algorithm

Recently I've looked through several spell checker algorithms including simple ones(like Peter Norvig's) and much more complex (like Brill and Moore's) ones. But there's a type of errors which none of them can handle. If for example I type stackoverflow instead of stack overflow these spellcheckers will fail to correct the mistype (unless the stack overflow in the dictionary of terms). Storing all the pairs of words is too expensive (and it will not help if the error is 3 single words without spaces between them). Is there an algorithm which can correct (despite usual mistypes) this type of errors?

Some examples of what I need:
spel checker -> spell checker
spellchecker -> spell checker
spelcheker -> spell checker

Solution

I hacked up Norvig's spell corrector to do this. I had to cheat a bit and add the word 'checker' to Norvig's data file because it never appears. Without that cheating, the problem is really hard.

expertsexchange expert exchange
spel checker spell checker
spellchecker spell checker
spelchecker she checker  # can't win them all
baseball base all  # baseball isn't in the dictionary either :(
hewent he went

Basically you need to change the code so that:

you add space to the alphabet to automatically explore the word breaks.
you first check that all of the words that make up a phrase are in the dictionary to consider the phrase valid, rather than just dictionary membership directly (the dict contains no phrases).
you need a way to score a phrase against plain words.

The latter is the trickiest, and I use a braindead independence assumption for phrase composition that the probability of two adjacent words is the product of their individual probabilities (here done with sum in log prob space), with a small penalty. I am sure that in practice, you'll want to keep some bigram stats to do that splitting well.

import re, collections, math

def words(text): return re.findall('[a-z]+', text.lower())

def train(features):
  counts = collections.defaultdict(lambda: 1.0)
  for f in features:
    counts[f] += 1.0
  tot = float(sum(counts.values()))
  model = collections.defaultdict(lambda: math.log(.1 / tot))
  for f in counts:
    model[f] = math.log(counts[f] / tot)
  return model

NWORDS = train(words(file('big.txt').read()))

alphabet = 'abcdefghijklmnopqrstuvwxyz '

def valid(w):
  return all(s in NWORDS for s in w.split())

def score(w):
  return sum(NWORDS[s] for s in w.split()) - w.count(' ')

def edits1(word):
  splits     = [(word[:i], word[i:]) for i in range(len(word) + 1)]
  deletes    = [a + b[1:] for a, b in splits if b]
  transposes = [a + b[1] + b[0] + b[2:] for a, b in splits if len(b)>1]
  replaces   = [a + c + b[1:] for a, b in splits for c in alphabet if b]
  inserts    = [a + c + b     for a, b in splits for c in alphabet]
  return set(deletes + transposes + replaces + inserts)

def known_edits2(word):
  return set(e2 for e1 in edits1(word) for e2 in edits1(e1) if valid(e2))

def known(words): return set(w for w in words if valid(w))

def correct(word):
  candidates = known([word]) or known(edits1(word)) or known_edits2(word) or [word]
  return max(candidates, key=score)

def t(w):
  print w, correct(w)

t('expertsexchange')
t('spel checker')
t('spellchecker')
t('spelchecker')
t('baseball')
t('hewent')