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What is Zero Mean and Unit Variance Normalization

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:

Advantages of Zero Mean and Unit Variance Normalization:

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.



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