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?

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Explain the relationship between vector spaces and linear combinations.

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

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How does dimensionality reduction relate to subspaces?

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How can data be compressed using the concept of subspaces?

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

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Describe the process of finding the basis of a subspace.

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

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

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

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