lib/nlp: introduce Vector Space Model with NLPVectors

Signed-off-by: Alexandre Terrasa <alexandre@moz-code.org>

diff --git a/lib/nlp/vsm.nit b/lib/nlp/vsm.nit
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+# This file is part of NIT ( http://www.nitlanguage.org ).
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+# NLPVector Space Model.
+#
+# The Vector Space Model (VSM) is used to compare natural language texts.
+# Texts are translated to multidimensionnal vectors then compared by cosine
+# similarity.
+module vsm
+
+import counter
+
+# A multi-dimensional vector.
+class NLPVector
+       super Counter[String]
+
+       # Cosine similarity of `self` and `other`.
+       #
+       # Gives the proximity in the range `[0.0 .. 1.0]` where 0.0 means that the
+       # two vectors are orthogonal and 1.0 means that they are identical.
+       #
+       # ~~~
+       # var v1 = new NLPVector
+       # v1["x"] = 1
+       # v1["y"] = 2
+       # v1["z"] = 3
+       #
+       # var v2 = new NLPVector
+       # v2["x"] = 1
+       # v2["y"] = 2
+       # v2["z"] = 3
+       #
+       # var v3 = new NLPVector
+       # v3["a"] = 1
+       # v3["b"] = 2
+       # v3["c"] = 3
+       #
+       # print v1.cosine_similarity(v2)
+       # #assert v1.cosine_similarity(v2) == 1.0
+       # print v1.cosine_similarity(v3)
+       # assert v1.cosine_similarity(v3) == 0.0
+       # ~~~
+       fun cosine_similarity(other: SELF): Float do
+               # Collect terms
+               var terms = new HashSet[String]
+               for k in self.keys do terms.add k
+               for k in other.keys do terms.add k
+
+               # Get dot product of two verctors
+               var dot = 0
+               for term in terms do
+                       dot += self.get_or_default(term, 0) * other.get_or_default(term, 0)
+               end
+
+               return dot.to_f / (self.norm * other.norm)
+       end
+
+       # The norm of the vector.
+       #
+       # `||x|| = (x1 ** 2 ... + xn ** 2).sqrt`
+       #
+       # ~~~
+       # var v = new NLPVector
+       # v["x"] = 1
+       # v["y"] = 1
+       # v["z"] = 1
+       # v["t"] = 1
+       # assert v.norm.is_approx(2.0, 0.001)
+       #
+       # v["x"] = 1
+       # v["y"] = 2
+       # v["z"] = 3
+       # v["t"] = 0
+       # assert v.norm.is_approx(3.742, 0.001)
+       # ~~~
+       fun norm: Float do
+               var sum = 0
+               for v in self.values do sum += v ** 2
+               return sum.to_f.sqrt
+       end
+end