13 | DW-3 | tSNE, UMAP

Question 1

(QUIZ 6)
t-SNE was invented by ______ in ______

Answer 1

Laurens van der Maaten, 2008

Question 2

(QUIZ 6)
t-SNE means ________________________ .

Answer 2

t-distributed stochastic neighbour embedding

Question 3

(QUIZ 6)
PCA is a ______ dimensionality reduction technique, whereas t-SNE is a ______ technique.

Answer 3

PCA: linear
t-SNE: non-linear
https://www.geeksforgeeks.org/difference-between-pca-vs-t-sne/

Question 4

(QUIZ 6)
PCA is focused on the ______ structure of the data, whereas t-SNE is focused on the ______ structure.

Answer 4

PCA: global
t-SNE: local
https://www.geeksforgeeks.org/difference-between-pca-vs-t-sne/

Question 5

(QUIZ 6)
PCA is a ______ algorithm whereas t-SNE is ______.
The above means that the results from a data set for ______ are always the same whereas for ______ they might differ in each analysis.

Answer 5

PCA: deterministic
t-SNE: non-deterministic
https://www.geeksforgeeks.org/difference-between-pca-vs-t-sne/

Question 6

(QUIZ 6)
We cannot preserve variance in ______, instead we can preserve distance using hyperparameters.

Answer 6

In ______ we decide on how much variance to preserve using eigen values.
t-SNE
PCA

Question 7

What does UMAP stand for?

Answer 7

Uniform Manifold Approximation and Projection

Question 8

What type of machine learning technique is UMAP?

Answer 8

A nonlinear dimensionality reduction technique

Question 9

What is UMAP based on?

Answer 9

Topological and geometric principles of manifold learning

Question 10

What kind of data is UMAP commonly used for?

Answer 10

High-dimensional data, such as transcriptomic, image, and clustering data

Question 11

What is the main goal of UMAP?

Answer 11

To reduce the dimensionality of high-dimensional data while preserving local and global structure

Question 12

How does UMAP compare to PCA in terms of aim?

Answer 12

Unlike PCA, which focuses on variance maximization, UMAP seeks to preserve the data’s intrinsic topological structure in a lower-dimensional space

Question 13

What type of visualization does UMAP aim to provide?

Answer 13

A meaningful, interpretable 2D or 3D projection of complex datasets

Question 14

What is the theoretical foundation of UMAP?

Answer 14

It is based on the concept of Riemannian geometry and algebraic topology

Question 15

What does UMAP assume about high-dimensional data?

Answer 15

That it lies on a low-dimensional manifold embedded in a higher-dimensional space

Question 16

What is the first step in UMAP?

Answer 16

Constructing a weighted graph representation of the data’s local manifold structure

Question 17

What does UMAP optimize to generate the final embedding?

Answer 17

A low-dimensional graph layout that approximates the original high-dimensional structure

Question 18

What are the main steps in UMAP’s algorithm?

Answer 18

Construct a k-nearest neighbors (kNN) graph
Apply a fuzzy simplicial set representation
Optimize a low-dimensional embedding that preserves the fuzzy topology

Question 19

What role does the k-nearest neighbors (kNN) graph play in UMAP?

Answer 19

It captures the local structure of the data

Question 20

How does UMAP embed the data in a lower-dimensional space?

Answer 20

By optimizing a cross-entropy loss between the high-dimensional and low-dimensional representations

Question 21

What are the key hyperparameters in UMAP?

Answer 21

n_neighbors
min_dist
metric
spread

Question 22

UMAP
What does n_neighbors control?

Answer 22

The balance between local and global structure preservation

Question 23

UMAP
What does min_dist affect?

Answer 23

The compactness of clusters in the lower-dimensional space

Question 24

How does the choice of metric influence UMAP?

Answer 24

It determines the distance function used to define neighborhood relationships

Question 25

How does UMAP compare to t-SNE in terms of computational efficiency?

Answer 25

UMAP is generally faster and scales better to large datasets

Question 26

UMAP Which method preserves more of the global structure?

Answer 26

UMAP tends to preserve more of the global structure, while t-SNE focuses on local relationships

Question 27

How do UMAP and t-SNE handle different perplexity-like parameters?

Answer 27

UMAP uses n_neighbors, while t-SNE uses perplexity, but they serve similar functions

Question 28

What is a major difference in the cost function optimization between UMAP and t-SNE?

Answer 28

t-SNE minimizes Kullback-Leibler divergence, whereas UMAP optimizes a fuzzy topological representation

Question 29

What is one major weakness of UMAP?

Answer 29

It can sometimes distort global relationships in favor of preserving local structures

Question 30

How does UMAP handle density variation across clusters?

