Data Science and Machine Learning (Theory and Projects) A to Z - Mathematical Foundation: SubSpace

The video tutorial explains the concept of subspace in vector spaces, emphasizing its importance in data science, particularly in dimensionality reduction. It discusses how data can lie in a subspace with fewer dimensions than the original space, allowing for data compression. The tutorial also covers the process of finding the basis of a subspace and touches on the concept of nonlinear manifolds, which may require different approaches for dimensionality reduction.

What is the definition of a subspace in the context of vector spaces?

Explain the relationship between vector spaces and linear combinations.

What are the properties that a subset must have to be considered a subspace?

How does dimensionality reduction relate to subspaces?

How can data be compressed using the concept of subspaces?

What is the significance of basis vectors in the context of subspaces?

Describe the process of finding the basis of a subspace.

Discuss the implications of data lying on a nonlinear manifold instead of a subspace.

Explain the concept of local subspaces in the context of nonlinear dimensionality reduction.

What challenges arise when data does not lie perfectly on a linear subspace?