Practical Intro to NLP 26: Theory - Data Visualization and Dimensionality Reduction

Summary

This video script discusses the importance of data visualization in identifying outliers and understanding data sets through movie plot examples. It explains dimensionality reduction techniques like PCA, t-SNE, and UMAP, which convert high-dimensional data into lower dimensions while preserving global and local structures. The script highlights UMAP as the current state-of-the-art for visualization and clustering, emphasizing its balance between local and global structure preservation. The benefits of visualization include quick data overviews, outlier detection, identifying clusters and similarities, and exploring relationships between different data entities.

Takeaways

• 📊 **Data Visualization Importance**: Visualization is crucial for identifying outliers and getting a high-level overview of data.
• 🎬 **Movie Plots Visualization**: Movie plots are visualized to spot patterns, clusters, and outliers among different movies.
• 🔢 **Dimensionality**: Movies are represented as high-dimensional vectors (e.g., 768 dimensions), which need to be reduced for visualization.
• 🌐 **Preserving Structure**: Dimensionality reduction aims to preserve both local and global structures of the data.
• 📉 **PCA Limitations**: Principal Component Analysis (PCA) is a linear technique that preserves global structure but may not be suitable for local structure preservation or nonlinear data.
• 🔄 **t-SNE for Nonlinear Data**: t-Distributed Stochastic Neighbor Embedding (t-SNE) is a nonlinear technique that focuses on preserving local structure and is effective for nonlinear data separation.
• 🚀 **UMAP Advantages**: Uniform Manifold Approximation and Projection (UMAP) is a state-of-the-art technique that balances local and global structure preservation and is faster than t-SNE.
• 🔍 **Outlier Detection**: Visualization helps in automatically detecting and removing outliers, which can improve the quality of algorithmic results.
• 👥 **Cluster Identification**: It's possible to identify clusters and similarities in data, such as grouping similar movies or movie series.
• 🔗 **Multi-Entity Visualization**: Visualizing different entities together, like movies and directors, can reveal interesting relationships and potential collaborations.

Q & A

What is the importance of data visualization in analyzing movie plots?

Data visualization is crucial for identifying outliers and getting a high-level overview of the data. It allows for the immediate detection of patterns, clusters, and anomalies within the dataset of movie plots.

How are movies represented in data visualization?

Movies are represented as high-dimensional vectors, such as 768-dimensional vectors, where each dimension corresponds to a specific feature of the movie.

Why is dimensionality reduction necessary for visualizing movie plots?

Dimensionality reduction is necessary because humans can only visualize data in two or three dimensions. It converts high-dimensional data into a lower-dimensional form that can be plotted on a 2D or 3D graph.

What does it mean to preserve local and global structure in dimensionality reduction?

Preserving local and global structure means maintaining the relative distances and relationships between data points in the reduced dimensions as they were in the original high-dimensional space. This ensures that similar items remain close together and dissimilar items remain distant.

How are the weights for the dimensions calculated in dimensionality reduction?

The weights are calculated using dimensionality reduction algorithms, which may employ techniques like matrix factorization. These algorithms determine the optimal weights to preserve the data's structure in the reduced dimensions.

What is the difference between linear and nonlinear dimensionality reduction?

Linear dimensionality reduction uses a weighted combination of dimensions, while nonlinear dimensionality reduction may involve more complex transformations, such as logarithmic or polynomial functions, to better capture the data's structure.

Why is PCA considered a linear dimensionality reduction technique?

PCA is considered linear because it uses a weighted sum of the original dimensions to create new dimensions, preserving the global structure but not necessarily the local structure.

What are the advantages of t-SNE over PCA in dimensionality reduction?

t-SNE is a nonlinear technique that better preserves local structure and can separate data that cannot be linearly separated. However, it is slower and may require tuning of hyperparameters for optimal results.

How does UMAP differ from t-SNE and PCA?

UMAP is a state-of-the-art, nonlinear dimensionality reduction technique that constructs a neighbor graph in higher dimensions and projects it into lower dimensions. It is faster than t-SNE and allows for a balance between preserving local and global structures.

