Question

1.  What do you mean by Principal Component?

2. Write the differences between first and last principal component?

3. Why KNN algorithms is said to work better on small data sets?
   

Answer 1

Answer to Q1

Principal component analysis, or PCA is a statistical procedure that allows you summarise the information content in large data tables by means of a smaller set of “summary indices” that can be more easily visualised and analysed

Or in other words we say that Principal component is dimensionality reduction method that is usually used to reduce large number of input variables to a small number of variables that still contains most of information as a large dataset.

There are several steps in computing Principal Componen :

Feature standardisation.

Obtain the covariance matrix.

Calculate the Eigen decomposition of the covariance matrix.

Sort the Eigen vectors from the highest Eigen value to the lowest

Select the number of principal components

Answer to Q2

First principal component	Last principal component
1. It explains the common set among variables	1. It explains total variance among the set of variable
2. It tries to identify unknown latent variables to explain the orignal data	2. It is used to reduce the number of variables by creating principal components
3. It find one or more common factors that account for the corelations between the observed variables	3. It have component are the lnear combination of variables that account as much variance as possible
4. It have Number of factors necessaily less than vriance	4. It Extracts as many component as there variables

Answer to Q3

KNN algorithms is said to work better on small data sets becouse KNN algorithm is a good choice if you have a small data sets and the data is noise free and labeled. When the data set is small, the classifier completes execution in shorter time duration.

If your dataset is large, then KNN, without any hacks, is of no use.