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)

10)

1 point

Which of the following are true for Principal Components Analysis (PCA)?

1. Parameter initialization is required

2. Parameter initialization is not required.

3. PCA can fall into local minima

4. PCA cannot fall into local minima

### 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.**

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Do you want any further details on the reasoning behind these answers?  

Here are 5 related questions for further study:

1. How do eigenvalues and eigenvectors relate to the principal components in PCA?
2. What is the purpose of standardizing data before applying PCA?
3. How do we determine the number of principal components to retain in PCA?
4. What is the difference between PCA and Linear Discriminant Analysis (LDA)?
5. 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.

What will be the information loss in dimensionality reduction using Principal Components Analysis (PCA) when eigenvalues are roughly equal? Which of the following are true for Principal Components Analysis (PCA)?

Explore how information loss occurs in Principal Components Analysis (PCA) when eigenvalues are roughly equal and understand true statements about PCA, including the need for parameter initialization and the possibility of local minima. Suitable for undergraduate students studying dimensionality reduction techniques.

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