# Session 22 11 2025 Summary Slides

course: Module 1 — Foundations of AI & ML
module: Module-1-Foundations-AI-ML
type: pdf
source_url: https://personal-learn.armco.dev/files/Module-1-Foundations-AI-ML/General/PPT_Slides_22-11-2025_and_23-11-2025/Session_22_11_2025_Summary_Slides.pdf
pages: 26

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[page 1]
IIT Roorkee – Futurense
PG Certification 
GenAI and Agentic AI for Engineers
Data Pre-Processing 
and Curation – III and EDA
Dr Durga Toshniwal
Professor (HAG)
Department of Computer Science & Engg.
Indian Institute of Technology Roorkee
durga.toshniwal@cs.iitr.ac.in, durgatoshniwal@gmail.com
www.durgatoshniwal.in

[page 2]
Major Tasks in Data Pre-processing
• Data cleaning
– Fill in missing values, smooth noisy data, and resolve 
inconsistencies
• Data integration
– Integration of multiple databases, or files
• Data transformation
– Normalization and aggregation
• Data reduction
– Obtain reduced representation in volume with same or similar 
analytical results
• Data discretization
– Part of data reduced by binning
GenAI and Agentic AI - Prof Durga Toshniwal

[page 3]
• Given N data vectors from k-dimensions, find c <=  k 
orthogonal vectors that can be best used to 
represent data 
– The original data set is reduced to one consisting of N 
data vectors on c principal components (reduced new 
or alternate set of dimensions) 
• Each data vector is a linear combination of the c 
principal component vectors
• Works for numeric data only
• Used when the number of dimensions is large
Data Reduction by Dimensionality Reduction – 
Principal Component Analysis (PCA) 
GenAI and Agentic AI - Prof Durga Toshniwal

[page 4]
X1
X2
Y1
Y2
Data Reduction by Dimensionality 
Reduction – Principal Component 
Analysis 
GenAI and Agentic AI - Prof Durga 
Toshniwal

[page 5]
What is Data?
• Collection of data objects 
and their attributes
• An attribute is a property 
or characteristic of an 
object
– Examples: eye color of a 
person, temperature, etc.
– Attribute is also known as 
variable, field, characteristic, 
dimension, or feature
• A collection of attributes 
describe an object
– Object is also known as 
record, point, case, sample, 
entity, or instance
Tid Refund Marital 
Status 
Taxable 
Income Cheat 
1 Yes Single 125K No 
2 No Married 100K No 
3 No Single 70K No 
4 Yes Married 120K No 
5 No Divorced 95K Yes 
6 No Married 60K No 
7 Yes Divorced 220K No 
8 No Single 85K Yes 
9 No Married 75K No 
10 No Single 90K Yes 
10 
 
Attributes
Objects
GenAI and Agentic AI - Prof Durga 
Toshniwal

[page 6]
Discrete and Continuous 
Attributes 
• Discrete Attribute
– Has only a finite set of values
– Examples: zip codes, counts, or the set of words in a 
collection of documents 
– Often represented as integer variables.   
– Note: binary attributes are a special case of discrete 
attributes 
• Continuous Attribute 
– Has real numbers as attribute values
– Examples: temperature, height, or weight.  
– Continuous attributes are typically represented as floating-
point variables.  
GenAI and Agentic AI - Prof Durga Toshniwal

[page 7]
Similarity and Dissimilarity
• Similarity
– Numerical measure of how alike two data objects are.
– Is higher when objects are more alike.
– Often falls in the range [0,1]
• Dissimilarity
– Numerical measure of how different two data objects are
– Lower when objects are more alike
– Minimum dissimilarity is often 0
– Upper limit varies
• Proximity refers to a similarity or dissimilarity
GenAI and Agentic AI - Prof Durga Toshniwal

[page 8]
Euclidean Distance
• Euclidean Distance
   

=
−=
n
k kk qpdist
1
2)( D(Q,C)
GenAI and Agentic AI - Prof Durga Toshniwal
Where n is the number of dimensions (attributes) and 
pk and qk are, respectively, the kth attributes 
(components) or data objects p and q.

[page 9]
Euclidean Distance
0
1
2
3
0 1 2 3 4 5 6
p1
p2
p3 p4
point x y
p1 0 2
p2 2 0
p3 3 1
p4 5 1
Distance Matrix
p1 p2 p3 p4
p1 0 2.828 3.162 5.099
p2 2.828 0 1.414 3.162
p3 3.162 1.414 0 2
p4 5.099 3.162 2 0
GenAI and Agentic AI - Prof Durga Toshniwal

[page 10]
Generalization : Minkowski Distance
• Minkowski Distance is a generalization of 
Euclidean Distance
   
   
rn
k
r
kk qpdist
1
1
)||( 
=
−=
GenAI and Agentic AI - Prof Durga Toshniwal
Where r is a parameter, n is the number of 
dimensions (attributes) and pk and qk are, respectively, 
the kth attributes (components) or data objects p and 
q.

