Answer: Zero Mean and Unit Variance normalization rescale data to have a mean of zero and a standard deviation of one.

Explanation:

1. Mean Centering: The first step of Zero Mean normalization involves subtracting the mean value of each feature from all data points. This centers the data around zero, meaning that the new mean of the feature becomes zero.
2. Scaling to Unit Variance: The second step involves dividing each centered feature by its standard deviation. This scales the data so that the variance of each feature becomes one, hence the term “Unit Variance.”

Mathematically, for a feature x, the Zero Mean and Unit Variance normalization can be expressed as follows:

Where:

• x is the original feature.
• μ is the mean of the feature.
• σ is the standard deviation of the feature.

Advantages of Zero Mean and Unit Variance Normalization:

• Improved Performance: Normalizing features helps algorithms converge faster and prevents certain features from dominating others.
• Robustness to Scale: It makes the algorithm less sensitive to the scale of features, ensuring that the optimization process behaves consistently across different features.
• Interpretability: Normalized features are easier to interpret as they are centered around zero and have a standard deviation of one.
• Better Handling of Outliers: It reduces the impact of outliers by shrinking the range of values and making the distribution more Gaussian-like.

Implementation:

1. Calculate the mean and standard deviation of each feature from the training data.
2. Subtract the mean from each feature and divide it by its standard deviation for both the training and test datasets.
3. Ensure the normalization parameters (mean and standard deviation) are preserved for scaling the test data.

Zero Mean and Unit Variance normalization is widely used in various machine learning algorithms, especially those that rely on distance-based metrics or gradient descent optimization, such as support vector machines, k-nearest neighbors, and neural networks. It facilitates better convergence, enhances model interpretability, and improves overall performance.