Matrix factorization basics in ML Python - Practice Problems & Coding Challenges

Challenge - 5 Problems

🧠 Conceptual

intermediate

What is the main goal of matrix factorization in machine learning?

Matrix factorization is often used in recommendation systems and dimensionality reduction. What is the primary goal when applying matrix factorization?

A To randomly shuffle the elements of the matrix to improve randomness

B To decompose a matrix into product of two or more matrices to capture latent features

C To convert a matrix into a single vector for easier processing

D To increase the size of the original matrix by adding more rows and columns

💡 Hint

Think about how matrix factorization helps reveal hidden patterns or features.

The main goal of matrix factorization is to break down a large matrix into smaller matrices that represent latent (hidden) features. This helps in understanding underlying structures like user preferences or item characteristics.

❓ Predict Output

intermediate

Output of matrix multiplication after factorization

Given matrices U and V below, what is the product U x V?

ML Python

import numpy as np
U = np.array([[1, 2], [3, 4]])
V = np.array([[2, 0], [1, 3]])
result = U @ V
print(result)

A

[[2 3]
 [6 7]]

B

[[4 6]
 [8 12]]

C

[[2 6]
 [3 12]]

D

[[4 6]
 [10 12]]

💡 Hint

Recall how matrix multiplication works: multiply rows of U by columns of V and sum.

Multiplying U and V: first row of U (1,2) times first column of V (2,1) = 1*2 + 2*1 = 4; similarly for other elements.

❓ Hyperparameter

advanced

Choosing the rank (k) in matrix factorization

In matrix factorization, the rank k controls the number of latent features. What is a common effect of choosing a very large k?

A The model will underfit and fail to capture important patterns

B The model will always perform better with no downsides

C The model may overfit the training data and lose generalization

D The model will ignore the latent features and use raw data only

💡 Hint

Think about what happens when a model is too complex for the data.

A very large rank means many latent features, which can cause the model to memorize training data (overfit) and not generalize well to new data.

❓ Metrics

advanced

Evaluating matrix factorization with RMSE

After training a matrix factorization model, you calculate the Root Mean Squared Error (RMSE) on test data. What does a lower RMSE indicate?

A The predicted values are closer to the actual values, indicating better performance

B The model predictions are more random and less reliable

C The model is underfitting and missing important patterns

D The model has a higher bias and lower variance

💡 Hint

RMSE measures the average difference between predicted and actual values.

A lower RMSE means the predictions are closer to the true values, showing the model fits the data better.

🔧 Debug

expert

Identifying error in matrix factorization code snippet

What error will this Python code raise when performing matrix factorization using numpy?

ML Python

import numpy as np
R = np.array([[5, 3], [4, 0], [1, 1]])
U = np.random.rand(3, 2)
V = np.random.rand(2, 3)
P = U @ V
print(P)

A No error, prints a 3x3 matrix

B TypeError: unsupported operand type(s) for @: 'list' and 'list'

C ValueError: shapes (3,2) and (3,2) not aligned: 2 (dim 1) != 3 (dim 0)

D IndexError: index out of bounds

💡 Hint

Check the shapes of matrices U and V before multiplication.

Matrix multiplication requires the inner dimensions to match. Here, U is (3,2) and V is (2,3), so multiplication U @ V is valid and results in a (3,3) matrix.