Gradient Descent in Spark ML for Linear Regression: The Apache Spark ML library predominantly employs gradient descent for linear regression, particularly with very large datasets. This optimization algorithm iteratively refines model parameters to reduce the cost function, often the mean squared error in linear regression scenarios. Its scalability and efficiency with large datasets stem from its ability to update model parameters incrementally, bypassing the need for simultaneous computation of the entire dataset. This makes it ideal for distributed computing frameworks like Spark.

Other Methods:

• Matrix Decomposition and Singular Value Decomposition (Options A & E): While applicable, these methods are less efficient for vast datasets due to their computational intensity.
• Least Square Method (Option B): Traditional yet computationally demanding for large datasets, as it involves extensive matrix operations that may not scale efficiently in distributed systems.
• Brute Force Algorithm (Option D): Impractical for large datasets owing to its inefficiency.

Gradient descent stands out in Spark ML for large-scale data processing, thanks to its scalability and efficiency, enabling distributed computation.