Syllabus for
Master of Science (Data Science)
Academic Year  (2019)

CIA - 50%

ESE - 50%

Linear Algebra plays a fundamental role in the theory of Data Science. This course aims at introducing the basic notions of vector spaces, Linear Algebra and the use of Linear Algebra in applications to Data Science.

CO2: Use the properties of Linear Maps in solving problems on Linear Algebra

CO3: Demonstrate proficiency on the topics Eigenvalues, Eigenvectors and Inner Product Spaces

CO4: Apply mathematics for some applications in Data Science.

Vector Spaces: Rⁿ and Cⁿ, lists, Fⁿand digression on Fields, Definition of Vector spaces, Subspaces, sums of Subspaces, Direct Sums, Span and Linear Independence, bases, dimension.

Definition of Linear Maps - Algebraic Operations on  - Null spaces and Injectivity - Range and Surjectivity - Fundamental Theorems of Linear Maps - Representing a Linear Map by a Matrix - Invertible Linear Maps - Isomorphic Vector spaces - Linear Map as Matrix Multiplication - Operators - Products of Vector Spaces - Product of Direct Sum - Quotients of Vector spaces.

Eigenvalues and Eigenvectors - Eigenvectors and Upper Triangular matrices - Eigenspaces and Diagonal Matrices - Inner Products and Norms - Linear functionals on Inner Product spaces.

Singular value decomposition - Handwritten digits and simple algorithm - Classification of handwritten digits using SVD bases - Tangent distance - Text Mining.

[2] Eldén Lars, Matrix methods in data mining and pattern recognition, Society for Industrial and Applied Mathematics, 2007.

[2] J. V. Kepner and J. R. Gilbert, Graph algorithms in the language of linear algebra, Society for Industrial and Applied Mathematics, 2011.

[3] D. A. Simovici, Linear algebra tools for data mining, World Scientific Publishing, 2012.

[4] P. N. Klein, Coding the matrix: linear algebra through applications to computer science, Newtonian Press, 2015.

ESE - 50%

To enable the students to understand the properties and applications of various probability functions.

CO2: Infer the expectations for random variable functions and generating functions.

CO3: Demonstrate various discrete and continuous distributions and their usage

Algebra of sets - fields and sigma - fields, Inverse function -Measurable function – Probability measure on a sigma field – simple properties - Probability space - Random variables and Random vectors – Induced Probability space – Distribution functions –Decomposition of distribution functions.

Definitions and simple properties - Moment inequalities – Holder, Jenson Inequalities – Characteristic function – definition and properties – Inversion formula. Convergence of a sequence of random variables - convergence in distribution - convergence in probability almost sure convergence and convergence in quadratic mean - Weak and Complete convergence of distribution functions – Helly - Bray theorem

Khintchin's weak law of large numbers, Kolmogorov strong law of large numbers (statement only) – Central Limit Theorem – Lindeberg – Levy theorem, Linderberg – Feller theorem (statement only), Liapounov theorem – Relation between Liapounov and Linderberg –Feller forms – Radon Nikodym theorem and derivative (without proof) – Conditional expectation – definition and simple properties.

Distribution of functions of random variables – Laplace, Cauchy, Inverse Gaussian, Lognormal, Logarithmic series and Power series distributions - Multinomial distribution - Bivariate Binomial – Bivariate Poisson – Bivariate Normal - Bivariate Exponential of Marshall and Olkin - Compound, truncated and mixture of distributions, Concept of convolution - Multivariate normal distribution (Definition and Concept only)

Sampling distributions: Non - central chi - square, t and F distributions and their properties - Distributions of quadratic forms under normality -independence of quadratic form and a linear form - Cochran’s theorem.

Order statistics, their distributions and properties - Joint and marginal distributions of order statistics - Distribution of range and mid range -Extreme values and their asymptotic distributions (concepts only) - Empirical distribution function and its properties – Kolmogorov - Smirnov distributions – Life time distributions -Exponential and Weibull distributions - Mills ratio – Distributions classified by hazard rate

[2]. An Introduction to Probability and Statistics, V.K Rohatgi and Saleh, 3^rd Edition, 2015.

[2]. Order Statistics, H.A David and H.N Nagaraja, John Wiley & Sons, 3^rd Edition, 2003.

ESE - 50%

To provide strong foundation for data science and application area related to it and understand the underlying core concepts and emerging technologies in data science.

CO2: Evaluate the data analysis techniques for applications handling large data

CO3: Demonstrate the various machine learning algorithms used in data science process

CO4: Understand the ethical practices of data science 

CO4:Visualize and present the inference using various tools

CO5:Learn to think through the ethics surrounding privacy, data sharing and algorithmic decision-making

Definition – Big Data and Data Science Hype – Why data science – Getting Past the Hype – The Current Landscape – Data Scientist - Data Science Process Overview – Defining goals – Retrieving data – Data preparation – Data exploration – Data modeling – Presentation.

Problems when handling large data – General techniques for handling large data – Case study – Steps in big data – Distributing data storage and processing with Frameworks – Case study.

Machine learning – Modeling Process – Training model – Validating model – Predicting new observations –Supervised learning algorithms – Unsupervised learning algorithms.

Introduction – Deep Feedforward Networks – Regularization – Optimization of Deep Learning – Convolutional Networks – Recurrent and Recursive Nets – Applications of Deep Learning.

Introduction to data visualization – Data visualization options – Filters – MapReduce – Dashboard development tools – Creating an interactive dashboard with dc.js-summary.

Data Science Ethics – Doing good data science – Owners of the data - Valuing different aspects of privacy - Getting informed consent - The Five Cs – Diversity – Inclusion – Future Trends.

