Machine Learning Lab Assignment for M.Tech and MCA course.

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Machine Learning Lab Assignment for M.Tech and MCA course:- 

 

Prior knowledge:- Brief mathematical knowledge of Regression, Minimum Distance Classifier's, Types of norms, k-means clustering Algo, K-nn Algo, Support Vector Machine, Density Based Spatial Clustering of Applications with Noise (DBSCAN) Algo, Parallel and Sequential Execution Algo.  Python Programming.

 

 

By default Datasets:- Iris Dataset, Cancer Daraset, User Input Dataset.

 

Lab 1:-    For practice only 

 

Assign 1:    Write a program to fit a line using the Gradient Descent Algorithm for the following pairs of values:

X = (1, 3, 5, 7, 9)
Y = (1, 3, 4, 3, 5)

Then, test the fitted line using the same data.

Assign 2:    Write a program to learn the Naive Bayes classification model using the following dataset:

Person	COVID (Yes/No)	Flu (Yes/No)	Fever (Yes/No)
1	Yes	No	Yes
2	No	Yes	Yes
3	Yes	Yes	Yes
4	No	No	No
5	Yes	No	Yes
6	No	No	Yes
7	Yes	No	Yes
8	Yes	No	No
9	No	Yes	Yes
10	No	Yes	No

Next, use the learned Naive Bayes model to determine the class of a person (Flu or COVID-19), assuming that Fever is classified into two categories: “Yes” and “No.”

Assign 3:    Linear regression is a linear approach to modeling the relationship between a dependent variable and one or more independent variables. Let X be the independent variable and Y be the dependent variable. We define the linear relationship between these two variables as follows:

$$Y = mx + c$$

where

$$m = \frac{\sum (x-\bar{x})(y-\bar{y})}{\sum (x-\bar{x})^2}$$

and $\bar{x}$ and $\bar{y}$ represent the means of X and Y, respectively.

Write a program to compute the goodness of fit of the model using the R² value for the following pairs of values:

$$X = (1,2,3,4,5)$$

$$Y = (3,4,2,4,5)$$

Determine the R² value, and identify its maximum and minimum possible values.  

Solution:-

$$\boxed{R^2 = 1 - \frac{SS_{\text{res}}}{SS_{\text{tot}}}}$$

Where:

• $R^2$ = coefficient of determination

• $SS_{\text{res}}$ = residual sum of squares (unexplained variation)

• $SS_{\text{tot}}$ = total sum of squares (total variation)

It can also be written as:

$$\boxed{R^2 = \frac{SS_{\text{reg}}}{SS_{\text{tot}}}}$$

because

$$SS_{\text{tot}} = SS_{\text{reg}} + SS_{\text{res}}$$

Assign 4:    The table below shows the number of hours each student spent studying and whether the student passed (1) or failed (0) the test.

Hours Studied (xₖ)	Pass/Fail (yₖ)
0.50	0
0.75	0
1.00	0
1.25	0
1.50	0
1.75	0
2.00	0
2.25	1
2.50	0
2.75	1
3.00	0
3.25	1
3.50	0
4.00	1
4.25	1
4.50	1
4.75	1
5.00	1
5.50	1

Write a program to fit a logistic regression function to the given data, where xₖ represents the number of hours studied and yₖ represents the test outcome, with yₖ = 1 indicating a pass and yₖ = 0 indicating a failure.

Lab 2:- 

Assign 1: Write a python program to use linear regression to perform prediction on any dataset.

 

Assign 2: Write a python program to implement logistic regression on any dataset. 

 

Assign 3: Write a python program to implement multinomial logistic regression on any dataset. 

 

Lab 3:-

 

Assign 1: Write a python program to implement the Minimum Distance Classifier Algorithm on Iris dataset. 

 

Assign 2: Write python program to implement the Bayes Classification Algorithm. 

 

Assign 3: Write a python program to implement the Naive Bayes Classifier's Algorithm.