What are some other use cases for dimensionality reduction besides visualization?

Dimensionality reduction can also be used for fast clustering, feature extraction, and improving the performance of machine learning algorithms by reducing the complexity of the data.

How can data visualization help in identifying outliers and clusters?

Data visualization allows for the quick detection of outliers and clusters by visually inspecting the plot for points that deviate from the norm or group together, which can be crucial for cleaning data or identifying trends.

Outlines

00:00

📊 Introduction to Data Visualization and Dimensionality Reduction

This paragraph introduces the concept of data visualization, emphasizing its importance in identifying outliers and obtaining a high-level overview of data. It uses the example of movie plots visualized in a two-dimensional space, despite being represented in higher dimensions like 768. The paragraph explains the necessity of dimensionality reduction techniques to convert high-dimensional data into a form that humans can visualize. It outlines the process of reducing dimensions while preserving both local and global structures, mentioning the use of algorithms like matrix factorization to determine the weights for the new dimensions.

05:01

🧩 Exploring Dimensionality Reduction Techniques: PCA, t-SNE, and UMAP

The second paragraph delves into three key algorithms used in dimensionality reduction: PCA, t-SNE, and UMAP. It explains that PCA is a linear technique that preserves global structure but may not be ideal for capturing local structure due to its reliance on linear combinations of dimensions. The paragraph contrasts this with t-SNE, a nonlinear technique that can separate nonlinear data but is slower and more focused on local structure. Finally, UMAP is introduced as a state-of-the-art algorithm that balances global and local structure preservation and is faster than t-SNE. The paragraph suggests UMAP as the preferred method for dimensionality reduction, with t-SNE as an alternative for specific cases.

10:02

🔍 Benefits of Data Visualization and Practical Applications

The third paragraph highlights the advantages of data visualization, such as providing a quick overview, detecting outliers, identifying clusters, and revealing similarities. It suggests using visualization for clustering at scale by reducing dimensions to a manageable level like 10 or 5. The paragraph also discusses the potential for combining multiple data entities in a single visualization to uncover relationships, such as plotting movies with directors or job descriptions with candidates. It encourages exploring these relationships through visualization to aid in decision-making and collaboration.

15:03

💻 Upcoming Section: Practical Implementation in Code

The final paragraph teases the upcoming section, which will demonstrate the practical implementation of the discussed concepts through code. It implies that the theoretical aspects covered in the previous paragraphs will be applied in a coding context, likely showcasing how to perform data visualization and dimensionality reduction using the mentioned techniques.

Keywords

💡Data Visualization

Data visualization refers to the graphical representation of information and data. It is a crucial aspect in the script as it allows for the immediate identification of outliers and provides a high-level overview of data sets. In the context of the video, data visualization is used to represent complex movie plots in a simplified, visual format, making it easier to spot patterns and anomalies.

💡Outliers

Outliers are data points that differ significantly from the majority of the data. In the video, the script mentions that through data visualization, one can quickly spot outliers or clusters in movie plots. These outliers could represent unique or atypical elements within the data set that might need further investigation or could be excluded from certain analyses.

💡Dimensionality

Dimensionality in the context of the video refers to the number of variables or features used to represent data. The script discusses how movies are represented as vectors in high-dimensional spaces, such as 768 dimensions, and the challenge of visualizing such complex data.

💡Vector

A vector in the video script represents a movie with a set of numerical values across multiple dimensions. For instance, 'Batman Begins' is described as a 768-dimensional vector. Vectors are the fundamental units that data visualization techniques aim to simplify for easier interpretation.

💡Dimensionality Reduction

Dimensionality reduction is a technique used to convert high-dimensional data into lower-dimensional data while preserving the essential characteristics. The script explains that this is necessary for visualization purposes, as humans can only visualize up to three dimensions effectively. The video discusses various algorithms for dimensionality reduction, emphasizing the importance of preserving both local and global structures.