[2]. An Introduction to Statistical Learning: with Applications in R, Gareth James, Daniela Witten, Trevor Hastie, Robert Tibshirani, Springer, 1^st edition, 2013

[3]. Deep Learning, Ian Goodfellow, Yoshua Bengio, Aaron Courville, MIT Press, 1^st edition, 2016

[4]. Ethics and Data Science, D J Patil, Hilary Mason, Mike Loukides, O’ Reilly, 1^st edition, 2018

[2]. Doing Data Science, Straight Talk from the Frontline, Cathy O'Neil, Rachel Schutt, O’ Reilly, 1^st edition, 2013

[3]. Mining of Massive Datasets, Jure Leskovec, Anand Rajaraman, Jeffrey David Ullman, Cambridge University Press, 2^nd edition, 2014

ESE - 50%

This course is intended to assist students in planning and carrying out research. The students are exposed to the principles, procedures and techniques of implementing a research project. The course starts with an introduction to research and leads through the various methodologies involved in the research process. It focus on finding out the research gap from the literature using computer technology,introduces basic statistics required for research and report the research outcomes scientifically with emphasis on research ethics.

CO2: Apply research methods and methodology including research design, data analysis, and interpretation.

CO3: Create scientific reports according to specified standards.

Defining research problem:Selecting the problem, Necessity of defining the problem ,Techniques involved in defining a problem- Ethics in Research.

Principles of experimental design,Working with Literature: Importance, finding literature, Using your resources, Managing the literature, Keep track of references,Using the literature, Literature review,On-line Searching: Database ,SCIFinder, Scopus, Science Direct ,Searching research articles , Citation Index ,Impact Factor ,H-index.

Measurement of Scaling: Quantitative, Qualitative, Classification of Measure scales, Data Collection, Data Preparation. 

Scientific Writing and Report Writing: Significance, Steps, Layout, Types, Mechanics and Precautions, Latex: Introduction, Text, Tables, Figures, Equations, Citations, Referencing, and Templates (IEEE style), Paper writing for international journals, Writing scientific report. 

[2] Zina O’Leary, The Essential Guide of Doing Research, New Delhi: PHI, 2005. 

[2] Kumar, Research Methodology: A Step by Step Guide for Beginners, 3rd. ed. Indian: PE, 2010. 

ESE - 50%

To enable the students to understand the fundamentals of statistics to apply descriptive measures and probability for data analysis.

CO2: Infer the concept of correlation and regression for relating two or more related variables.

CO3: Demonstrate the probabilities for various events.

Origin and development of Statistics, Scope, limitation and misuse of statistics. Types of data: primary, secondary, quantitative and qualitative data. Types of Measurements: nominal, ordinal, discrete and continuous data. Presentation of data by tables: construction of frequency distributions for discrete and continuous data, graphical representation of a frequency distribution by histogram and frequency polygon, cumulative frequency distributions

Measures of location or central tendency: Arthimetic mean, Median, Mode, Geometric mean, Harmonic mean. Partition values: Quartiles, Deciles and percentiles. Measures of dispersion: Mean deviation, Quartile deviation, Standard deviation, Coefficient of variation. Moments: measures of skewness, Kurtosis.

Correlation: Scatter plot, Karl Pearson coefficient of correlation, Spearman's rank correlation coefficient, multiple and partial correlations (for 3 variates only). Regression: Concept of errors, Principles of Least Square, Simple linear regression and its properties.

Random experiment, sample point and sample space, event, algebra of events. Definition of Probability: classical, empirical and axiomatic approaches to probability, properties of probability. Theorems on probability, conditional probability and independent events, Laws of total probability, Baye’s theorem and its applications

[2]. Gupta S.C and Kapoor V.K, Fundamentals of Mathematical Statistics, 11th edition, Sultan Chand & Sons, New Delhi, 2014.

[2]. Walpole R.E, Myers R.H, and Myers S.L, Probability and Statistics for Engineers and Scientists, Pearson, New Delhi, 2017.

[3]. Montgomery D.C and Runger G.C, Applied Statistics and Probability for Engineers, Wiley India, New Delhi, 2013.

[4]. Mood A.M, Graybill F.A and Boes D.C, Introduction to the Theory of Statistics, McGraw Hill, New Delhi, 2008.

ESE - 50%

To enable the students to understand the fundamental concepts of problem solving and programming structures.  

CO2: Apply different programming structure with suitable logic for computational problems.  

Number Representation – Decimal, Binary, Octal, Hexadecimal and BCD numbers – Binary Arithmetic – Binary addition – Unsigned and Signed numbers – one’s and two’s complements of Binary numbers – Arithmetic operations with signed numbers - Number system conversions – Boolean Algebra – Logic gates – Design of Circuits – K - Map

Types of Problems – Problem solving with Computers – Difficulties with problem solving – problem solving concepts for the Computer – Constants and Variables – Rules for Naming and using variables – Data types – numeric data – character data – logical data – rules for data types – examples of data types – storing the data in computer - Functions – Operators – Expressions and Equations

Communicating with computer – organizing the solution – Analyzing the problem – developing the interactivity chart – developing the IPO chart – Writing the algorithms – drawing the flow charts – pseudocode – internal and external documentation – testing the solution – coding the solution – software development life cycle.

Introduction to programming structure – pointers for structuring a solution – modules and their functions – cohesion and coupling – problem solving with logic structure. Problem solving with decisions – the decision logic structure – straight through logic – positive logic – negative logic – logic conversion – decision tables – case logic structure -  examples.

[2] Peter Norton “Introduction to Computers”,6th Edition, Tata Mc Graw Hill, New Delhi,2006.

[3] Maureen Sprankle and Jim Hubbard, Problem solving and programming concepts, PHI, 9^th Edition, 2012

ESE - 50%

To Enable the students to excel in the Linux Platform

CO2: Manage the Linux environment to work with open source data science tools

RHEL7.5,breaking root password, Understand and use essential tools for handling files, directories, command-line environments, and documentation - Configure local storage using partitions and logical volumes

Swapping, Extend LVM Partitions,LVM Snapshot - Manage users and groups, including use of a centralized directory for authentication

Kernel updations,yum and nmcli configuration, Scheduling jobs,at,crontab -  Configure firewall settings using firewall config, firewall-cmd, or iptables , Configure key-based authentication for SSH ,Set enforcing and permissive modes for SELinux , List and identify SELinux file and process context ,Restore default file contexts

ESE - 50%

The main objective of this course is to fundamental knowledge and practical experience with, database concepts. It includes the concepts and terminologies which facilitate the construction of database tables and write effective queries. Also, to Comprehend Data warehouse and its functions.