 

Assign 4: Write a python program to implement the Support Vector Machine (SVM) Algorithm on user input data. 

 

Assign 5: Write a python program to implement the Support Vector Machine (SVM) Algorithm on Iris dataset / Cancer dataset.

 

Assign 6: Write a python program to implement the XOR-Gate by using Support Vector Machine (SVM) Algorithm. 

 

Assign 7: Write a python program to implement the X-NOR-Gate by using Support Vector Machine (SVM) Algorithm.  

 

Assign 8: Write a python program to implement the OR-Gate by using Support Vector Machine (SVM) Algorithm. 

 

Assign 9: Write a python program to implement the AND-Gate by using Support Vector Machine (SVM) Algorithm.  

 

Assign 10: Write a python program to find the optimal value of 'K' in k-means Algorithm by using elbow method. 

 

Assign 11: Write a python program to implement the K-means Algorithm on user input data. 

 

Assign 12: Write a python program to implement the K-means Algorithm on Iris dataset. 

 

Assign 12: Write a python program to find the optimal value of 'K' in K-nearest neighbor (K-nn) Algorithm.  

 

Assign 13: Write a python program to implement the K-nearest neighbor (K-nn) Algorithm. 

 

Assign 14: Write a python program to find the 'ε' (epsilon) and 'MinPts' parameters uses in DBSCAN Algorithm.

 

Assign 15: Write a python program to find the contour of a binary image by using DBSCAN Algorithm.

 

Assign 16: Write a python program to implement the Bagging concept in ML. 

 

Assign 17: Write a python program to implement the Boosting concept in ML.  

 

 Lab 4:-    For practice only

 

Assign 1:    Write python code to compute the decision function’s of a minimum distance classifier’s for the following pattern.

C₁:{(0,0)^T,(2,0)^T,(2,2)^T,(0,2)^T}

C₂:{(4,4)^T,(6,4)^T,(6,6)^T,(4,6)^T}

Now, test for for the input (4,4) belong to the class C₂, and input (2,2) belongs to the class C₁ .

 

Assign 2:    Write python code to compute the decision function’s of a minimum distance classifier’s for the following pattern.

C₁:{(0,0)^T,(2,0)^T,(2,2)^T,(0,2)^T}

C₂:{(4,4)^T,(6,4)^T,(6,6)^T,(4,6)^T}

Plot the decision boundary implemented by the decision function’s as a output.

 

Assign 3:    Compute decision functions of a minimum distance classifier for Iris data set (Iris versicolor, Iris setosa) taking two features only petal length and petal width. Then find the decision boundary for the two classes. Show it pictorially.

 

Assign 4:    Write python code to test the input (4,4) belong to class C₂, and the input (2,2) belong to class C₁ , by using Bayes decision boundary for the following two pattern classes have Gaussian probability density functions:

C₁:{(0,0)^T,(2,0)^T,(2,2)^T,(0,2)^T}

C₂:{(4,4)^T,(6,4)^T,(6,6)^T,(4,6)^T}

Assume that p(c₁) = p(c₂) =1/2 .

 

 Assign 5:    Write python code to plot Bayes decision boundary for the following two pattern classes have Gaussian probability density functions:

C₁:{(0,0)^T,(2,0)^T,(2,2)^T,(0,2)^T}

C₂:{(4,4)^T,(6,4)^T,(6,6)^T,(4,6)^T}

Assume that p(c₁) = p(c₂) = 1/2 .

 

Assign 6:    Write python code to realize the logical AND function with a neural net that learns the desired function through perceptron learning rule.

 

Assign 7:    Write python code to realize the logical NAND function with a neural net that learns the desired function through perceptron learning rule.

Operating Systtem Lab

Operating System Lab:-

 

System call:- It provides a mechanism to access the services of the operating system.

Software Engineering Lab - I, II

Software Engineering Lab:-

• Software Engineering Lab is aimed to provide you hands-on experience with different aspects of Software Engineering through UML.
• UML including requirements identification, DFD, behavioral and structural design using UML diagrams, implementation, testing, and so on.
• Working with UML on above aspects of an assigned project to get a feel of the real-life software development process.
• By making UML we can inderstand the behavior of the project in different ways.