💡PCA (Principal Component Analysis)

PCA is a statistical procedure that uses an orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables. In the video, PCA is introduced as a linear dimensionality reduction technique that preserves global structure but may not be as effective in preserving local structure.

💡t-SNE (t-Distributed Stochastic Neighbor Embedding)

t-SNE is a machine learning algorithm for the visualization of high-dimensional datasets. It is mentioned in the script as a nonlinear dimensionality reduction technique that focuses more on preserving local structure. The video notes that while t-SNE was a popular choice for visualization, it has been largely superseded by UMAP due to its computational inefficiency.

💡UMAP (Uniform Manifold Approximation and Projection)

UMAP is a relatively new technique for dimension reduction that is particularly effective for the visualization of high-dimensional data. The script highlights UMAP as the current state-of-the-art algorithm for dimensionality reduction, balancing both local and global structure preservation and being faster than t-SNE.

💡Matrix Factorization

Matrix factorization is a technique used in dimensionality reduction algorithms to split high-dimensional data into lower dimensions. The script mentions that the weights for the transformation of data into lower dimensions, such as for PCA, can be obtained through matrix factorization.

💡Clustering

Clustering in the context of the video refers to the process of grouping similar data points together. Dimensionality reduction aids in clustering by simplifying the data into a format that makes it easier to identify and group similar items. The video suggests that reduced-dimensional data can be used for fast and efficient clustering.

💡High-Level Overview

A high-level overview is a broad understanding or summary of data. The video script emphasizes the value of data visualization in providing a quick high-level overview of complex data sets, such as movie plots, allowing for the easy identification of patterns, outliers, and clusters.

Highlights

Data visualization is crucial for identifying outliers and getting a high-level overview of data.

Movies can be represented as high-dimensional vectors, such as 768 dimensions for 'Batman Begins'.

Dimensionality reduction is necessary to visualize high-dimensional data on 2D or 3D plots.

Local and global structures of data must be preserved during dimensionality reduction.

Weights for dimensionality reduction are calculated using algorithms like matrix factorization.

UMAP is the current state-of-the-art algorithm for dimensionality reduction, surpassing t-SNE and PCA.

PCA is a linear dimensionality reduction technique that preserves global structure but not local structure as effectively.

t-SNE is a nonlinear dimensionality reduction method that focuses on preserving local structure.

UMAP constructs a neighbor graph in higher dimensions and projects it into lower dimensions for visualization.

Dimensionality reduction techniques are not only for visualization but also for fast clustering and data analysis.

Data visualization allows for quick detection of outliers which can be removed to improve algorithm quality.

Clusters of similar data points, like movie genres, can be easily identified through visualization.

Visualization can reveal interesting relations, such as similarities between movie plots and directors.

Multiple entities can be visualized together, such as job descriptions and candidates, to find close matches.

Visualization can aid in exploring collaborations, like matching startups with research professors.

The next section will cover the implementation of these concepts in code.