CO2: Create and populate a RDBMS for a real life application, with constraints and keys, using SQL

CO3: Retrieve any type of information from a data base by formulating complex queries in SQL

CO4: Demonstrate various databases

CO5: Distinguish database from data warehouse and examine ETL process

Concept & Overview of DBMS, Data Models, Database Languages, Database Administrator, Database Users, Three Schema architecture of DBMS. Basic concepts, Design Issues, Mapping Constraints, Keys, Entity-Relationship Diagram, Weak Entity Sets, Extended E-R features

Lab Exercises

1.      Data Definition,

2.      Table Creation

3.      Specification of Constraints

SQL and Integrity Constraints, Concept of DDL, DML, DCL. Basic Structure, Set operations, Aggregate Functions, Null Values, Domain Constraints, Referential Integrity Constraints, assertions, views, Nested Subqueries, Functional Dependency, Different anomalies in designing a Database, Normalization : using functional dependencies, Boyce-Codd Normal Form, 4NF, 5NF

Lab Exercises

1.   Insert, Select, Update & Delete Commands

2.   Nested Queries & Join Queries

3.  Views

Active databases, Deductive Databases, Knowledge bases, Multimedia Databases, Multidimensional Data Structures, Image Databases, Text/Document Databases, Video Databases, Audio Databases, Multimedia Database Design.

Defining Features, Data Warehouses and Data Marts, Architectural Types, Overview of the Components, Metadata in the Data warehouse, Data Design and Data Preparation: Principles of Dimensional Modeling, Dimensional Modeling Advanced Topics From Requirements To Data Design, The Star Schema, Star Schema Keys, Advantages of the Star Schema, Star Schema: Examples, Dimensional Modeling: Advanced Topics, Updates to the Dimension Tables, Miscellaneous Dimensions, The Snowflake Schema, Aggregate Fact Tables, Families Oo Stars

Requirements, ETL Data Structures, Extracting, Cleaning and Conforming, Delivering Dimension Tables, Delivering Fact Tables (CH:1,2,3,4,5,6)

Lab Exercises:

1.      Importing source data structures

2.      Design Target Data Structures

3.      Create target structure

4.      Design and build the ETL mapping

Development, Operations, Metadata, Real-Time ETL Systems. (CH:7,8,9,11)

Lab Exercises:

1.      Perform the ETL process and transform into data map

2.      Create the cube and process it

3.      Generating Reports

4.      Creating the Pivot table and pivot chart using some existing data

[2]. Thomas Cannolly and Carolyn Begg, “Database Systems, A Practical Approach to Design, Implementation and Management”, Third Edition, Pearson Education, 2007.

[3]. The Data Warehouse Toolkit: The Complete Guide to Dimensional Modeling, 2nd John Wiley & Sons, Inc. New York, USA, 2002

ESE - 50%

This course is designed to introduce the concepts of theory of estimation and testing of hypothesis. This paper also deals with the concept of parametric tests for large and small samples. It also provides knowledge about non-parametric tests and its applications.

CO2: Apply the idea of sampling distributions of difference statistics in testing of hypotheses.

CO3: Infer the concept of nonparametric tests for single sample and two samples.

Neyman - Fisher Factorisation theorem - the existence and construction of minimal sufficient statistics - Minimal sufficient statistics and exponential family - sufficiency and completeness - sufficiency and invariance.

Lab Exercise

1. Drawing random samples using random number tables .
2. Point estimation of parameters and obtaining estimates of standard errors.

Minimum variance unbiased estimation - locally minimum variance unbiased estimators - Rao Blackwell – theorem – Completeness: Lehmann Scheffe theorems - Necessary and sufficient condition for unbiased estimators - Cramer- Rao lower bound - Bhattacharya system of lower bounds in the 1-parameter regular case - Chapman -Robbins inequality

Lab Exercise

1. Comparison of estimators by plotting mean square error.
2. Computing maximum likelihood estimates -1
3. Computing maximum likelihood estimates - 2
4. Computing moment estimates

Computational routines - strong consistency of maximum likelihood estimators - Asymptotic Efficiency of maximum likelihood estimators - Best Asymptotically Normal estimators - Method of moments - Bayes’ and minimax estimation: The structure of Bayes’ rules - Bayes’ estimators for quadratic and convex loss functions - minimax estimation - interval estimation.

Lab Exercise

1. Constructing confidence intervals based on large samples.
2. Constructing confidence intervals based on small samples.
3. Generating random samples from discrete distributions.
4. Generating random samples from continuous distributions.

Uniformly most powerful tests - the Neyman-Pearson fundamental Lemma - Distributions with monotone likelihood ratio - Problems - Generalization of the fundamental lemma, two sided hypotheses - testing the mean and variance of a normal distribution.

Lab Exercise

1. Evaluation of probabilities of Type-I and Type-II errors and powers of tests.
2. MP test for parameters of binomial and Poisson distributions.
3. MP test for the mean of a normal distribution and power curve.
4. Tests for mean, equality of means when variance is (i) known, (ii) unknown under normality (small and large samples)

Unbiasedness for hypotheses testing - similarity and completeness - UMP unbiased tests for multi parameter exponential families - comparing two Poisson or Binomial populations - testing the parameters of a normal distribution (unbiased tests) - comparing the mean and variance of two normal distributions - Symmetry and invariance - maximal invariance - most powerful invariant tests.

Lab Exercise

1. Tests for single proportion and equality of two proportions.
2. Tests for variance and equality of two variances under normality
3. Tests for correlation and regression coefficients.

