12-05-2025

UNIT - I LECTURE - 06
What is meant by Linear Discriminant?
• Linear discriminant analysis (LDA) is an approach used in supervised
machine learning to solve multi-class classification problems.
• LDA separates multiple classes with multiple features through data
dimensionality reduction.
• This technique is important in data science as it helps optimize machine
learning models.
• One such technique is Linear Discriminant Analysis (LDA) which helps in
reducing the dimensionality of data while retaining the most significant
features for classification tasks. (supervised Learning problems)
5/12/2025 Department of CSE (SB-ET) 1

UNIT - I How does LDA work? LECTURE - 06

• LDA works by finding directions in the feature space that best separate the
classes.
• It does this by maximizing the difference between the class means while
minimizing the spread within each class.
• Learning classification algorithms such as
• Decision tree
• Random forest
• Support vector machines (SVM).

5/12/2025 Department of CSE (SB-ET) 2

1
 12-05-2025

UNIT - I Example : SVM Algorithm LECTURE - 06

5/12/2025 Department of CSE (SB-ET) 3

UNIT - I Pros and Cons LECTURE - 06

Pros:
• Use simplicity and efficiency of computation
• Manage high-dimensional data
• Handle multicollinearity
Cons:
• Shared mean distributions
• Not suitable for unlabeled data

5/12/2025 Department of CSE (SB-ET) 4

2
 12-05-2025

UNIT - I What is Perceptron? LECTURE - 06

• Perceptron is a type of neural network that performs binary classification that

maps input features to an output decision, usually classifying data into one of two
categories, such as 0 or 1.
• Perceptron was introduced by Frank Rosenblatt in 1957.
• He proposed a Perceptron learning rule based on the original MCP neuron.
• A Perceptron is an algorithm for supervised learning of binary classifiers.
• This algorithm enables neurons to learn and processes elements in the training set
one at a time.

5/12/2025 Department of CSE (SB-ET) 5

UNIT - I Structure of Neuron LECTURE - 06

5/12/2025 Department of CSE (SB-ET) 6

3
 12-05-2025

UNIT - I How Perceptron works? LECTURE - 06

The perceptron works on these simple steps which are given below:
• In the first step, all the inputs x are multiplied with their
weights w.
• In this step, add all the increased values and call them
the Weighted sum.
• In our last step, apply the weighted sum to a correct Activation
Function.
For Example:
A Unit Step Activation Function

5/12/2025 Department of CSE (SB-ET) 7

UNIT - I Components of Perceptron LECTURE - 06

A Perceptron is composed of key components that work together to process information and make predictions.
• Input Features: The perceptron takes multiple input features, each representing a characteristic of the input data.
• Weights: Each input feature is assigned a weight that determines its influence on the output. These weights are
adjusted during training to find the optimal values.
• Summation Function: The perceptron calculates the weighted sum of its inputs, combining them with their
respective weights.
• Activation Function: The weighted sum is passed through the Heaviside step function, comparing it to a threshold
to produce a binary output (0 or 1).
• Output: The final output is determined by the activation function, often used for binary classification tasks.
• Bias: The bias term helps the perceptron make adjustments independent of the input, improving its flexibility in
learning.
• Learning Algorithm: The perceptron adjusts its weights and bias using a learning algorithm, such as the Perceptron
Learning Rule, to minimize prediction errors.

5/12/2025 Department of CSE (SB-ET) 8

4
 12-05-2025

UNIT - I How Perceptron works? LECTURE - 06

• A perceptron consists of a single layer of Threshold Logic Units (TLU), with each TLU fully connected to all
input nodes.

• Activation Function :

5/12/2025 Department of CSE (SB-ET) 9

UNIT - I LECTURE - 06
Example 1 : Classifying whether a given fruit is an apple or not

5/12/2025 Department of CSE (SB-ET) 10

5
 12-05-2025

UNIT - I LECTURE - 06
Example 1 : Classifying whether a given fruit is an apple or not
• Let’s take a simple example of classifying whether a given fruit is an apple or not based on two inputs:
its weight (in grams) and its color (on a scale of 0 to 1, where 1 means red). (Attributes)
• The perceptron receives these inputs, multiplies them by their weights, adds a bias, and applies the
activation function to decide whether the fruit is an apple or not.
•Input 1 (Weight): 150 grams
•Input 2 (Color): 0.9 (since the fruit is mostly red)
•Weights: [0.5, 1.0]
•Bias: 1.5
The perceptron’s weighted sum would be:
(150∗0.5)+(0.9∗1.0)+1.5=76.4(150∗0.5)+(0.9∗1.0)+1.5=76.4
Let’s assume the activation function uses a threshold of 75. Since 76.4 > 75, the perceptron classifies the
fruit as an apple (output = 1).

5/12/2025 Department of CSE (SB-ET) 11

UNIT - I Types of Perceptron LECTURE - 06

There are two types of Perceptron:

• Single Layer Perceptron
• Multi Layer Perceptron

5/12/2025 Department of CSE (SB-ET) 12

6
 12-05-2025

UNIT - I Single Layer Perceptron LECTURE - 06

• Single-Layer Perceptron is a type of perceptron is limited to learning linearly separable patterns.
• It is effective for tasks where the data can be divided into distinct categories through a straight line.
• While powerful in its simplicity, it struggles with more complex problems where the relationship
between inputs and outputs is non-linear.

5/12/2025 Department of CSE (SB-ET) 13

UNIT - I Multi Layer Perceptron LECTURE - 06

• Multi-Layer Perceptron possess enhanced processing capabilities as they
consist of two or more layers, adept at handling more complex patterns and
relationships within the data. (hidden Layers)

5/12/2025 Department of CSE (SB-ET) 14