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.

Practice

1. What is the main advantage of using sparse data structures in data analysis?

easy

A. They make data harder to read

B. They increase the number of zeros in the data

C. They convert data into images

D. They save memory by storing only non-zero values

Solution

1. Step 1: Understand sparse data concept

   Sparse data structures store only the important non-zero values instead of all values.

2. Step 2: Identify the benefit

   By storing only non-zero values, sparse structures save memory and improve efficiency.

3. Final Answer:

   They save memory by storing only non-zero values -> Option D

4. Quick Check:

   Sparse data saves memory = A [OK]

Hint: Sparse means store only non-zero values to save memory [OK]

Common Mistakes:

• Thinking sparse data increases zeros
• Confusing sparse with data visualization
• Assuming sparse data stores all values

2. Which of the following is the correct way to import the sparse matrix module from SciPy in Python?

easy

A. import scipy.sparse as sp

B. import sparse from scipy

C. from scipy import sparse_matrix

D. import scipy.sparse_matrix

Solution

1. Step 1: Recall correct import syntax

   The SciPy sparse module is imported as import scipy.sparse as sp to use sparse matrix functions.

2. Step 2: Check other options

   Options A, B, and C use incorrect syntax or module names that do not exist.

3. Final Answer:

   import scipy.sparse as sp -> Option A

4. Quick Check:

   Correct import = D [OK]

Hint: Use 'import scipy.sparse as sp' to access sparse matrices [OK]

Common Mistakes:

• Using wrong import syntax
• Trying to import non-existent modules
• Confusing module names

3. What will be the output of the following Python code?

import numpy as np
from scipy.sparse import csr_matrix

arr = np.array([[0, 0, 1], [1, 0, 0], [0, 1, 0]])
sparse_mat = csr_matrix(arr)
print(sparse_mat.nnz)

medium

A. 6

B. 9

C. 3

D. 0

Solution

1. Step 1: Understand the input array

   The array has three non-zero elements: 1 at (0,2), 1 at (1,0), 1 at (2,1), and zeros elsewhere.

2. Step 2: Use csr_matrix and check nnz

   The csr_matrix stores only non-zero elements. The nnz attribute counts these non-zero values, which is 3.

3. Final Answer:

   3 -> Option C

4. Quick Check:

   Count non-zero elements = 3 [OK]

Hint: nnz counts non-zero elements in sparse matrix [OK]

Common Mistakes:

• Counting total elements instead of non-zero
• Confusing nnz with shape
• Assuming zeros are counted

4. Identify the error in this code snippet that tries to create a sparse matrix:

from scipy.sparse import csr_matrix

matrix = csr_matrix([1, 0, 0, 2, 0, 3])
print(matrix.shape)

medium

A. The input should be a 2D array, not a 1D list

B. csr_matrix does not accept lists

C. Missing import for numpy

D. The print statement is incorrect

Solution

1. Step 1: Check input format for csr_matrix

   The csr_matrix expects a 2D array or matrix-like input, but a 1D list is given.

2. Step 2: Understand error cause

   Passing a 1D list causes shape ambiguity. The input should be reshaped or given as 2D, e.g., [[1,0,0,2,0,3]].

3. Final Answer:

   The input should be a 2D array, not a 1D list -> Option A

4. Quick Check:

   csr_matrix needs 2D input = C [OK]

Hint: csr_matrix input must be 2D array or matrix [OK]

Common Mistakes:

• Passing 1D list directly
• Ignoring input shape requirements
• Assuming csr_matrix accepts any iterable

5. You have a large dataset with many zero values stored as a dense NumPy array. Which approach best converts it to a sparse matrix and then back to a dense array without losing data?

hard

A. Use csc_matrix to convert, then .todense() to convert back

B. Use csr_matrix to convert, then .toarray() to convert back

C. Use dok_matrix to convert, then .to_list() to convert back

D. Use lil_matrix to convert, then .to_numpy() to convert back

Solution

1. Step 1: Choose correct sparse format for conversion

   csr_matrix is efficient for large sparse data and supports easy conversion back to dense.

2. Step 2: Convert back to dense array

   Use .toarray() method on the sparse matrix to get the original dense NumPy array without data loss.

3. Final Answer:

   Use csr_matrix to convert, then .toarray() to convert back -> Option B

4. Quick Check:

   csr_matrix + toarray() preserves data = A [OK]

Hint: csr_matrix and toarray() convert sparse to dense safely [OK]

Common Mistakes:

• Using .todense() which returns matrix, not array
• Using .to_list() which does not exist
• Assuming .to_numpy() works on sparse matrices