SPRT procedures - likelihood ratio tests - locally most powerful tests - the concept of confidence sets - non parametric tests.

Lab Exercise

1. Tests for the independence of attributes, analysis of categorical data and tests for the goodness of fit.(For uniform, binomial and Poisson distributions)
2. Nonparametric tests.
3. SPRT for binomial proportion and mean of a normal distribution.

[2]. An Introduction to Probability and Statistics, V.K Rohatgi and Saleh, 3rd Edition, 2015.

[2]. Linear Statistical Inference and its Applications, Rao C.R, Willy Publications, 2nd Edition, 2001.

ESE - 50%

The objective of this course is to provide comprehensive knowledge of python programming paradigms required for Data Science.

CO2: Analyze the significance of  python program development environment by working on real world examples

CO3: Implement numerical programming, data handling and visualization through NumPy, Pandas and MatplotLib modules.

Structure of Python Program-Underlying mechanism of Module Execution-Branching and Looping-Problem Solving Using Branches and Loops-Functions - Lists and Mutability- Problem Solving Using Lists and Functions

Lab Exercises

1.      Demonstrate usage of branching and looping statements

2.      Demonstrate Recursive functions

3.      Demonstrate Lists

Sequences, Mapping and Sets- Dictionaries- -Classes: Classes and Instances-Inheritance-Exceptional Handling-Introduction to Regular Expressions using “re” module.

Lab Exercises

1.      Demonstrate Tuples and Sets

2.      Demonstrate Dictionaries

3.      Demonstrate inheritance and exceptional handling

4.   Demonstrate use of “re”.

Basics of NumPy-Computation on NumPy-Aggregations-Computation on Arrays-Comparisons, Masks and Boolean Arrays-Fancy Indexing-Sorting Arrays-Structured Data: NumPy’s Structured Array.

Lab Exercises

1.      Demonstrate Aggregation

2.      Demonstrate Indexing and Sorting

Introduction to Pandas Objects-Data indexing and Selection-Operating on Data in Pandas-Handling Missing Data-Hierarchical Indexing - Combining Data Sets

Lab Exercises

1.      Demonstrate handling of missing data

2.      Demonstrate hierarchical indexing

Aggregation and Grouping-Pivot Tables-Vectorized String Operations -Working with Time Series-High Performance Pandas- and query()

Lab Exercises

1.      Demonstrate usage of Pivot table

2.      Demonstrate use of and query()

Basic functions of matplotlib-Simple Line Plot, Scatter Plot-Density and Contour Plots-Histograms, Binnings and Density-Customizing Plot Legends, Colour Bars-Three-Dimensional Plotting in Matplotlib.

Lab Exercises

1.      Demonstrate Scatter Plot

2.      Demonstrate 3D plotting

[2]. Zhang.Y ,An Introduction to Python and Computer Programming, Springer Publications,2016

[2]. T.R.Padmanabhan, Programming with Python,Springer Publications,2016

This course aims at introducing the basic notions of multivariable calculus and graph theory in applications to Data Science.

CO2: Understand the properties of graphs

CO2: Apply mathematics for some applications in Data Science

Functions of Several Variables - Limits and continuity in HIgher Dimensions - Partial Derivatives - The Chain Rule - Directional Derivative and Gradient vectors - Tangent Planes and Differentials - Extreme Values and Saddle Points - Lagrange Multipliers.

Affine and Convex Sets - Hyperplanes and half-spaces - Euclidean balls and ellipsoids - Norm balls and Norm cones - polyhedra - simplexs - The positive definite cone.- separating and supporting hyperplanes.

Introduction - Inequalities on Linear Spaces - Norms on Linear Spaces - Inner products - Orthogonality - Unitary and Orthogonal Matrices - norms for matrices

Graphs - subgraphs - factors - Paths - cycles - connectedness - trees - Euler tours - Hamiltonian cycles - Planar Graphs - Digraphs.

Algorithms - Representing Graphs - The algorithm of Hierholzer - Writing algorithms - Complexity of Algorithms.

[2]. S. P. Boyd and L. Vandenberghe, Convex optimization. Cambridge Univ. Pr., 2011.

[3]. D. Jungnickel, Graphs, networks and algorithms. Springer, 2014.

[2]. S. Sra, S. Nowozin, and S. J. Wright, Optimization for machine learning. MIT Press, 2012.

ESE - 50%

This course aims to provide the grounding knowledge about the regression model building of simple and multiple regression.

CO2: Evaluate R-square criteria for model selection

CO3: Understand the forward, backward and stepwise methods for selecting the variables

CO4: Understand the importance of multicollinearity in regression modelling

CO5: Ability touse and understand generalizations of the linear model to binary and count data

Introduction to regression analysis: Modelling a response, overview and applications of regression analysis, major steps in regression analysis. Simple linear regression (Two variables): assumptions, estimation and properties of regression coefficients, significance and confidence intervals of regression coefficients, measuring the quality of the fit.

Multiple linear regression model: assumptions, ordinary least square estimation of regression coefficients, interpretation and properties of regression coefficient, significance and confidence intervals of regression coefficients.

Mean Square error criteria, R2 and  criteria for model selection; Need of the transformation of variables; Box-Cox transformation; Forward, Backward and Stepwise procedures.

Residual analysis, Departures from underlying assumptions, Effect of outliers, Collinearity, Non-constant variance and serial correlation, Departures from normality, Diagnostics and remedies.

Introduction to nonlinear regression, Least squares in the nonlinear case and estimation of parameters, Models for binary response variables, estimation and diagnosis methods for logistic and Poisson regressions. Prediction and residual analysis.

[2]. S. Chatterjee and AHadi, Regression Analysis by Example, 4^th Ed., John Wiley and Sons, Inc, 2006

[3].Seber, A.F. and Lee, A.J. (2003) Linear Regression Analysis, John Wiley, Relevant sections from chapters 3, 4, 5, 6, 7, 9, 10.

