Sparse data handling in Data Analysis Python - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of sparse matrix multiplication

What is the output of this code that multiplies two sparse matrices using SciPy?

Data Analysis Python

import numpy as np
from scipy.sparse import csr_matrix

A = csr_matrix([[0, 0, 1], [1, 0, 0], [0, 0, 0]])
B = csr_matrix([[0, 2, 0], [0, 0, 0], [3, 0, 0]])

C = A.dot(B)
print(C.toarray())

A

[[0 0 0]
 [3 0 0]
 [0 0 0]]

B

[[0 2 0]
 [0 0 0]
 [0 0 0]]

C

[[0 0 3]
 [0 0 0]
 [0 0 0]]

D

[[3 0 0]
 [0 2 0]
 [0 0 0]]

💡 Hint

Remember that sparse matrix multiplication follows normal matrix multiplication rules but only non-zero elements are stored.

Matrix A has a 1 at position (0,2) and (1,0). Matrix B has 3 at (2,0) and 2 at (0,1). Multiplying A and B, the element at (0,0) is 1*3=3, and at (1,1) is 1*2=2. Others are zero.

❓ data_output

intermediate

Number of non-zero elements in sparse matrix

Given this sparse matrix, how many non-zero elements does it contain?

Data Analysis Python

from scipy.sparse import coo_matrix

row = [0, 3, 1, 0]
col = [0, 3, 1, 2]
data = [4, 5, 7, 9]

matrix = coo_matrix((data, (row, col)), shape=(4, 4))

print(matrix.nnz)

A 5

B 3

C 4

D 6

💡 Hint

nnz attribute counts all stored non-zero elements.

The data list has 4 values, so the sparse matrix stores 4 non-zero elements.

🔧 Debug

advanced

Identify error in sparse matrix conversion

What error does this code raise when converting a dense numpy array with NaN to a sparse CSR matrix?

Data Analysis Python

import numpy as np
from scipy.sparse import csr_matrix

dense = np.array([[1, 0, np.nan], [0, 2, 3]])
sparse = csr_matrix(dense, dtype=int)
print(sparse.toarray())

A ValueError: cannot convert float NaN to integer

B TypeError: unsupported operand type(s) for *: 'float' and 'NoneType'

C No error, prints array with NaN replaced by zero

D RuntimeWarning: invalid value encountered in multiply

💡 Hint

Sparse matrices do not support NaN values directly in integer dtype arrays.

csr_matrix tries to convert the dense array to integer dtype by default, but NaN cannot be converted to int, causing ValueError.

🚀 Application

advanced

Choosing sparse format for efficient row slicing

You have a large sparse dataset and need to frequently access rows quickly. Which sparse matrix format is best suited for this?

A COO (Coordinate list) format

B CSR (Compressed Sparse Row) format

C CSC (Compressed Sparse Column) format

D DOK (Dictionary of Keys) format

💡 Hint

Think about which format stores data optimized for row access.

CSR format stores data compressed by rows, making row slicing very fast compared to other formats.

🧠 Conceptual

expert

Impact of sparsity on machine learning model training

How does high sparsity in input data typically affect training of linear models like logistic regression?

A Training is faster and requires less memory due to fewer non-zero features

B Training is slower because sparse data requires dense conversion internally

C Model accuracy always decreases because sparse data lacks information

D Sparse data causes models to overfit more easily due to many zeros

💡 Hint

Consider how sparse data reduces computation and storage needs.

Sparse data reduces the number of features processed, speeding up training and lowering memory use without necessarily harming accuracy.