Merge: Vector Space Model

# Vector Space Model

Vector Space Model (VSM) is an algebraic model for representing text documents
(and any objects, in general) as vectors of identifiers, such as, for example,
index terms.

It is used in information filtering, information retrieval, indexing and
relevancy rankings.

The `vsm` package provides the following features:
* Vector comparison with cosine similarity.
* Vector indexing and matching with tf * idf.
* File indexing and matching to free text queries.

## Vectors

With VSM, documents are represented by a n-dimensions vector.
Each dimension represent an attribute of the document or object.

For text document, the count of each term found in the document if often used to
build vectors.

### Creating a vector

~~~nit
var vector = new Vector
vector["term1"] = 2.0
vector["term2"] = 1.0
assert vector["term1"] == 2.0
assert vector["term2"] == 1.0
assert vector.norm.is_approx(2.236, 0.001)
~~~

### Comparing vectors

~~~nit
var v1 = new Vector
v1["term1"] = 1.0
v1["term2"] = 2.0

var v2 = new Vector
v2["term2"] = 1.0
v2["term3"] = 3.0

var query = new Vector
query["term2"] = 1.0

var s1 = query.cosine_similarity(v1)
var s2 = query.cosine_similarity(v2)
assert s1 > s2
~~~

## VSMIndex

VSMIndex is a Document index based on VSM.

Using VSMIndex you can index documents associated with their vector.
Documents can then be matched to query vectors.

This represents a minimalistic search engine.

~~~nit
var index = new VSMIndex

var d1 = new Document("Doc 1", "/uri/1", v1)
index.index_document(d1)

var d2 = new Document("Doc 2", "/uri/2", v2)
index.index_document(d2)

assert index.documents.length == 2

query = new Vector
query["term1"] = 1.0

var matches = index.match_vector(query)
assert matches.first.document == d1
~~~

## StringIndex

The StringIndex provides usefull services to index and match strings.

~~~nit
index = new StringIndex

d1 = index.index_string("Doc 1", "/uri/1", "this is a sample")
d2 = index.index_string("Doc 2", "/uri/2", "this and this is another example")
assert index.documents.length == 2

matches = index.match_string("this sample")
assert matches.first.document == d1
~~~

## FileIndex

The FileIndex is a StringIndex able to index and retrieve files.

~~~nit
index = new FileIndex

index.index_files(["/path/to/doc/1", "/path/to/doc/2"])
~~~

Pull-Request: #2556
Reviewed-by: Jean Privat <jean@pryen.org>