[2]. P. McCullagh, J.A. Nelder, Generalized Linear Models, Chapman & Hall, 1989.

ESE - 50%

This course aims to introduce the methods to analyze and evaluate the performance of an algorithm. It introduces the different design techniques for designing efficient algorithms.

CO2: Design and develop algorithms using various design techniques.

CO3: Evaluate the efficiency of Algorithms by analyzing the running time of algorithms for problems in various domain

Algorithm Specification – Analysis of Insertion sort – Performance Analysis  - Space complexity – Time Complexity – Asymptotic notations – Amortized Analysis

Divide and Conquer – Binary search – Quick sort – Strassen’s Matrix Multiplication Greedy Approach – Knapsack problem – Minimum cost spanning tree – PRIM’s and Kruskal’s Algorithm – single source shortest path.

– Dynamic Programming – All pairs shortest path – longest common sequence - The general method – 8 Queens problem – Sum of subsets

Branch and Bound – 0/1 knapsack problem – Travelling salesperson problem

Basic Concepts – NP hard Graph problems -  NP Hard Scheduling problems – NP hard code generation problems

Approximation Algorithms – Polynomial time approximation schemes – PRAM Algorithms – Computational model – merge sort – Mesh Algorithms – Computational model – odd–even merge in a mesh – Hypercube Algorithms – Computational model – merge sort

[2]. Coremen T H, Leiserson C E, Rivest R L and Stein, Clifford, Introduction to Algorithms, PHI, Third Edition, 2010.

[2]. GAV PAI, Data structures and Algorithms, Tata McGraw Hill, Jan 2008

ESE - 50%

This course aims to provide sound foundation to fundamental concepts of machine learning and its application and prepare students for advanced research and real time problem solving in machine learning and related fields.

CO2: Apply a variety of learning algorithms to different domain data.

CO3: Analyse and perform evaluation of learning algorithms and model selection.

Machine Learning-Examples of Machine Applications-Learning Associations-Classification-Regression-Unsupervised Learning-Reinforcement Learning. Supervised Learning: Learning class from examples-Vapnik-Chervonenkis  Dimension-Probably Approach Corre(PAC)Learning-Noise-Learning Multiple classes.Regression-Model Selection and Generalization.

Introduction to Parametric methods-Maximum Likelihood  Estimation:Bernoulli Density-Multinomial Density-Gaussian Density.Evaluating an Estimator:Bias and Variance-The Bayes Estimator-Parametric Classification.

Introduction-Nonparametric Density Estimation: Histogram Estimator-Kernel Estimator-K-Nearest Neighbour Estimator-Generalization to Multivariate Data-Nonparametric Classification-Distance Based Classification-Outlier Detection.

Multivariate Data-Parameter Estimation-Estimation of Missing Values-Multivariate  Normal Distribution- Multivariate Classification-Tuning Complexity-Discrete Features.

Dimensionality Reduction: Introduction- Subset Selection-Principal Component Analysis, Feature Embedding-Factor Analysis-Singular Value Decomposition-Multidimensional Scaling-Linear Discriminant Analysis-Canonical Correlation Analysis-Laplacian Eigenmaps

Linear Discrimination:Introduction- Generalizing the Linear Model-Geometry of the Linear Discriminant- Pairwise Separation-Gradient Descent-Logistic Discrimination.

Bayesian Estimation:Introduction-Estimating the Parameter of a Discrete Distribution-Bayesian Estimation of the Parameters of a  Gaussian Distribution-Bayesian Estiamtion of the Parameters of a Function-Bayesian Classification-Bayesian Models Comparison.

Clustering:Introduction-Mixture Densities, K-Means Clustering- Expectation-Maximization algorithm- Mixtures of Latent Varaible Models-Supervised Learning after Clustering-Spectral Clustering-Hierachial Clustering-Clustering, Choosing the number of Clusters.

[2]. T. Hastie, R. Tibshirani and J. Friedman, The Elements of Statistical Learning: Data Mining, Inference and Prediction, Springer, 2nd Edition, 2009

[3]. K. P. Murphy, Machine Learning:A Probabilistic Perspective, MIT Press, 2012.

ESE - 50%

 This course lays the foundation of Multivariate data analysis. The exposure provided to multivariate data structure, multinomial and multivariate normal distribution, estimation and testing of parameters, various data reduction methods would help the students in having a better understanding of research data, its presentation and analysis.

CO2: Apply Multivariate analysis of variance (MANOVA) of one and two-way classified data.

Basic concepts on multivariate variable. Multivariate normal distribution, Marginal and conditional distribution, Concept of random vector: Its expectation and Variance-Covariance matrix. Marginal and joint distributions. Conditional distributions and Independence of random vectors. Multinomial distribution. Sample mean vector and its distribution.

Sample mean vector and its distribution. Likelihood ratio tests: Tests of hypotheses about the mean vectors and covariance matrices for multivariate normal populations. Independence of sub vectors and sphericity test.

Multivariate analysis of variance (MANOVA) of one and two- way classified data. Multivariate analysis of covariance.  Wishart distribution, Hotelling’s T2 and Mahalanobis’ D2 statistics, Null distribution of Hotelling’s T2. Rao’s U statistics and its distribution.

Bayes, minimax, and Fisher’s criteria for discrimination between two multivariate normal populations. Sample discriminant function. Tests associated with discriminant functions. Probabilities of misclassification and their estimation. Discrimination for several multivariate normal populations

Principal components, sample principal components asymptotic properties. Canonical variables and canonical correlations: definition, estimation, computations. Test for significance of canonical correlations.

Factor analysis: Orthogonal factor model, factor loadings, estimation of factor loadings, factor scores.  Applications

[2]. Everitt B, Hothorn T, 2011. An Introduction to Applied Multivariate Analysis with R, Springer.

