Mathematics

• Mean and Covariance
• Statistical Independent inference
• Correlation (Pearson coefficient)
• Correlation matrix & covariance matrix
• K-L Divergence
• mutual information measure
• entropy
• Correlation Matrix Diagonalization
• Eigenvector and Eigenvalue

Chapter 2

• Bayes Rule
• Minimizing the Classification Error Probability & minimizing the average risk
• Bayesian classification for normal distributions , Example 2.2
• MLE/MAP, Example 2.4, 2.5
• Nonparametric Estimation – K-Nearest neighbours, Example 2.9
• Problem 2.2: minimizing the average risk
• Problem 2.29: ML with the lognormal distribution

Chapter 3

• Perceptron Algorithm and its Geometry Explanation
• v-SVM Inference

Chapter 4

• Multilayer Perceptron Network
• BP Network, Computation of the Gradients, Algorithm
• Problem 4.3: multilayer perceptron based on cube vertexes

Chapter 5

Statistical Hypothesis Testing:

• The Known Variance Case: Example 5.1
• The Unknown Variance Case: Example 5.2
• t-Test for the feature significance: Example 5.3

Chapter 6

• K-L transform and PCA, SVD
• Problem 6.3, 6.5

Chapter 9: Context-Dependent (PR07)

• The Viterbi algorithm and Example 9.1

Cluster(PR08)

• Proximity measures between two points:

  • Real-Valued Vectors(DM/SM), Discrete-Valued Vectors (DM/SM)

• Proximity functions between a point and a set : Example 11.9, 11.10

• Problem 11.2

• BSAS, MBSAS, TTSAS and final refined algorithm in 12.6

• Example 12.3, Problem 12.3