Math Problem Statement
What will be the information loss in dimensionality reduction using Principal Components Analysis (PCA) when eigen values are roughly equal?
a. Information loss will be more
b. Information loss will be minimum
c. Can't say anything based on eigen value
d. There will be no information loss
Oa)
b)
Oc)
Od)
1 point
Which of the following are true for Principal Components Analysis (PCA)?
-
Parameter initialization is required
-
Parameter initialization is not required.
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PCA can fall into local minima
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PCA cannot fall into local minima
Solution
Question 1: Information Loss in Dimensionality Reduction using PCA
When eigenvalues are roughly equal, this means that each principal component explains approximately the same amount of variance in the data. Therefore, the distribution of information across dimensions is even, and discarding some components (in the process of dimensionality reduction) could lead to a significant loss of information. The answer is:
a) Information loss will be more
Question 2: True Statements about Principal Components Analysis (PCA)
- PCA does not involve an optimization process where parameters need to be initialized, so parameter initialization is not required.
- PCA is a deterministic method and does not involve any iterative processes that could lead to local minima, as it is based on linear algebra.
Thus, the correct answers are:
2. Parameter initialization is not required.
4. PCA cannot fall into local minima.
Do you want any further details on the reasoning behind these answers?
Here are 5 related questions for further study:
- How do eigenvalues and eigenvectors relate to the principal components in PCA?
- What is the purpose of standardizing data before applying PCA?
- How do we determine the number of principal components to retain in PCA?
- What is the difference between PCA and Linear Discriminant Analysis (LDA)?
- Can PCA be used for classification tasks?
Tip: When eigenvalues are close to each other, reducing dimensions may discard essential information, so carefully analyze eigenvalue magnitudes when applying PCA.
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Math Problem Analysis
Mathematical Concepts
Dimensionality Reduction
Principal Components Analysis (PCA)
Eigenvalues and Eigenvectors
Formulas
Covariance matrix formula
Eigenvalue decomposition
Theorems
Principal Component Theorem
Suitable Grade Level
Undergraduate Level