[3]. Barry J. Babin, Hair, Rolph E Anderson, and William C. Blac, 2013,  Multivariate Data Analysis, Pearson New International Edition, 

[2] Chatfield, C. and Collins, A.J. 1982. Introduction to Multivariate analysis. Prentice Hall

[3] Srivastava, M.S. and Khatri, C.G. 1979. An Introduction to Multivariate Statistics. North Holland

ESE - 50%

This course is designed to introduce the concepts of theory of estimation and testing of hypothesis. This paper also deals with the concept of parametric tests for large and small samples. It also provides knowledge about non-parametric tests and its applications.

CO2: Apply the idea of sampling distributions of difference statistics in testing of hypotheses.

CO3: Infer the concept of nonparametric tests for single sample and two samples.

Classification of Stochastic Processes, Markov Processes – Markov Chain - Countable State Markov Chain. Transition Probabilities, Transition Probability Matrix. Chapman - Kolmogorov's Equations, Calculation of n - step Transition Probability and its limit.

Classification of States, Recurrent and Transient States - Transient Markov Chain, Random Walk and Gambler's Ruin Problem. Continuous Time Markov Process:, Poisson Processes, Birth and Death Processes, Kolmogorov’s Differential Equations, Applications.

Branching Processes – Galton – Watson Branching Process - Properties of Generating Functions – Extinction Probabilities – Distribution of Total Number of Progeny. Concept of Weiner Process.

Renewal Processes – Renewal Process in Discrete and Continuous Time – Renewal Interval – Renewal Function and Renewal Density – Renewal Equation – Renewal theorems: Elementary Renewal Theorem. Probability Generating Function of Renewal Processes.

Stationary Processes: Discrete Parameter Stochastic Process – Application to Time Series. Auto-covariance and Auto-correlation functions and their properties. Moving Average, Autoregressive, Autoregressive Moving Average, Autoregressive Integrated Moving Average Processes. Basic ideas of residual analysis, diagnostic checking, forecasting.

[2]. Stochastic Processes, S.M Ross, Wiley India Pvt. Ltd, 2008.

[2]. Introduction to Probability and Stochastic Processes with Applications, B..C. Liliana, A Viswanathan, S. Dharmaraja, Wiley Pvt. Ltd, 2012.

ESE - 50%

This lab is designed to introduce implementation of practical machine learning algorithms using R programming language. The lab will extensively use datasets from real life situations.

CO2: Analyse the use of basic functions of R Package.

CO3: Demonstrate exploratory data analysis (EDA) for a given data set.

CO4: Create and edit visualizations with R

CO5: Implement and assess relevance and effectiveness of machine learning algorithms for a given dataset.

Download and install R – R IDE environments – Why R – Getting started with R – Vectors and Data Frames – Loading Data Frames – Data analysis with summary statistics and scatter plots – Summary tables -  Working with Script Files

 Linear Regression – Introduction – Regression model for one variable regression – Selecting best model – Error measures SSE, SST, RMSE, R² – Interpreting R² – Multiple linear regression – Lasso and ridge regression – Correlation – Recitation – A minimum of  3 data sets for practice

Logistic Regression – The Logit – Confusion matrix – sensitivity, specificity – ROC curve – Threshold selection with ROC curve – Making predictions – Area under the ROC curve (AUC)  - Recitation – A minimum of 3 data sets for practice

Approaches to missing data – Data imputation – Multiple imputation – Classification and Regression Tress (CART) – CART with Cross Validation – Predictions from CART – ROC curve for CART – Random Forests – Building many trees – Parameter selection – K-fold Cross Validation – Recitation – A minimum of 3 data sets for practice

Using text as data – Text analytics – Natural language processing – Bag of words – Stemming – word clouds – Recitation – min 3 data sets for practice – Time series analysis – Clustering – k-mean clustering – Random forest with clustering – Understanding cluster patterns – Impact of clustering – Heatmaps – Recitation – min 3 data sets for practice

Support Vector Machines – Gradient Boosting – Naive Bayes - Bayesian GLM – GLMNET - Ensemble modeling – Experimenting with all of the above approaches (Units 1-5) with and without data imputation and assessing predictive accuracy – Recitation – min 3 data sets for practice

PROJECT – A concluding project work carried out individually for a common data set

[2]. R for everyone, Jared Lander, Pearson, 1^st Edition, 2014

ESE - 50%

The subject is intended to give the knowledge of Big Data evolving in every real-time applications and how they are manipulated using the emerging technologies. This course breaks down the walls of complexity in processing Big Data by providing a practical approach to developing Java applications on top of the Hadoop platform. It describes the Hadoop architecture and how to work with the Hadoop Distributed File System (HDFS) and HBase in Ubuntu platform.

CO2: Understand the big data systems and identify the main sources of Big Data in the real world.

CO3: Demonstrate an ability to use Hadoop framework for processing Big Data for Analytics. 

CO4: Evaluate the Map reduce approach for different domain problems. 

Distributed file system – Big Data and its importance, Four Vs, Drivers for Big data, Big data analytics, Big data applications, Algorithms using map reduce, Matrix-Vector Multiplication by Map Reduce.

Apache Hadoop– Moving Data in and out of Hadoop – Understanding inputs and outputs ofMapReduce - Data Serialization, Problems with traditional large-scale systems-Requirements for a new approach-Hadoop – Scaling-Distributed Framework-Hadoop v/s RDBMS-Brief history of Hadoop.

Lab Exercise

1. Installing and Configuring Hadoop

Hadoop Processes (NN, SNN, JT, DN, TT)-Temporary directory – UI-Common errors when running Hadoop cluster, solutions.

Setting up Hadoop on a local Ubuntu host: Prerequisites, downloading Hadoop, setting up SSH, configuring the pseudo-distributed mode, HDFS directory, NameNode, Examples of MapReduce, Using Elastic MapReduce, Comparison of local versus EMR Hadoop.

Understanding MapReduce:Key/value pairs,TheHadoop Java API for MapReduce, Writing MapReduce programs, Hadoop-specific data types, Input/output.

