computing the euclidean distance for KNN

Question

I've been seeing a lot of examples of computing euclidean distance for KNN but non for sentiment classification.

For example I have a sentence "a very close game"

How do I compute the euclidean distance for the sentence "A great game"?

Answer 1

Think about a sentence as about a point in multi-dimensional space, only after you will defined system of coordinates you can calculate Euclidean distance. For instance. You can introduce

1. O1 - A sentence length (Length)
2. O2 - A words number (WordsCount)

3. O2 - Alphabetical center(I just thought of it). It can be calculated as arithmetical mean of alphabetical center of each work in a sentence.

   CharsIndex = Sum(Char.indexInWord) / CharsCountInWord; CharsCode = Sum(Char.charCode) / CharsCount; AlphWordCoordinate = [CharsIndex, CharsCode]; WordsIndex = Sum(Words.CharsIndex) / WordsCount; WordsCode = Sum(Words.CharsCode) / WordsCount; AlphaSentenceCoordinate = (WordsIndex ^2+WordsCode^2+WordIndexInSentence^2)^1/2;

So, the Euclidean distance can be calculated no as following:

EuclidianSentenceDistance = (WordsCount^2 + Length^2 + AlphaSentenceCoordinate^2)^1/2

No every sentence can be transformed to point in three-dimensional space, like P[Length, Words, AlphaCoordinate]. Having a distance you can compare and classify sentences.

It is not ideal approach I guess, but I wanted to show you an idea.

import math

def calc_word_alpha_center(word):
    chars_index = 0;
    chars_codes = 0;
    for index, char in enumerate(word):
        chars_index += index
        chars_codes += ord(char)
    chars_count = len(word)
    index = chars_index / len(word)
    code = chars_codes / len(word)
    return (index, code)


def calc_alpha_distance(words):
    word_chars_index = 0;
    word_code = 0;
    word_index = 0;
    for index, word in enumerate(words):
        point = calc_word_alpha_center(word)
        word_chars_index += point[0]
        word_code += point[1]
        word_index += index
    chars_index = word_chars_index / len(words)
    code = word_code / len(words)
    index = word_index / len(words)
    return math.sqrt(math.pow(chars_index, 2) + math.pow(code, 2) + math.pow(index, 2))

def calc_sentence_euclidean_distance(sentence):
    length = len(sentence)

    words = sentence.split(" ")
    words_count = len(words)

    alpha_distance = calc_alpha_distance(words)

    return math.sqrt(math.pow(length, 2) + math.pow(words_count, 2) + math.pow(alpha_distance, 2))


sentence1 = "a great game"
sentence2 = "A great game"

distance1 = calc_sentence_euclidean_distance(sentence1)
distance2 = calc_sentence_euclidean_distance(sentence2)

print(sentence1)
print(str(distance1))

print(sentence2)
print(str(distance2))

Console output

a great game
101.764433866
A great game
91.8477000256