[page 11]
Minkowski Distance: Examples
• r = 1.    
– L 1 Norm, A common example of this is the 
Manhattan, Hamming distance, which is just 
the number of bits that are different between 
two binary vectors
• r = 2.  Euclidean distance, L2 norm
GenAI and Agentic AI - Prof Durga Toshniwal

[page 12]
Minkowski Distance
Distance Matrix
point x y
p1 0 2
p2 2 0
p3 3 1
p4 5 1
L1 p1 p2 p3 p4
p1 0 4 4 6
p2 4 0 2 4
p3 4 2 0 2
p4 6 4 2 0
L2 p1 p2 p3 p4
p1 0 2.828 3.162 5.099
p2 2.828 0 1.414 3.162
p3 3.162 1.414 0 2
p4 5.099 3.162 2 0
GenAI and Agentic AI - Prof Durga Toshniwal

[page 13]
Common Properties of a Distance
• Distances, such as the Euclidean distance, 
have some well-known properties.
1. d(p, q)  0   for all p and q and d(p, q) = 0 only if 
p = q. (Positivity)
2. d(p, q) = d(q, p)   for all p and q. (Symmetry)
3. d(p, r)  d(p, q) + d(q, r)   for all points p, q, and r.  
(Triangle Inequality)
 
• A measure that satisfies these properties is 
a metric
GenAI and Agentic AI - Prof Durga Toshniwal

[page 14]
Pearson Correlation Coefficient
• Correlation measures the linear relationship between 
data objects, range is -1 to 1
• Where ꝩ = Correlation Coefficient
• Xi = Value of x-variable in a sample
• X-Bar = Mean of values of x-variable
• Yi = Value of y-variable in a sample
• Y-Bar = Mean of values of y-variable
GenAI and Agentic AI - Prof Durga Toshniwal

[page 15]
Visually Evaluating Correlation
Scatter plots showing the similarity from –1 to 1.GenAI and Agentic AI - Prof Durga Toshniwal

[page 16]
Box Plots
A box plot (or box-and-whisker plot) is a statistical chart used to 
display the distribution, central tendency, and spread of 
data. It highlights key summary statistics visually.
Key Components :
• Lower Quartile (Q1): 25% of the data lies below this value.
• Median (Q2): The middle value of the dataset.
• Upper Quartile (Q3): 75% of the data lies below this value.
• Box: Shows the interquartile range (IQR = Q3 - Q1), where the 
middle 50% of the data lies.
• Whiskers: Extend from Q1 to the minimum value and Q3 to the 
maximum value (excluding outliers).
• Outliers: Points that lie outside 1.5 × IQR from Q1 or Q3, 
shown as small circles.
GenAI and Agentic AI - Prof Durga Toshniwal

[page 17]
Box Plots
A shorter box = tighter clustering of values.
A taller box = greater variability in the middle 50%.
GenAI and Agentic AI - Prof Durga Toshniwal

[page 18]
Kernel Density Estimate (KDE) Plots
• A KDE plot smooths a histogram using a kernel to 
produce a continuous curve.
• A kernel is a mathematical function used to smooth 
data points
• It shows where data values are concentrated and 
helps identify modes (peaks) in the distribution.
GenAI and Agentic AI - Prof Durga Toshniwal

[page 19]
Kernel Density Estimate (KDE) Plots
Key Features:
• Sky blue curve: The estimated distribution of the data.
• Shaded area: Represents density under the curve.
• Red dashed line: Marks the mean of the data.
• Most common is Gaussian Kernel gives Bell shaped curve
GenAI and Agentic AI - Prof Durga Toshniwal

[page 20]
Violin Plots
Violin plot is a combination of a box plot and a kernel density plot.  
Components:
Vertical shape: The width of the "violin" at any point represents the 
density of the data at that value. Thicker = more data points 
there.
• White line (median): Shows the median (Q2) of the data.
• Box lines inside the violin:
• Q1 (25%): Lower quartile.
• Q3 (75%): Upper quartile.
• Whiskers: Indicate the data range excluding outliers (similar to 
box plots).
Benefits:
• Violin plots show distribution shape and density, which box plots 
do not.
• Useful for comparing multiple distributions side-by-side.
.
GenAI and Agentic AI - Prof Durga Toshniwal

[page 21]
Violin Plots
Vertical shape: The width of the "violin" at any point represents the density of the data at that 
value. Thicker = more data points there.
• White line (median): Shows the median (Q2) of the data.
• Box lines inside the violin:
• Q1 (25%): Lower quartile.
• Q3 (75%): Upper quartile.
• Whiskers: Indicate the data range excluding outliers (similar to box plots).
.
GenAI and Agentic AI - Prof Durga Toshniwal

[page 22]
Heatmaps
Heatmap is a data visualization technique that uses color 
to represent values in a matrix-like format. 
• It allows to easily identify patterns, correlations, and 
outliers in data.
• Rows and columns usually represent variables
• Cell color intensity reflects the magnitude of the 
corresponding value.
Correlations can also show how strongly each variable 
is related to every other variable.
GenAI and Agentic AI - Prof Durga Toshniwal

[page 23]
Heatmaps
GenAI and Agentic AI - Prof Durga Toshniwal

[page 24]
Heatmaps
Row/Column Anomalies
• If an entire row or column stands out from the others either much lighter 
or darker, the corresponding observation (row) or variable (column) might 
have outlier values.
GenAI and Agentic AI - Prof Durga Toshniwal

[page 25]
Books
Foundational / Introductory
1. "Hands-On Machine Learning with Scikit-Learn, Keras, 
and TensorFlow"
by Aurélien Géron
o Practical, code-heavy introduction to ML and DL 
using Python.
2. "Pattern Recognition and Machine Learning"
by Christopher M. Bishop
o Theoretical foundation of ML 
3. "Machine Learning: A Probabilistic Perspective"
by Kevin P . Murphy
o Deep and rigorous, focuses on probabilistic models.  
GenAI and Agentic AI - Prof Durga Toshniwal

[page 26]
Books
Deep Learning  
4. "Deep Learning"
by Ian Goodfellow, Yoshua Bengio, and Aaron Courville
o The covers theory in depth with math-heavy content.
5. "Deep Learning with Python"
by François Chollet
o It's hands-on  
6. "Neural Networks and Deep Learning"
by Michael Nielsen
o Theory
GenAI and Agentic AI - Prof Durga Toshniwal