Developing MapReduce Programs: Using languages other than Java with Hadoop, Analysing a large dataset.

Lab Exercise

1.      1. Word count application in Hadoop.

2.      2. Sorting the data using MapReduce.

3.      3. Finding max and min value in Hadoop.

Simple, advanced, and in-between Joins, Graph algorithms, using language-independent data structures.

Hadoop configuration properties - Setting up a cluster, Cluster access control, managing the NameNode, Managing HDFS, MapReduce management, Scaling.

Lab Exercise: 

1. Implementation of decision tree algorithms using MapReduce.

 2. Implementation of K-means Clustering using MapReduce.

3. Generation of  Frequent Itemset using MapReduce. 

Hadoop Streaming  -   Streaming  Command  Options - Specifying  a  Java  Class  as  the  Mapper/Reducer - Packaging Files With Job Submissions - Specifying Other Plug-ins for Jobs.

Lab Exercise: 

1.      1. Count the number of missing and invalid values through joining two large given datasets.

2.      2. Using hadoop’s map-reduce, Evaluating Number of Products Sold in Each Country in the online shopping portal. Dataset is given.

3.      3. Analyze the sentiment for product reviews, this work proposes a MapReduce technique provided by Apache Hadoop.

Architecture, Installation, Configuration, Hive vs RDBMS, Tables, DDL & DML, Partitioning & Bucketing, Hive Web Interface, Pig, Use case of Pig, Pig Components, Data Model, Pig Latin.

Lab Exercise

1. Trend Analysis based on Access Pattern over Web Logs using Hadoop.

2. Service Rating Prediction by Exploring Social Mobile Users Geographical Locations.

RDBMS VsNoSQL, HBasics, Installation, Building an online query application – Schema design, Loading Data, Online Queries, Successful service.

Hands On: Single Node Hadoop Cluster Set up in any cloud service provider- How to create instance.How to connect that Instance Using putty.InstallingHadoop framework on this instance. Run sample programs which come with Hadoop framework.

Lab Exercise:

1.      1. Big Data Analytics Framework Based Simulated Performance and Operational Efficiencies Through Billons of Patient Records in Hospital System.

[2] Tom White, Hadoop: The Definitive Guide, O’Reilly Media Inc., 2015.

[3] Garry Turkington, Hadoop Beginner's Guide, Packt Publishing, 2013.

[2] Jonathan R. Owens, Jon Lentz and Brian Femiano, Hadoop Real-World Solutions Cookbook, Packt Publishing, 2013.

[3] Tom White, HADOOP: The definitive Guide, O Reilly, 2012.

ESE - 50%

This course will provide a basic foundation towards digital image processing and video analysis. This course will also provide brief introduction about various Object Detection, Recognition, Segmentation and Compression methods which will help the students to demonstrate real-time image and video analytics applications.

CO2: Apply the image and video analysis approaches to solve real world problems

Digital image representation, Sampling and Quantization, Types of Images, Basic Relations between Pixels - Neighbors, Connectivity, Distance Measures between pixels, Linear and Non Linear Operations, Introduction to Digital Video, Sampled Video, Video Transmission.

Gray-Level Processing: Image Histogram, Linear and Non-linear point operations on Images, Arithmetic Operations between Images, Geometric Image Operations.

Binary Image Processing: Image Thresholding, Region labeling, Binary Image Morphology.

Lab Exercise:

1.   Implement basic gray-scale and binary processing - image histogram, image labeling, image thresholding

2. Implementing Image Database Analysis

Spatial domain - Linear and Non-linear Filtering, Morphological filtering, Frequency domain – Homomorphic Filtering, Blotch Detection and Removal - Blotch Detection, Motion Vector Repair and Interpolating Corrupted Intensities, Intensity Flicker Correction - Flicker Parameter Estimation, Brief introduction towards Wavelets, Wavelet based image denoising, Basic methods for image restoration using deconvolution filters.

Lab Exercise: 

1. Extraction of frames from videos and analyzing frames

2.      Implement spatial domain - linear and non-linear filtering

Image Compression: Huffman coding, Run length coding, LZW coding, Lossless Coding, Wavelets based image compression.

Lab Exercise

1.      1. Frequency domain – homomorphic filtering on gray scale and color images

2.      2. mplement image restoration methods on images

Video Compression: Basic Concepts and Techniques of Video Coding and the H.264 Standard, MPEG-1 and MPEG-2 Video Standards

Lab Exercise:

1.      1. Implement flicker correction on video datasets

2.      2. mplement multi-resolution image decomposition and reconstruction using wavelet

Introduction to feature detectors, descriptors, matching and tracking, Basic edge detectors – canny, sobel, prewitt etc., Image Segmentation - Region Based Segmentation – Region Growing and Region Splitting and Merging, Thresholding – Basic global thresholding, optimum global thresholding using Otsu’s Method.

Lab Exercise: 

1. Implement image compression using wavelets

2.      Implement image segmentation using thresholding

Object detection and recognition in image and video, basic texture descriptors –GLCM, LBP and its applications in image and video analysis, object tracking in videos.

Lab Exercise

1. Implement Local Binary Pattern texture descriptor

[2] Rafael C. Gonzalez and Richard E. Woods, Digital Image Processing, Third Edition, Pearson Education, 2008.

[3] Richard Szeliski, Computer Vision – Algorithms and Applications, Springer, 2011.

[2] Oge Marques, Practical Image and Video Processing Using MatLab, Wiley, 2011.

[3] John W. Woods, Multidimensional Signal, Image, Video Processing and Coding, Academic Press, 2006.

ESE - 50%

The explosive growth of the “Internet of Things” is changing our world and the rapid growth of IoT components is allowing people to innovate new designs and products at home.  Wireless Sensor Networks form the basis of the Internet of Things. To latch on to the applications in the field of IoT of the recent times, this course provides a deeper understanding of the underlying concepts of IoT and Wireless Sensor Networks.

