Curse of dimensionality quiz

Question 1

What does the term 'curse of dimensionality' refer to in machine learning?

Accepted Answer

Problems that arise when there are too many features, making data sparse and models harder to train

Answer

A bug that occurs only in deep neural networks

Answer

The slowness of computers when sorting numbers

Answer

An error caused by having too few features

Question 2

Who first coined the phrase 'curse of dimensionality'?

Accepted Answer

Richard Bellman

Answer

Alan Turing

Answer

Geoffrey Hinton

Answer

Andrew Ng

Question 3

As the number of dimensions increases, what happens to the volume of the data space and the density of data points?

Accepted Answer

Volume grows exponentially and data becomes sparse

Answer

Volume shrinks and data becomes denser

Answer

Volume stays constant and density doubles

Answer

Volume grows but density increases

Question 4

To keep data density constant, how does the required number of samples scale with the number of dimensions?

Accepted Answer

Exponentially (about n^d)

Answer

Linearly (about n×d)

Answer

Logarithmically

Answer

It does not change

Question 5

In high dimensions, what happens to the difference between the nearest and farthest neighbor distances of a point?

Accepted Answer

They become nearly equal, so distance loses its discriminating power

Answer

The nearest becomes zero and farthest becomes infinite

Answer

The difference grows larger and more meaningful

Answer

Distances stop being computable

Question 6

Which common algorithm is especially harmed by the curse of dimensionality because it relies on distance measurements?

Accepted Answer

k-Nearest Neighbors

Answer

Linear regression with one feature

Answer

A decision stump

Answer

Computing the mean of a column

Question 7

Consider points placed uniformly in a unit hypercube. As dimensions increase, where does most of the volume of the cube concentrate?

Accepted Answer

Near the corners and outer shell, away from the center

Answer

At the exact center

Answer

Evenly throughout

Answer

Along a single diagonal only

Question 8

What happens to the ratio of the volume of an inscribed unit hypersphere to its enclosing hypercube as the number of dimensions grows?

Accepted Answer

It approaches zero

Answer

It approaches one

Answer

It stays at 0.5

Answer

It grows without bound

Question 9

How does increasing the number of features generally affect a model's risk of overfitting?

Accepted Answer

It increases the risk of overfitting

Answer

It always reduces overfitting

Answer

It has no effect on overfitting

Answer

It makes the model immune to noise

Question 10

What is dimensionality reduction, and why is it useful against the curse of dimensionality?

Accepted Answer

Reducing the number of features while keeping useful structure to fight sparsity

Answer

Adding more features to increase accuracy

Answer

Increasing the dataset size only

Answer

Removing all the training data

Question 11

Which popular linear technique reduces dimensions by projecting data onto directions of maximum variance?

Accepted Answer

Principal Component Analysis (PCA)

Answer

k-Means clustering

Answer

Linear regression

Answer

Naive Bayes

Question 12

In PCA, what do the principal components with the largest eigenvalues represent?

Accepted Answer

Directions of greatest variance in the data

Answer

Directions of least variance

Answer

The mean of the dataset

Answer

Random noise directions

Question 13

What is the difference between feature selection and feature extraction as ways to reduce dimensionality?

Accepted Answer

Selection keeps a subset of original features; extraction creates new combined features

Answer

They are exactly the same thing

Answer

Selection creates new features; extraction deletes data points

Answer

Both add new random features

Question 14

Why does the curse of dimensionality make distance-based clustering algorithms like k-Means less reliable?

Accepted Answer

Distances become nearly uniform, so clusters are poorly separated

Answer

Distances become exactly zero

Answer

k-Means cannot run on more than 2 features

Answer

Clusters always merge into one point

Question 15

A dataset has 1000 samples and 5 features. If you increase to 50 features without adding samples, what is the main concern?

Accepted Answer

Data becomes sparse, raising overfitting risk with the same sample count

Answer

The model will automatically improve

Answer

Distances become more accurate

Answer

Training becomes faster and more reliable

Question 16

What does it mean that high-dimensional data is often 'sparse'?