Install Star UML on your system.     Alternative:- " Rational Rose Software "

Aim:- The student can install Star UML(tool) and execute experiments on this plateform.

• Open google chrome.
• Write Download tools to create UMLs.
• Click on Star UML.
• Click on the downloaded file and install it on your respective plateform.
• Finally open it and start working with your given assignments.

Software Engineering Lab - I :-

1.    Prepare and draw CLASS diagram using UML tool. Illustrate the Aggregation and association with class diagram.

2.    Draw an E-R diagram and describe it with all entities and relationships.

3.    Draw the Data Flow Diagrams at level 0 and level 1.

4.    Illustrate all the attribute of USE CASE diagram and draw USE CASE diagram.

5.    Create a sequence diagram using UML tool.

Software Engineering Lab - II :-

1.    Problem analysis and project planning - through study of the problem - identify project scope, objectives and infrastructure.

2.    Software Requirement Analysis - Describe the individual phases/modules of the project and identify deliverables. Identify functional and non-functional requirements.

3.    Develop use case diagram.

4.    Build and test class diagram.

5.    Software design using sequence diagram.

6.    Software design using activity diagram.

7.    Component diagram and deployment diagram.

8.    Estimation of project size using Functional Point (FP) calculation.

9.    Design test script and test plan using both black box and white box approach.

10.    Software Requirements Specification - Develop the product prototype.

References:

• Roger S Pressman, Software Engineering: A Practitioner's Approach, 7th Edition, McGraw Hill Education,2009.
• Rajib Mall, Fundamentals of Software Engineering, Prentice Hall India, 2014
• Bjarne Stroustrup, The C++ Programming Language, 4th Edition, Addison-Wesley, 2013
• Erich Gamma, Richard Helm, Ralph Johnson, John Vlissides, Design Patterns: Elements of Reusable Object-Oriented Software, Addison Wesley, 1994

Soft Computing Laboratory Assignments - I, II, III, IV, V

Syllabus

---

An outline of the course is as follows.

Introduction to Soft Computing

• Concept of computing systems.
• "Soft" compiting versus "Hard" computing
• Characteristics of Soft computing
• Some applications of Soft computing techniques

Fuzzy logic

• Introduction to Fuzzy logic.
• Fuzzy sets and membership functions.
• Operations on Fuzzy sets.
• Fuzzy relations, rules, propositions, implications and inferences.
• Defuzzification techniques.
• Fuzzy logic controller design.
• Some applications of Fuzzy logic.

Genetic Algorithms

• Concept of "Genetics" and "Evolution" and its application to proablistic search techniques
• Basic GA framework and different GA architectures.
• GA operators: Encoding, Crossover, Selection, Mutation, etc.
• Solving single-objective optimization problems using GAs.

Multi-objective Optimization Problem Solving

• Concept of multi-objective optimization problems (MOOPs) and issues of solving them.
• Multi-Objective Evolutionary Algorithm (MOEA).
• Non-Pareto approaches to solve MOOPs
• Pareto-based approaches to solve MOOPs
• Some applications with MOEAs.

Artificila Neural Networks

• Biological neurons and its working.
• Simulation of biolgical neurons to problem soloving.
• Different ANNs architectures.
• Trainging techniques for ANNs.
• Applications of ANNs to solve some real life problems.
  

end

---

Soft Computing:- It is a family of techniques with the capacity to solve a class of problems for which other conventional techniques are inadequate to solve.

Example:-    The differentiation of any equation of straight lines in slope-intercept form always yields slope.

y = f(x) = mx + c ;    (dy/dx) =m 

y = f(x) = 2D matrix;   (dy/dx) = can not be solved by any traditional techniques; need a soft computing approach for finding the first-order differentiation.

