Sparse SVD (svds) in SciPy - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to import the sparse SVD function from scipy.

SciPy

from scipy.sparse.linalg import [1]

Drag options to blanks, or click blank then click option'

Asparse_svd_solver

Bsvd

Csparse_svd

Dsvds

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'svd' which is for dense matrices.

Trying to import a non-existent function like 'sparse_svd'.

The function svds is the correct sparse SVD function in scipy.sparse.linalg.

2fill in blank

medium

Complete the code to create a sparse matrix using scipy.

SciPy

from scipy.sparse import [1]
data = [1]((3, 3))

Drag options to blanks, or click blank then click option'

Acoo_matrix

Bcsr_matrix

Ccsc_matrix

Ddense_matrix

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'dense_matrix' which does not exist in scipy.sparse.

Choosing 'csc_matrix' which is column-based, not row-based.

csr_matrix creates a compressed sparse row matrix, commonly used for sparse data.

3fill in blank

hard

Fix the error in the code to compute the top 2 singular values and vectors of a sparse matrix.

SciPy

u, s, vt = svds(data, k=[1])

Drag options to blanks, or click blank then click option'

A2

B3

C1

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Using k=3 when the matrix dimension is smaller.

Using k=0 which is invalid.

The parameter k specifies the number of singular values and vectors to compute. For top 2, use k=2.

4fill in blank

hard

Fill both blanks to create a sparse matrix and compute its sparse SVD with 1 singular value.

SciPy

from scipy.sparse import [1]
from scipy.sparse.linalg import svds
matrix = [1]([[1, 0], [0, 1]])
u, s, vt = svds(matrix, k=[2])

Drag options to blanks, or click blank then click option'

Acsr_matrix

Bcsc_matrix

C1

D2

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'csc_matrix' instead of 'csr_matrix'.

Setting k to 2 when only 1 singular value is needed.

Use csr_matrix to create the sparse matrix and k=1 to compute one singular value.

5fill in blank

hard

Fill all three blanks to compute sparse SVD and reconstruct the original matrix.

SciPy

u, s, vt = svds(matrix, k=[1])
S = np.diag(s)
reconstructed = u [2] S [3] vt

Drag options to blanks, or click blank then click option'

A2

B@

C*

D1

Attempts:

3 left

💡 Hint

Common Mistakes

Using '*' which does element-wise multiplication, not matrix multiplication.

Setting k to 2 when only 1 singular value is needed.

Use k=1 for one singular value. Matrix multiplication is done with the @ operator in Python for arrays.

Practice

1. What is the main purpose of using svds from scipy.sparse.linalg in data science?

easy

A. To efficiently compute singular value decomposition on large sparse matrices

B. To perform dense matrix multiplication

C. To sort data in ascending order

D. To calculate the determinant of a matrix

Solution

1. Step 1: Understand the function purpose

   svds is designed for sparse matrices, which are mostly empty, to find singular values and vectors efficiently.

2. Step 2: Compare options with function use

   Options A, B, and C describe unrelated matrix operations. Only To efficiently compute singular value decomposition on large sparse matrices matches the purpose of svds.

3. Final Answer:

   To efficiently compute singular value decomposition on large sparse matrices -> Option A

4. Quick Check:

   svds = sparse SVD computation [OK]

Hint: Remember svds is for sparse matrices, not dense operations [OK]

Common Mistakes:

• Confusing svds with dense SVD functions
• Thinking svds sorts or multiplies matrices
• Assuming svds calculates determinants

2. Which of the following is the correct way to import the svds function from SciPy?

easy

A. from scipy.sparse.linalg import svds

B. import svds from scipy.linalg

C. from scipy.linalg import svds

D. import svds from scipy.sparse

Solution

1. Step 1: Identify the correct module for svds

   The svds function is part of scipy.sparse.linalg, which handles sparse linear algebra.

2. Step 2: Check import syntax

   Python import syntax requires 'from module import function'. from scipy.sparse.linalg import svds matches this correctly.

