Compare LDA with PCA. Choose what is true about LDA and PCA.
\text {LDA}: \text {PCA}:
(Choose all that apply.)
The projection is linear.
It needs data that have class labels.
The dimension of the target space is always smaller than k where k is the number of classes of data
unanswered
The projection is linear.
It needs data that have class labels.
The dimension of the target space is always smaller than k where k is the number of classes of data
unanswered
Both LDA and PCA have a linear projection, require data with class labels, and the dimension of the target space is always smaller than k where k is the number of classes of data.
The statements that are true about LDA and PCA are:
- The projection is linear.
- LDA needs data that have class labels.
- PCA does not require class labels.
- The dimension of the target space in LDA is typically smaller than the number of classes (k) in the data.
To compare LDA (Linear Discriminant Analysis) with PCA (Principal Component Analysis), let's discuss each statement individually.
1. The projection is linear:
- This statement is true for both LDA and PCA. Both methods perform linear transformations on the data.
2. It needs data that have class labels:
- This statement is true for LDA, but not for PCA. LDA is a supervised learning algorithm that requires labeled data, where each sample is assigned a specific class. In contrast, PCA is an unsupervised learning algorithm that does not require class labels and operates purely based on the data's variance.
3. The dimension of the target space is always smaller than k, where k is the number of classes of data:
- This statement is true for LDA. LDA aims to find a lower-dimensional representation of the data while maximizing the class separability. The number of resulting dimensions in LDA is at most k-1, where k is the number of classes. Each dimension represents a discriminant function. In contrast, PCA does not consider class labels, and the resulting dimensions may not be directly related to class separability.
In summary, the correct statements about LDA and PCA are:
- The projection is linear.
- LDA needs data that have class labels.
- The dimension of the target space in LDA is always smaller than k, where k is the number of classes.