Components of soft computing:-

1.    Fuzzy Systems

2.    Neural Networks

3.    Evolutionary Search Strategies

Hybrid Components of Soft Computing:-

1.    Evolutionary-Fuzzy Systems

2.    Neuro-Evolutionary Systems

3.    Neuro-Fuzzy Systems

4.    Neuro-Fuzzy-Evolutionary Systems

Soft Computing Laboratory Assignments-I

Crisp Sets and Basic Operations

1.    Write python functions to generate the n-population from a given set.

2.    Write python functions to generate the n-sampling sets, each of size k, from a given set.  

3.    Write python functions to compute the union of two crisp sets.

4.    Write python functions to compute the intersection of two crisp sets.

5.    Write python functions to compute the symmetric difference of two crisp sets.

6.    Write python functions to compute the power set of a crisp set.

7.    Write python functions to check whether a crisp set is a subset of another set.

8.    Write python functions to check whether a crisp set is a superset of another set.

9.    Write python functions to check whether two input crisp sets is disjoint or not.

 

10.    Write python functions to implement the following:

            (a)    Add an element in a given set. 

            (b)    Update the set.

            (c)    Remove an element from the set. 

            (e)    Discard an element from the set. 

            (f)     Pop the element from the set.

            (g)    Clear the set. 

            (h)   Distinguish between remove() and discard() functions in python.

 

Soft Computing Laboratory Assignments-II

Fuzzy Membership Functions and Basic Operations

1.    Write python functions to generate the following parameterized fuzzy membership functions and visualize them for different parameter values:

        (a)    Triangular MF

        (b)    Trapezoidal MF

        (c)    Gaussian MF

        (d)    Generalized Bell MF

         

        (e)    PI-MF 

 

        (f)    Z-MF 

 

        (g)    S-MF

 

        (h)    Sigmoid MF

2.    Write python functions to generate asymmetric MF using sigmoidal MFs by the following methods and visualize them:

        (a)    Absolute difference

        (b)    Product

3.    Write python functions to implement following fuzzy complement operations and visualize them for different parameter values:

        (a)    Classical fuzzy complement

        (b)    Sugeno's fuzzy complement

        (c)    Yager's fuzzy complement

4.    Write python functions to implement following fuzzy intersection operations (T-norms) and visualize them for different parameter values:

        (a)    Minimum

        (b)    Algebraic product

        (c)    Bounded product

        (d)    Drastic product

5.    Write python functions to implement following fuzzy union operations (S-norms) and visualize them for different parameter values:

        (a)    Minimum

        (b)    Algebraic product

        (c)    Bounded product

        (d)    Drastic product

Soft Computing Laboratory Assignments-III

Extension Principle, Fuzzy Relations, Linguistic Variables and Fuzzy Reasoning

1.    Write a python function to compute the image of a fuzzy set  A  using extension principle given a mapping function f(x). Test your program for the following cases:

    (a)    A is Triangular MF in the range [1 to 10] and f(x) = x⁴ + 3x³ .

    (b)    A is Trapezoidal MF in the range [1 to 10] and f(x) = x⁴ + 3x³ .

    (c)    A Gaussian MF in the range [1 to 10] and f(x) = x⁴ + 3x³ .

    (d)    A Generalized Bell MF in the range [1 to 10] and f(x) = x⁴ + 3x³ .

    (e)    A Triangular MF in the range [1 to 5] and f(x) = (x-3)² + 2 .

    (f)    A Trapezoidal MF in the range [1 to 5] and f(x) = (x-3)² + 2 .

    (g)    A Gaussian MF in the range [1 to 5] and f(x) = (x-3)² + 2 .

    (h)    A Generalized Bell MF in the range [1 to 5] and f(x) = (x-3)² + 2 .