Transcripts

hello everyone welcome back and in this

section we are going to see

visualization of movie plots that we

collected so data visualization is a

crucial aspect because you can

immediately identify outliers and also

get a high level overview of all the

data that we have for example here you

can see all our movie plots visualized

and you can see there are some outliers

or clusters that are formed so you can

do all of these things using data

visualization now the first thing that

occurs to your mind is a movie for

example will be represented in 768

Dimensions or 360 Dimensions Etc so

essentially a movie like Batman Begins

will be a long 768 dimensional Vector

similarly all the movies that we have

either Star Wars or fast and Furious

everything is 768 dimensional Vector how

do you visualize this so in order to

visualize this we need to convert this

into a two-dimensional vector or

three-dimensional Vector because that's

what we can visualize as humans on a 2d

plot or a 3D

plot so essentially you need to

convert every Vector of higher

Dimensions into a lower dimensional

Vector let's say two dimensional vector

and you need to convert in such a way

that the local as well as Global

structure is preserved why because let's

say if Batman Begins and uh Dark Knight

and Joker all these movies are together

or all the Star Wars movies are together

in higher Dimensions that is 768

Dimensions even you want to preserve the

same thing that all the Star Wars movies

are closer together in a cluster even in

a two Dimension Vector so you need to

preserve that structure and also you

need to make sure that for example if

Star Wars is farther away from Batman

Begins than some other movie you also

need to preserve the same thing so you

need to also preserve Global structure

to some level so essentially

dimensionality reduction is this Tech

technique of converting any higher

dimensional vectors into lower

dimensional vectors while preserving

Global and local structures and uh you

might confuse how this conversion

exactly occurs for Simplicity let's just

assume that you're converting it into

two dimensions and those two dimensions

are X and Y and how X is formed is just

with some weighted combination of

Dimension One weighted combination of

Dimension two so it's just a weighted

multiplication with all the dimensional

values that we have for 768

dimensions and similarly you can have a

different weight combination for y and

you'll get the dimensional Vector for y

all you need to do is plug in these

values of Dimension 1 to Dimension 768

and you'll get Batman Begins X and Y

Vector Etc now how are these weights

calculated so you can use several

dimensionality reduction algorithms and

the algorithms internally use let's say

m Matrix factorization Etc to split it

into lower dimensions and those weights

could be obtained from The Matrix

factorization values Etc so essentially

mathematical operations extract these

exact values because we as humans cannot

come up with what are the correct values

for weights such that the global and

local structure is preserved so all this

is taken care by the mathematical

algorithms you can see that any higher

dimensional Vector can be converted into

L lower Dimensions using dimensionality

reduction techniques here we are taking

a linear combination of everything but

not Al not all algorithms operate on

linear combination they could use some

other nonlinear combination of these

Dimensions as well to obtain X and Y if

you want the third dimension Z you can

just introduce x y z or Z where Z is

also some linear combination of these

values let's take a brief look at what

are the different dimensionality

reduction approaches are for Simplicity

if you want to remember one takeaway

remember that U map is better than

T which is better than p principal

component analysis over the years people

have developed several algorithms and

you can kind of assume that these are

the three defining algorithms in

dimensionality reductions that have

evolved over the years barring some

exceptions you can generally assume um

map is the current state of the art and

that's what is popularly used for

dimensionality reduction and

visualization so just for Simplicity in

order to understand these techniques on

a high level let's understand PCA tne um

map and what are their main differences

pros and cons so PCA is a linear

dimensionality reduction so like I

mentioned it's a linear combinations of

the dimensions and those and those

weight parameters are obtained using

Matrix factorization methods Etc and PCA

mostly preserves Global structure as

opposed to local structure you can

reduce any higher Dimensions into any

number of lower dimensions and the

primary Dimension will preserve the most

data and then the secondary Dimension

Etc so in our case perhaps you can

convert 768 Dimensions into two

Dimensions X and Y or X Y and Z three

dimensions as well using PCA but the

main thing to remember is that it's a

linear dimensionality reduction

technique what that means is that uh

here I have this image from statistics

for you.info

if the data is linear as you can see

just a line or in high higher dimensions

a hyper plane can separate this and even

when the data is something like this

still it's called linear because you can

use two lines and uh take a weighted

combination and separate this exact

points from the squares that you have

here but if the data is nonlinear as you

can see here you cannot use weighted

combination of the dimensions to be able

to classify accordingly which is to

separate these things so that's why PCA

is not perfect for everything you cannot

say that you will you can convert it

into X and Y Dimensions while preserving

let's say local and Global structures

but you'll have only a linear

combination it might be a nonlinear

combination as well by nonlinear I mean

there could be a logarithm log of dim