3. Final Answer:

   from scipy.sparse.linalg import svds -> Option A

4. Quick Check:

   Correct import syntax = from scipy.sparse.linalg import svds [OK]

Hint: Use 'from scipy.sparse.linalg import svds' to import correctly [OK]

Common Mistakes:

• Using wrong module like scipy.linalg instead of sparse.linalg
• Incorrect import syntax like 'import svds from ...'
• Importing from scipy.sparse which lacks svds

3. Given the following code, what will be the shape of the matrix U returned by svds?

import numpy as np
from scipy.sparse.linalg import svds
from scipy.sparse import csr_matrix

A = csr_matrix(np.array([[1, 0, 0], [0, 2, 0], [0, 0, 3]]))
U, S, Vt = svds(A, k=2)

medium

A. (3, 3)

B. (3, 2)

C. (2, 3)

D. (2, 2)

Solution

1. Step 1: Understand svds output shapes

   For an input matrix of shape (m, n) and parameter k, svds returns U with shape (m, k), S with length k, and Vt with shape (k, n).

2. Step 2: Apply to given matrix

   Matrix A is 3x3, k=2, so U shape is (3, 2).

3. Final Answer:

   (3, 2) -> Option B

4. Quick Check:

   U shape = (rows, k) = (3, 2) [OK]

Hint: U shape is (rows, k) where k is number of singular values [OK]

Common Mistakes:

• Confusing U shape with Vt shape
• Assuming U is square matrix
• Mixing up k with matrix dimensions

4. What is wrong with the following code snippet that tries to compute sparse SVD?

from scipy.sparse.linalg import svds
import numpy as np

A = np.array([[1, 0], [0, 1]])
U, S, Vt = svds(A, k=1)

medium

A. svds does not return three outputs

B. Parameter k cannot be 1

C. Matrix A is not a sparse matrix

D. Import statement is incorrect

Solution

1. Step 1: Check matrix type requirement

   svds expects a sparse matrix input, but A is a dense numpy array.

2. Step 2: Validate other parts

   Parameter k=1 is valid, svds returns three outputs, and import is correct. So only matrix type is wrong.

3. Final Answer:

   Matrix A is not a sparse matrix -> Option C

4. Quick Check:

   Input must be sparse matrix [OK]

Hint: Convert dense arrays to sparse before svds [OK]

Common Mistakes:

• Passing dense numpy arrays directly to svds
• Thinking k=1 is invalid
• Misunderstanding svds output count

5. You have a large sparse user-item rating matrix with shape (10000, 5000). You want to reduce its dimensionality to 50 features using svds. Which of the following code snippets correctly performs this and returns the reduced user features matrix?

hard

A. from scipy.sparse.linalg import svds
U, S, Vt = svds(ratings_sparse, k=50)
user_features = np.diag(S) @ Vt

B. from scipy.sparse.linalg import svds
U, S, Vt = svds(ratings_sparse, k=50)
user_features = Vt.T @ np.diag(S)

C. from scipy.linalg import svd
U, S, Vt = svd(ratings_sparse)
user_features = U[:, :50]

D. from scipy.sparse.linalg import svds
U, S, Vt = svds(ratings_sparse, k=50)
user_features = U @ np.diag(S)

Solution

1. Step 1: Understand svds output and dimensionality reduction

   svds returns U (users x k), S (k,), and Vt (k x items). Multiplying U by diag(S) gives user features in reduced space.

2. Step 2: Analyze options for correct user features

   from scipy.sparse.linalg import svds U, S, Vt = svds(ratings_sparse, k=50) user_features = U @ np.diag(S) correctly computes user_features = U @ diag(S). from scipy.sparse.linalg import svds U, S, Vt = svds(ratings_sparse, k=50) user_features = np.diag(S) @ Vt mixes user and item matrices. from scipy.linalg import svd U, S, Vt = svd(ratings_sparse) user_features = U[:, :50] uses dense svd, not sparse. from scipy.sparse.linalg import svds U, S, Vt = svds(ratings_sparse, k=50) user_features = Vt.T @ np.diag(S) computes item features, not user features.

3. Final Answer:

   from scipy.sparse.linalg import svds U, S, Vt = svds(ratings_sparse, k=50) user_features = U @ np.diag(S) -> Option D

4. Quick Check:

   User features = U * S diagonal [OK]

Hint: Multiply U by diag(S) for user features after svds [OK]

Common Mistakes:

• Using Vt for user features instead of U
• Using dense svd on sparse data
• Not multiplying U by singular values