UMAP for dimensionality reduction in ML Python - Practice Problems & Coding Challenges

Challenge - 5 Problems

🧠 Conceptual

intermediate

Understanding UMAP's Core Idea

What is the main goal of UMAP when reducing data dimensions?

A To cluster data points into predefined groups

B To maximize the variance of the data in the reduced space

C To preserve the local structure of data points while reducing dimensions

D To increase the number of features for better model training

💡 Hint

Think about what UMAP tries to keep similar between high and low dimensions.

UMAP focuses on preserving the local relationships between points, meaning points close in high dimensions remain close in the reduced space.

❓ Predict Output

intermediate

UMAP Output Shape

What will be the shape of the output after applying UMAP with n_components=2 on a dataset X with shape (100, 50)?

ML Python

import numpy as np
import umap
X = np.random.rand(100, 50)
reducer = umap.UMAP(n_components=2)
X_reduced = reducer.fit_transform(X)
print(X_reduced.shape)

A (100, 50)

B (100, 2)

C (50, 2)

D (2, 50)

💡 Hint

The number of rows stays the same; only the number of features changes.

UMAP reduces the feature dimension from 50 to 2 but keeps the number of samples (100) unchanged.

❓ Hyperparameter

advanced

Effect of 'n_neighbors' in UMAP

What is the effect of increasing the 'n_neighbors' parameter in UMAP?

A It increases the focus on preserving global structure over local details

B It speeds up the computation by reducing data points considered

C It decreases the number of output dimensions

D It changes the distance metric used internally

💡 Hint

Think about how many neighbors UMAP considers when building the graph.

A higher 'n_neighbors' means UMAP considers more neighbors, capturing broader structure and less local detail.

❓ Metrics

advanced

Evaluating UMAP Embedding Quality

Which metric is commonly used to evaluate how well UMAP preserves local neighborhood structure?

A Mean squared error

B Accuracy score

C F1 score

D Trustworthiness score

💡 Hint

This metric measures how well neighbors in high dimensions remain neighbors in low dimensions.

Trustworthiness measures how many neighbors in the low-dimensional space were also neighbors in the original space, indicating local structure preservation.

🔧 Debug

expert

UMAP Runtime Error Diagnosis

Given the code below, what is the most likely cause of the error? import numpy as np import umap X = np.array([[1, 2], [3, 4], [5, 6]]) reducer = umap.UMAP(n_components=3) X_reduced = reducer.fit_transform(X)

ML Python

import numpy as np
import umap
X = np.array([[1, 2], [3, 4], [5, 6]])
reducer = umap.UMAP(n_components=3)
X_reduced = reducer.fit_transform(X)

A n_components cannot be greater than the original feature dimension

B Input data X must be a pandas DataFrame

C UMAP requires at least 10 samples to run

D The distance metric is not specified

💡 Hint

Check the relationship between n_components and input feature size.

UMAP cannot reduce to more dimensions than the original features; here, original features are 2 but n_components is 3.