1. Basics of Probability, Random Processes and Linear Algebra (recap) : Probability : independence of events, conditional and joint probability, Bayes theorem Random Processes : Stationary and non-stationary processes, Expectation, Autocorrelation, Cross-Correlation, spectra. (Chapter - 1) 2. Linear Algebra : Inner product, outer product, inverses, eigen values, eigen vectors, singular values, singular vectors. (Chapter - 2) 3. Bayes Decision Theory : Minimum-error-rate classification. Classifiers, Discriminant functions, Decision surfaces. Normal density and discriminant functions. Discrete features. (Chapter - 3) 4. Parameter Estimation Methods : Maximum-Likelihood Estimation : Gaussian case. Maximum a Posteriori estimation. Bayesian estimation: Gaussian case. Unsupervised learning and clustering - Criterion functions for clustering. Algorithms for clustering : K-Means, Hierarchical and other methods. Cluster validation. Gaussian mixture models, Expectation-Maximization method for parameter estimation. Maximum entropy estimation. Sequential Pattern Recognition. Hidden Markov Models (HMMs). Discrete HMMs. Continuous HMMs. Nonparametric techniques for density estimation, K-Nearest Neighbour method. (Chapter - 4) 5. Dimensionality reduction : Principal component analysis - it relationship to Eigen analysis. Fisher discriminant analysis - Generalized Eigen analysis. Eigen vectors/Singular vectors as dictionaries. Factor Analysis, Total variability space - a dictionary learning methods. Non negative matrix factorization - a dictionary learning method. (Chapter - 5) 6. Linear discriminant functions : Gradient descent procedures, Perceptron, Support vector machines - a brief introduction. (Chapter - 6) 7. Artificial neural networks : Multilayer perceptron - feed forward neural network. A brief introduction to deep neural networks, convolutional neural networks, recurrent neural networks. (Chapter - 7) 8. Non-metric methods for pattern classification : Non-numeric data or nominal data. Decision trees : Classification and Regression Trees (CART). (Chapter - 8)