    (i)    A Triangular MF in the range [0 to 8] and f(x) = sin(x)

    

    (j)    A Trapezoidal MF in the range [0 to 8] and f(x) = sin(x)

    (k)    A Gaussian MF in the range [0 to 8] and f(x) = sin(x)

    (l)    A Generalized Bell MF in the range [0 to 8] and f(x) = sin(x)

2.    Write a python function to compute the max-min composition of two fuzzy relations.

3.    Write a python function to compute the max-product composition of two fuzzy relations.

4.    Define two suitable primary linguistic terms (using Gaussian MF or Generalized Bell MF) representing old and young people respectively over the age range [0 to 100]. Now obtain the membership functions for the following non-primary terms:

    (a)    not very young and not very old.

    (b)    very young or very old.

    (c)    young but not very young.

    (d)    extremely young or more or less old.

Plot the membership functions for all the primary and non-primary terms on a single plot with proper legends.

5.    Demonstrate the effect of contrast intensification on a fuzzy membership function.

6.    Write python functions for implementing cylindrical extension of a 1 D membership function and projection of a 2 D membership function. Demonstrate the result visually.

7.    Demonstrate the interpretation of fuzzy implication as coupling and entailment with relevent plots.

8.    Given a fuzzy membership function function mf(X) representing the fact x is A and a fuzzy relation R(X,Y) representing the fuzzy implication if x is A then y is B, find the consequent membership function representing y is B. Implement this for both max-min and max-product compositions and demonstrate the process visually. 

9.    Implement the fuzzy reasoning procedure for the following:

        Premise 1 (fact):    x is A' and y is B'

        

        Premise 2 (rule 1):    if x is A1 and y is B1 then z is C1

        Premise 3 (rule 2):    if x is A2 and y is B2 then z is C2

---------------------------------------------------------------------------------------------

        Consequence (conclusion):  z is C'

The notations have usual meaning. Demonstrate the procedure visually.

Soft Computing Laboratory Assignments-IV

Fuzzy Inference Systems(FIS)

 

1.    Fuzzy-Logic-Heart-Diagnosis: Use age, trestbps, chol, fbs, ldl and hdl values from this dataset for your FIS.

 

 

 

 

Soft Computing Laboratory Assignments-V

ANN, Pattern Classifiers, Pattern Associators, Backpropagation

1.    Write a python function to realizing the logical AND function through Hebb learning.

 

2.    Write a python function to realizing the logical AND function by a perceptron.

3.    Write a python function to realizing the logical AND function by a Least Mean Square(LMS) or Delta or Widrow Hoff Learning Rule.

4.    Write a python function to realizing the logical AND function by a Extended Delta Learning Rule.

5.    

Soft Computing Laboratory Assignments-VI

Elementary Search Techniques (like-Travelling Salesperson Problem, Knapsack Problem), Advanced Search Strategies, Hybrid Systems 

1.    

BOOKS :-

[1]. J.S.R.Jang, C.T.Sun and E.Mizutani, “Neuro-Fuzzy and Soft Computing”, PHI, 2004, Pearson Education 2004. 

[2]. Timothy J.Ross, “Fuzzy Logic with Engineering Applications”, McGraw-Hill, International Editions, Electrical Engineering Series, Singapore, 1997. 

[3]. Davis E.Goldberg, “Genetic Algorithms: Search, Optimization and Machine Learning”, Addison Wesley, N.Y., 1989. 

[4]. R.Eberhart, P.Simpson and R.Dobbins, “Computational Intelligence - PC Tools”, AP Professional, Boston, 1996. 

[5]. Stamatios V. Kartalopoulos “Understanding Neural Networks and Fuzzy Logic Basic concepts & Applications”, IEEE Press, PHI, New Delhi, 2004. 

[6]. Vojislav Kecman, “Learning & Soft Computing Support Vector Machines, Neural Networks, and Fuzzy Logic Models”, Pearson Education, New Delhi,2006. 