Accepted Answer

Data points fill only a tiny fraction of the space, leaving most of it empty

Answer

Most feature values are exactly zero by design

Answer

The dataset has too few features

Answer

The data is stored efficiently in memory

Question 17

How can adding irrelevant features hurt a machine learning model even if useful features are present?

Accepted Answer

They add noise and increase sparsity, diluting the useful signal

Answer

They always improve accuracy

Answer

They have absolutely no effect

Answer

They reduce the dataset size

Question 18

Which of these is a manifold-learning technique commonly used for visualizing high-dimensional data in 2D or 3D?

Accepted Answer

t-SNE

Answer

Gradient descent

Answer

One-hot encoding

Answer

Bubble sort

Question 19

What is the 'manifold hypothesis' and how does it offer hope against the curse of dimensionality?

Accepted Answer

Real data often lies near a low-dimensional manifold, so it can be compressed

Answer

Data always fills the entire high-dimensional space

Answer

Manifolds make the curse worse

Answer

All features are always independent

Question 20

What is the 'intrinsic dimensionality' of a dataset?

Accepted Answer

The minimum number of variables truly needed to describe the data

Answer

The number of rows in the dataset

Answer

Always equal to the number of features

Answer

The number of output classes

Question 21

Why can adding more features sometimes increase accuracy at first but then decrease it (the 'peaking phenomenon')?

Accepted Answer

Useful features help first, then added sparsity and noise hurt (Hughes phenomenon)

Answer

Accuracy always rises with more features

Answer

Accuracy always falls with more features

Answer

Features never affect accuracy

Question 22

In Python with scikit-learn, which class would you use to perform PCA for dimensionality reduction?

Accepted Answer

sklearn.decomposition.PCA

Answer

sklearn.linear_model.LinearRegression

Answer

sklearn.tree.DecisionTreeClassifier

Answer

sklearn.cluster.KMeans

Question 23

After fitting PCA, which attribute tells you the fraction of variance captured by each principal component?

Accepted Answer

explained_variance_ratio_

Answer

feature_importances_

Answer

coef_

Answer

n_clusters_

Question 24

Why is it generally recommended to standardize (scale) features before applying PCA?

Accepted Answer

Because PCA is scale-sensitive and large-scale features would dominate the components

Answer

Because PCA cannot handle decimals

Answer

Because scaling adds more dimensions

Answer

Scaling is never needed for PCA

Question 25

How does the curse of dimensionality affect the reliability of density estimation (estimating how data is distributed)?

Accepted Answer

Sparsity makes local density estimates unreliable, needing far more data

Answer

Density estimation becomes easier and faster

Answer

It has no effect on density estimation

Answer

Density estimates become perfectly accurate

Question 26

Which regularization techniques help control overfitting that worsens with high dimensionality?

Accepted Answer

L1 (Lasso) and L2 (Ridge) regularization

Answer

Increasing the learning rate only

Answer

Adding more random features

Answer

Removing the loss function

Question 27

Two random points are drawn uniformly inside a high-dimensional cube. What tends to happen to the Euclidean distance between such random point pairs as dimensions grow?

Accepted Answer

Distances concentrate around one typical value

Answer

Distances spread out widely

Answer

All distances go to zero

Answer

Distances become negative

Question 28

How might the curse of dimensionality influence the choice between L1 (Manhattan) and L2 (Euclidean) distance metrics?

Accepted Answer

L1 (Manhattan) often preserves more contrast than L2 in very high dimensions

Answer

L2 is always strictly better in any dimension

Answer

Distance metrics never matter in any dimension

Answer

Both metrics always give identical results everywhere

Question 29

Why do tree-based models like Random Forests tend to handle many features somewhat better than k-NN?

Accepted Answer

They split on individual features and can ignore irrelevant ones

Answer

They compute full Euclidean distances like k-NN

Answer

They require fewer features than k-NN to run

Answer

They are unaffected because they ignore all features

Question 30

What is a practical sign in your results that the curse of dimensionality may be hurting your model?

Accepted Answer

Test accuracy drops while training accuracy stays high as features increase

Answer

Both training and test accuracy keep rising forever

Answer

Training time decreases sharply

Answer

The data automatically gets denser

Test yourself