Word similarity and analogies in NLP - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is word similarity in NLP?

Word similarity measures how close or related two words are in meaning, often using numbers to show how similar they are.

beginner

How do word embeddings help find word similarity?

Word embeddings turn words into numbers (vectors) so we can use math to find how close words are, showing their similarity.

intermediate

What is a common method to measure similarity between word vectors?

Cosine similarity measures the angle between two word vectors to find how similar their meanings are.

beginner

Explain word analogies with an example.

Word analogies show relationships like 'king is to queen as man is to woman'. It means the difference between king and queen is like the difference between man and woman.

intermediate

How can word embeddings solve analogies?

By using vector math: for example, vector('king') - vector('man') + vector('woman') is close to vector('queen'). This helps find the missing word in analogies.

What does a high cosine similarity between two word vectors indicate?

A The words appear in the same sentence

B The words are spelled similarly

C The words have similar meanings

D The words have opposite meanings

Cosine similarity measures how close two word vectors are in meaning, so a high value means similar meanings.

Which of these is an example of a word analogy?

A 'cat' is to 'kitten' as 'dog' is to 'puppy'

B 'cat' rhymes with 'hat'

C 'cat' and 'dog' are both animals

D 'cat' is spelled with three letters

Word analogies show relationships between pairs of words, like parent to child.

What is the main purpose of word embeddings?

A To translate words into another language

B To count how many times a word appears

C To check spelling mistakes

D To convert words into numbers for math operations

Word embeddings turn words into vectors so computers can understand and compare their meanings.

In the analogy 'man is to king as woman is to ?', which word fits best?

A lady

B queen

C girl

D prince

The relationship between man and king is similar to woman and queen.

Which metric is commonly used to measure similarity between word vectors?

A Cosine similarity

B Euclidean distance

C Jaccard index

D Manhattan distance

Cosine similarity measures the angle between vectors, which works well for word meaning comparison.

Describe how word embeddings help in finding word similarity and solving analogies.

Think about how numbers can represent words and how math can find relationships.

Explain the concept of word analogies with a simple example.

Use a real-life example comparing two pairs of related words.

Practice

1. What does word similarity measure in natural language processing?

easy

A. How close two words are in meaning using numbers

B. How often two words appear together in a sentence

C. The length difference between two words

D. The number of letters two words share

Solution

1. Step 1: Understand the concept of word similarity

   Word similarity measures how close two words are in meaning, often represented by a number like cosine similarity.

2. Step 2: Differentiate from other word properties

   Frequency or letter count does not capture meaning closeness, so those options are incorrect.

3. Final Answer:

   How close two words are in meaning using numbers -> Option A

4. Quick Check:

   Word similarity = meaning closeness [OK]

Hint: Similarity means meaning closeness, not letter or frequency count [OK]

Common Mistakes:

• Confusing similarity with word frequency
• Thinking similarity is about word length
• Assuming similarity counts shared letters

2. Which of the following is the correct way to find the cosine similarity between two word vectors vec1 and vec2 in Python using NumPy?

easy

A. np.dot(vec1, vec2) / (np.linalg.norm(vec1) * np.linalg.norm(vec2))

B. np.dot(vec1, vec2) * (np.linalg.norm(vec1) + np.linalg.norm(vec2))

C. np.dot(vec1, vec2) - (np.linalg.norm(vec1) * np.linalg.norm(vec2))

D. np.dot(vec1, vec2) / (np.linalg.norm(vec1) + np.linalg.norm(vec2))

Solution

1. Step 1: Recall cosine similarity formula

   Cosine similarity = dot product of vectors divided by product of their norms.

2. Step 2: Match formula to code

   np.dot(vec1, vec2) / (np.linalg.norm(vec1) * np.linalg.norm(vec2)) matches the formula exactly using np.dot and np.linalg.norm.