[7] S. Rajasekaran & GA Vijayalakshmi Pai “Neural Networks, Fuzzy Logic, and Genetic Algorithms synthesis and application”, PHI

B.Tech. Pt-III (IT) 1 st Semester Examination, 2023. Subject: Graph Theory (Elective I). Paper: IT506B

 

B.Tech. Pt-III (IT) 1st Semester Examination, 2023 Subject: Graph Theory (Elective I) Paper: IT506B

Department of Engineering and Technological

 Studies, University of Kalyani

B.Tech. Pt-III (IT) 1^st Semester

 Examination, 2023

Subject: Graph Theory (Elective I)

Paper: IT506B

Full marks=70 Time: 3 Hours

The figures in the right-hand margin indicate 

marks.

Candidate are required to give their answers 

in their own words as far as possible.

The notations follow their 

standard meanings.

Answer question number one and any 

five from rest.

1. Answer any ten questions: (2 x 10 = 20)

a) Define a graph and a subgraph.

b) What are the edge and vertex labeling?

c) Define order and size of a graph.

d) What do you mean by cut edge and

 cut vertex?

e) Explain union and intersection of two graphs.

f) A non-directed graph G has 8 edges. 

Find the number of vertices, 

if the degree of each vertex in G is 2.

g) What is cycle graph, 

differentiate it from wheel graph?

h)What is meant by complement of a graph? 

Find the complement of the cycle (C₅) graph?

i) What is a complete graph? 

Find the degree of each vertex in a 

complete(K₅) graph?

j) If G is a simple connected graph with 

70 vertices, 

then the number of edges of G is 

between --------- 

and --------- . Explain.

k) Suppose that G is a graph such that 

each vertex has degree 4 and 

|E|=4*|V| - 36. Then |V| = --------- 

and |E| = --------- .

l) What is rooted tree? 

Define level of a vertex in a rooted tree.

m) Determine the order and size of 

k-partite complete K_n1,n2,...nk graph.

n) Define simple path and circuit in a graph.

o) Define loop-graph and multi-graph.

2. a) Prove that, in any non-directed graph

 there is an even number of vertices of odd

 degree.

b) How many different simple graphs are 

there with the give verticex set

 {v₁, v₂,...., v_n}? 

c) Suppose that G is a non directed graph 

with 12 edges. Suppose that G has 

6 vertices of degree 3 and the rest 

have degrees less than 3. 

Determine the minimum number of vertices

 G can have. 

                                                                                                               

          (2+4+4)

3. a) Is there a graph with degree sequence

 (1, 3, 3, 3, 5, 6, 6) ?

b) Draw a nonsimple graph ‘G’ with degree 

sequence (1, 1, 3, 3, 3, 4, 6, 7) .

c) For any simple graph G, 

prove that the number of edges of G is less 

than or equal to n(n-1)/2, where n is the 

number of vertices of G.                                                                 

                                                                                                                                                                                                                                                                                                    ( 2+3+5)

4. a) Define isomorphism. 

Determine whether the following 

pair of graphs ‘H’ and ‘I’ are isomorphic.

b) Determine the graph G with adjacency

 matrix A such that

and (5+5)

5. a) If G is a connected planar graph,

then prove that the Euler’s formula

 (|V|-|E|+|R| = 2).

b) In a connected simple-plane graph G,

with |E| > 1, prove that |E| ≤ 3|V| - 6.

c) A complete graph K_n is planar iff n ≤ 4,

 justify. 

                                                                                                               

      (4+4+2)

6. a) What do you mean by planar graphs?

b) Define dual graph and self-dual graph?

c) Show that the graph ‘I’ given below is

 planar. 

Find the dual graph of a planar graph ‘J’. 

Is it self-dual graph?

7. a) Differentiate between Euler path and

 Hamiltonian path.

b) Define chromatic number X(G). 

Find the X(G) of a graph ‘M’. 

c) What do you mean by a bipartite graph?

d) Find number of all possible binary tree of 

3-node.

                                                                                                                       (2+3+2+3)

8. Short notes:

                                                                        (2 x 5)

Answer any two of the following:

a) The four-color Problem.

b) The Hamiltonian Graphs.

c) The Königsberg Bridges Problem.

d) The Catalan numbers.

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