CO2: Apply knowledge on IoT programming to develop IoT applications

CO3: Identify different issues in wireless ad hoc and sensor networks

CO4: Analyse the different sensor network architectures from a design and performance perspective

CO5: Understand the layered approach in sensor networks and WSN protocols

Introduction to IoT - Definition and Characteristics, Physical Design Things- Protocols, Logical Design- Functional Blocks, Communication Models- Communication APIs- Introduction to measure the physical quantities, IoT Enabling Technologies - Wireless Sensor Networks, Cloud Computing Big Data Analytics, Communication Protocols- Embedded System- IoT Levels and Deployment Templates.

lab Exercise:

1. Introduction to ICs and Sensors. A basic program can be shown which makes use of logic gates ICs for understanding the basics of sensor nodes. Different sensors which find application in IoT projects can be shown, their working explained.

2.      Introduction to Arduino/Raspberry Pi. Sample sketches or code can be selected from the Arduino software and executed, making use of different sensors.

Introduction to Smart Systems using IoT - IoT Design Methodology- IoT Boards (Rasberry Pi, Arduino) and IDE - Case Study: Weather Monitoring- Logical Design using Python, Data types & Data Structures- Control Flow, Functions- Modules- Packages, File Handling - Date/Time Operations, Classes- Python Packages of Interest for IoT.

Lab Exercise

1. Use of sensors to detect the temperature/humidity in a room and having appropriate actions performed such as changing the LED color and turning the speaker on as an alarm and using serial monitor to see these values.

2.      A basic parking system making use of multiple IR sensors, Ultrasonic Sensors, LED bulbs, Speakers etc, to identify if a slot is empty or full and using the LED and speakers to alert the user about the availability.

Home Automation – Smart Cities- Environment, Energy- Retail, Logistics- Agriculture, Industry- Health and Lifestyle- IoT and M2M.

Lab Exercise:

1. An Agricultural System (Greenhouse System) that makes use of sensors like humidity, temperature etc, to identify the current situation of the agricultural area and taking necessary measures such as activating the water spraying motor, the alarm system (to indicate if there is excess heat) etc.

2.      Create a basic sound system by making use of knobs, speakers, LED bulbs etc., to mimic the sound produced by a race car, ambulance, siren etc.

Sensing and Sensors - Wireless Sensor Networks, Challenges and Constraints - Applications:  Structural Health Monitoring, Traffic Control, Health Care - Node Architecture - Operating system.

Lab Exercise:

1. A basic obstacle avoiding robot by making use of Ultrasonic sensors, dc motors, and the chassis kit for robotic car.

2.      Making use of GSM for communication in the obstacle avoiding robot. Using sensors such as flame sensors, PIR human motion sensor, IR sensor, LED bulbs etc for better inputs regarding the environment.

3.     A garbage level indicator which makes use of IR proximity sensors, WiFi modules etc to detect the rising amount of garbage and sending data to a server and channelling that data to the owner of the module. Can be introduced as the application IoT. If needed, IoT introduction can be done much earlier and the sharing of data can be shown, for better functionality of later projects.

Introduction – Fundamentals of MAC Protocols – MAC protocols for WSN – Sensor MAC Case Study – Routing Challenges and Design Issues – Routing Strategies – Transport Control Protocols – Transport Protocol Design Issues – Performance of Transport Protocols

Lab Exercise:

1. Elderly care: We want to monitor very senior citizens whether they had a sudden fall. If a very senior citizen falls suddenly while walking, due to stroke or slippery ground etc, a notification should be sent out so that he/she can get immediate medical attention.

2. Smart street lights: The street lights should increase or decrease their intensity based on the actual requirements of the amount of light needed at that time of the day. This will save a lot of energy for the municipal corporation.

3. Implement 3-bit Binary Counter using 3 LED Module. 

1. Glow RED if the Binary bit is '0'.  Glow GREEN if the binary bit is '1'

                                                              i.      For example:

                                                            ii.      000 = 0 (all LED should be RED) 

                                                          iii.      001 = 1 (Two LEDs Should be RED , and one LED should be GREEN) 

                                                          iv.      If Button is pressed in between, Reset the counter and Re-start from 0.

Theft prevention system for night: When the room is dark and Board is moved or tilted (say around 90 degree), it should alarm.

[2] KazemSohraby, Daniel Minoli and TaiebZnati, Wireless Sensor Networks: Technology. Protocols and Application, Wiley Publications, 2010.

[3] WaltenegusDargie and Christian Poellabauer, Fundamentals of Wireless Sensor Networks: Theory and Practice, AJohn Wiley and Sons Ltd., 2010.

[2] Michael Miller, The Internet of Things, Pearson Education, 2015.

[3] Holger Karl and Andreas Willig, Protocols and Architectures for Wireless Sensor Networks, John Wiley & Sons Inc., 2005.

[4] ErdalÇayırcıandChunmingRong, Security in Wireless Ad Hoc and Sensor Networks, John Wiley and Sons, 2009.

[5] Carlos De MoraisCordeiro and Dharma PrakashAgrawal, Ad Hoc and Sensor Networks: Theory and Applications, World Scientific Publishing, 2011.

[6] WaltenegusDargie and Christian Poellabauer, Fundamentals of Wireless Sensor Networks Theory and Practice, John Wiley and Sons, 2010

[7] Adrian Perrig and J. D. Tygar, Secure Broadcast Communication: In Wired and Wireless Networks, Springer, 2006.

ESE - 50%

This research inclusive curriculum is designed with two main objectives:

1. Inculcating research culture among the post graduate students.

2.Enhancing employability skills of students by providing necessary research foundation

CO2: Understand the basics of research data collection and research paper writing.

There is only CIA for this course. Students should do a thorough literature review in their research area. They should give a presentation and submit a document containing the following:

Introduction to topic, existing scenario and applications (5 marks)

Literature review  (Minimum 25 references) (15 marks)

Existing Model and Methodology (5 marks)

Concrete problem statement definition (10 marks)

ESE - 50%