3. Final Answer:

   np.dot(vec1, vec2) / (np.linalg.norm(vec1) * np.linalg.norm(vec2)) -> Option A

4. Quick Check:

   Cosine similarity = dot / (norm1 * norm2) [OK]

Hint: Cosine similarity divides dot product by product of norms [OK]

Common Mistakes:

• Adding norms instead of multiplying
• Subtracting norms from dot product
• Multiplying dot product by sum of norms

3. Given the following word vectors:

king = [0.5, 0.8, 0.3]
queen = [0.45, 0.75, 0.35]
man = [0.6, 0.7, 0.2]
woman = [0.55, 0.65, 0.25]

What is the closest word to the vector king - man + woman?

medium

A. king

B. man

C. queen

D. woman

Solution

1. Step 1: Calculate the vector for king - man + woman

   Subtract man from king: [0.5-0.6, 0.8-0.7, 0.3-0.2] = [-0.1, 0.1, 0.1]. Add woman: [-0.1+0.55, 0.1+0.65, 0.1+0.25] = [0.45, 0.75, 0.35].

2. Step 2: Compare result to known vectors

   The resulting vector matches queen exactly: [0.45, 0.75, 0.35].

3. Final Answer:

   queen -> Option C

4. Quick Check:

   king - man + woman = queen [OK]

Hint: king - man + woman equals queen vector [OK]

Common Mistakes:

• Not subtracting man vector before adding woman
• Mixing up vector addition order
• Choosing original words instead of analogy result

4. The following code tries to find the word most similar to king - man + woman but has a flaw:

import numpy as np
words = {'king': np.array([0.5, 0.8, 0.3]), 'queen': np.array([0.45, 0.75, 0.35]), 'man': np.array([0.6, 0.7, 0.2]), 'woman': np.array([0.55, 0.65, 0.25])}
result = words['king'] - words['man'] + words['woman']
max_word = None
max_sim = -1
for word, vec in words.items():
    sim = np.dot(result, vec) / (np.linalg.norm(result) * np.linalg.norm(vec))
    if sim > max_sim:
        max_word = word
print(max_word)

What is the main flaw?

medium

A. The variable max_sim is initialized incorrectly

B. Division by zero occurs due to zero vector norm

C. The dot product is computed without normalizing vectors

D. The code does not exclude the original words from similarity search

Solution

1. Step 1: Analyze the similarity search loop

   The loop compares the result vector to all words including 'king', 'man', and 'woman' which are part of the calculation.

2. Step 2: Understand why this is problematic

   Including original words can cause the highest similarity to be the input words themselves, which is usually unwanted and can cause misleading results.

3. Final Answer:

   The code does not exclude the original words from similarity search -> Option D

4. Quick Check:

   Exclude input words to avoid bias [OK]

Hint: Exclude input words from similarity search to avoid bias [OK]

Common Mistakes:

• Assuming zero division error without checking norms
• Thinking max_sim initialization causes error
• Ignoring normalization in dot product

5. You want to find the word that fits the analogy: Paris is to France as Tokyo is to ? Using pre-trained word vectors, which approach is best to find the answer?

hard

A. Calculate vector: France - Tokyo + Paris, then find closest word vector

B. Calculate vector: Tokyo - Paris + France, then find closest word vector

C. Calculate vector: Paris + France - Tokyo, then find closest word vector

D. Calculate vector: Tokyo + Paris - France, then find closest word vector

Solution

1. Step 1: Understand analogy vector arithmetic

   Analogies use the formula: word2 - word1 + word3 to find the missing word. Here, Paris is word1, France is word2, Tokyo is word3.

2. Step 2: Apply formula to this analogy

   Calculate Tokyo - Paris + France to get the vector representing the answer.

3. Final Answer:

   Calculate vector: Tokyo - Paris + France, then find closest word vector -> Option B

4. Quick Check:

   Analogy vector = word3 - word1 + word2 [OK]

Hint: Use analogy formula: word3 - word1 + word2 [OK]

Common Mistakes:

• Swapping order of subtraction and addition
• Adding all vectors without subtraction
• Using wrong words in formula