One log of dim2 or you can square dim

one or Square dim2 or you can do any

other nonlinear combination right so

most of the times those nonlinear

combinations are also inherently

obtained using

algorithms that you don't need to do

anything uh separately simply put PCA

has limitations because not all the data

points are a linear combination

inherently if you want to preserve

Global and local structure so there

comes tne which is a nonlinear which is

a nonlinear dimensionality reductions

and it separates data that cannot be

separated in let's say hyper plane or

single straight line if the data is

nonlinear like this it can it can

convert these points into twood

dimensional cluster and these points

into two dimensional cluster effectively

there is no way you can apply some

linear combin a in order to separate

these points effectively it preserves

local structure as well that's the

advantage with tne the thing with tne

algorithm is there is a little bit of

randomization and you can control how

the tne algorithm performs with Hyper

parameters so you can change different

hyper parameters and get different

output every time a few years ago tne

was the best performing algorithm in

order to do two two dimensional

visualization Etc but still it had some

uh constraints one thing is that it is

slow and uh it focuses a lot more on the

local structure so we need to strike a

good balance between Global and local

structure preservation because as I

mentioned you want to keep all the Star

Wars movies still together even in the

two Dimensions but you also want to

separate the from other movies and

preserve the distances as well so um map

is the current state-of-the-art

algorithm which is used for

dimensionality reduction and it is also

a nonlinear dimensionality reduction

techniques how it operates is that it

constructs a neighbor graph uh in higher

dimensions and projects that into lower

Dimensions so it's a graph based

algorithm and U map is faster than tne

that is the advantage and with parameter

control you can strike a good balance

between preserving local and Global

structures with um map as opposed to tne

so the biggest takeaway is that uh use

umap and get started with it and if you

encounter specific use cases with your

data where umap doesn't fit then

probably try out tne but other than that

that's the biggest takeaway which is use

um map to convert any High dimensional

Vector into low dimensional Vector now

this dimensionality reduction technique

is not only just used for visualization

which is 768

Dimensions is converted into two two

Dimensions or three dimensions for

visualization but there are many other

use cases where you want to do fast

clustering of dat data Etc in order to

do those cluster you can get to any

lower Dimensions like let's say 10

Dimensions or five Dimensions even so

what I'm saying is that it need not be

necessary that you are always converting

from higher Dimension 768 to always 2D

or 3D dimensions for example if your

goal is just clustering and you want to

do it at scale and fast all you can do

is convert the long vectors into a lower

Dimensions let a 10 Dimensions or Etc so

it is easier to operate and faster to

calculate those cluster clusters Etc and

what are the biggest advantages of data

visualization first of all it gives a

very quick highlevel overview of all the

data that we

have here we are plotting all the 3,600

movie plots that we

collected and you can immediately see

that there are points like these and

these which are kind of like outlier

clusters these are not single points if

you zoom in you'll see that maybe Star

Wars movies all those movies are present

here or some other movie series are

present here

Etc so you can immediately get a good

high level overview you can

automatically detect if there are any

outliers so that if you're training some

algorithm or some other classifier Etc

you can remove those outliers

automatically just looking at them

visually you can identify and remove

those so that they don't affect your

quality of the results and you can also

identify clusters and you can do

similarity for example you can look here

and probably that's all Fast and Furious

movies so you can see how many movies

are together that are in the similar

genre

or talk about cars Etc so you can

identify clusters and similarities

easily and the fourth and uh very

interesting thing is that you can

actually

visualize two

different entities together for example

you can plot all the movies as well as

plot all the directors together and

color code them such that for example

let's say if if you have a new movie

plot and you can just plot that along

with these vectors and you can easily

see which director is closest to that

movie plot so that you can see if the

director is available to direct that

movie Etc and also you can easily see

which directors are closer to which

movies Etc so you can do multiple

visualizations and those reveal

interesting relations with the data for

example you can do movies and directors

or you can

take the job

descriptions that are given out by the

companies and plot all the job

descriptions as well as plot all the

candidates then if you how over any job

description you can immediately see

which candidates are closer

together or you can go to any job

candidate and you can see which job

description are closer together so that

he or she can apply so you can do all

these kinds of interesting

visualizations and the other thing is

you can also plot let's say all the

startups and their descriptions and all

the professors who are doing research at

research Labs of universities Etc and

you can quickly see which startups can

approach which professors so that they

can collaborate and fasten the research

Etc so you can do all these kinds of

interesting Explorations by visualizing

multiple items together and we will see

everything in code in the next section