Answer 30

It may struggle with variable-density clusters, sometimes overcompressing sparse regions

Question 31

Why is UMAP not always deterministic?

Answer 31

Because of its reliance on stochastic processes in initialization and optimization

Question 32

What challenge does UMAP face with very high-dimensional sparse data?

Answer 32

It may require careful tuning of hyperparameters to avoid misleading embeddings

Question 33

Why is UMAP commonly used in transcriptomic analysis?

Answer 33

It effectively visualizes complex gene expression patterns in a low-dimensional space

Question 34

What type of transcriptomic data is UMAP often applied to?

Answer 34

Single-cell RNA sequencing (scRNA-seq) data

Question 35

How does UMAP help in scRNA-seq analysis?

Answer 35

It reveals cell clusters and differentiation pathways in an intuitive way

Question 36

What preprocessing steps are typically required before applying UMAP to transcriptomic data?

Answer 36

Normalization Feature selection Distance metric selection

Question 37

Which of the following dimensionality reduction methods use density aware distances? - PCA - ICA - MDS - t-SNE - UMAP

Answer 37

- t-SNE (via perplexity parameter) - UMAP random ( via k-nearest neighbour graph and fuzzy simplical complex.)

Question 38

What does t-SNE stand for?

Answer 38

t-Distributed Stochastic Neighbor Embedding

Question 39

What is t-SNE used for?

Answer 39

A nonlinear dimensionality reduction technique for high-dimensional data visualization

Question 40

In what field is t-SNE commonly used?

Answer 40

Single-cell RNA sequencing (scRNA-seq) and other biological data analyses

Question 41

What problem does t-SNE aim to solve?

Answer 41

The challenge of representing high-dimensional data in 2D or 3D while keeping similar points close together Embeds high dimensional data by preserving local similarity (probabilistic)

Question 42

What are the main steps in t-SNE?

Answer 42

* Compute pairwise similarities in high-dimensional space * Define a low-dimensional probability distribution * Optimize the embedding using gradient descent

Question 43

How does t-SNE measure similarity in high-dimensional space?

Answer 43

Using a Gaussian distribution around each point

Question 44

How does t-SNE define similarity in low-dimensional space?

Answer 44

Using a Student’s t-distribution with one degree of freedom

Question 45

What does the perplexity parameter control in t-SNE?

Answer 45

The balance between local and global structure

Question 46

How does changing perplexity affect t-SNE results?

Answer 46

* Low perplexity favors local structure * High perplexity includes more global relationships

Question 47

t-SNE: Cost Function What function does t-SNE minimize?

Answer 47

Kullback-Leibler (KL) divergence between high- and low-dimensional probability distributions

Question 48

t-SNE: Cost Function Why does t-SNE use a Student’s t-distribution in low-dimensional space?

Answer 48

To avoid overcrowding and better separate clusters

Question 49

What are the advantages of t-SNE?

Answer 49

* Excellent for visualizing complex datasets * Captures non-linear relationships * Good for clustering high-dimensional data

Question 50

What are the main weaknesses of t-SNE?

Answer 50

* Computationally expensive * Non-deterministic (results vary across runs) * Poor at preserving global structure

Question 51

How does t-SNE handle large datasets?

Answer 51

It struggles with large datasets due to high computational cost

Question 52

How does t-SNE compare to UMAP in terms of speed?

Answer 52

UMAP is generally faster than t-SNEWhich method preserves global structure better? UMAP preserves more global structure than t-SNE

Question 53

Why might someone choose UMAP over t-SNE?

Answer 53

UMAP is deterministic, faster, and better at maintaining overall data structure

Question 54

_____ prioritises local structure, ignores global distances

Answer 54

tSNE

Question 55

______ captures both local and some global structure

Answer 55

UMAP

Question 56

How are tSNE and UMAP similar?

Answer 56

- non-linear - density-aware distances - random (but can be made deterministic with fixed seed) - NO variable importance assessment

Question 57

Which dimensionality reduction technique(s) include(s) variable importance assessment?

Answer 57

PCA, ICA

Question 58

Which dimensionality reduction technique(s) are or can be made deterministic?

Answer 58

is deterministic: - PCA - classical MDS can be made deterministc: - ICA - depends on implementation - tSNE, UMAP: can be made deterministic with fixed seeds not deterministic: - metric/non-metric MDS

Question 59

Which dimensionality reduction technique(s) capture global structure?

Answer 59

- PCA - MDS can be tuned for local or global (classical MDS - global) - UMAP: captures some global structure (but focuses on local)

Question 60

Which dimensionality reduction technique(s) ignores global distances?

Answer 60

tSNE

Question 61

re local/global distances: Which dimensionality reduction technique(s) focuses on statistically independent directions, ie not distance based?

Answer 61

ICA