Data Science and Machine Learning (Theory and Projects) A to Z - Mathematical Foundation: SubSpace
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Mathematics
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11th - 12th Grade
•
Hard
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10 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is a key property of a vector space?
It is open under scalar multiplication.
It is closed under linear combinations.
It is closed under addition only.
It is open under linear combinations.
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the context of data science, what type of vector spaces are most commonly used?
Hyperbolic vector spaces
Spherical vector spaces
Euclidean vector spaces
Cylindrical vector spaces
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does it mean if data lies in a D-dimensional space?
The data has D features.
The data has D data points.
The data has D subspaces.
The data has D bases.
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the benefit of finding a subspace where data lies?
It reduces the number of data points.
It increases the number of dimensions.
It makes data more complex.
It allows for data compression.
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How can data be reconstructed after compression?
By using the original data points.
By using the basis vectors and coefficients.
By using the compressed data only.
By using a different set of basis vectors.
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is a nonlinear manifold?
A linear structure in a high-dimensional space.
A nonlinear structure in a high-dimensional space.
A nonlinear structure in a low-dimensional space.
A linear structure in a low-dimensional space.
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the role of local subspaces in unfolding a manifold?
They eliminate the need for a manifold.
They decrease the data points.
They provide a linear approximation.
They increase the dimensionality.
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