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Week 4: Vector Representations & Similarity Measures

Knowledge Check — Select an answer to see immediate feedback.

Questions 10

Question 1

What does cosine similarity measure between two vectors?

A) The Euclidean distance between their endpoints
B) The cosine of the angle between them, normalized by their magnitudes
C) The sum of their element-wise differences
D) The ratio of their dot product to the sum of their lengths

Question 2

A key advantage of cosine similarity over Euclidean distance for comparing preference vectors is that cosine similarity:

A) Always produces a value between 0 and 1
B) Is less sensitive to absolute magnitude and more focused on relative patterns
C) Can handle negative values in vectors, while Euclidean distance cannot
D) Is computationally faster for high-dimensional vectors

Question 3

When representing food preferences at the individual ingredient level, vectors become extremely sparse. What does "sparse" mean in this context?

A) The vectors have very few dimensions overall
B) Most elements in the vector are zero because users interact with only a small subset of possible ingredients
C) The vectors are stored in a compressed format to save memory
D) The similarity scores between users are very low on average

Question 4

The "curse of dimensionality" in the context of sparse representations refers to:

A) The difficulty of visualizing vectors with more than three dimensions
B) The exponential growth of space volume as dimensions increase, making distance measures less meaningful
C) The increased computational cost of matrix multiplication in high dimensions
D) The tendency for machine learning models to overfit with many features

Question 5

Two users both enjoy spicy food but have no overlap in the specific ingredients they use. Using highly specific ingredient-level binary vectors, their cosine similarity score will likely be:

A) High, because their shared preference for spice is captured
B) Moderate, around 0.5
C) Near zero, because their non-zero elements do not overlap
D) Negative, indicating dissimilarity

Question 6

Why is over-generalization of categories problematic for similarity measures? Consider two users both labeled as preferring "protein."

A) It makes vectors denser, which slows down computation
B) It can create false equivalences — one user may be vegan preferring plant proteins while another eats only meat
C) Broad categories cause cosine similarity scores to exceed 1.0
D) It prevents the use of PCA for dimensionality reduction

Question 7

In a food preference survey using a Likert scale, what is the primary purpose of using controlled vocabularies?

A) To limit the number of questions respondents must answer
B) To reduce ambiguity and improve consistency across responses
C) To ensure all vectors have the same magnitude
D) To convert categorical data into binary format automatically

Question 8

Principal Component Analysis (PCA) helps address which core challenge in preference data collected from surveys?

A) It removes noise from Likert scale ratings
B) It transforms high-dimensional data into a lower-dimensional space ordered by explained variance
C) It guarantees that learned representations are interpretable
D) It converts sparse vectors into dense binary vectors

Question 9

A key advantage of deep learning-based learned representations over manually engineered feature vectors is:

A) Learned representations always require less training data
B) They can automatically discover non-obvious relationships and represent preferences at multiple scales simultaneously
C) They eliminate the need for any similarity measure
D) They always outperform PCA on reconstruction tasks

Question 10

One user rates every movie a 5 out of 10. Another user rates every movie a 10 out of 10. They have identical taste — they both love everything equally. What would their cosine similarity be?

A) 0 — they use different rating scales so they appear unrelated
B) -1 — one rates twice as high, which cosine similarity treats as opposite
C) 1 — perfectly similar, because they have identical relative preferences
D) 0.5 — somewhat similar because the scales overlap halfway