SRM Section 6 Study Guide 100% Guaranteed Pass.
Unsupervised learning - Analyzes data without a response variable
Principal components analysis (PCA) - A statistical tool that finds a low-dimensional representation of
a dataset that contains as much information from the dataset as possible.
In other words, it aims to reduce the number of variables (features) in a dataset by finding the first
few principal components that explain a sufficient amount of variability in the dataset. Principal
components are new variables calculated using the original features in an attempt to best summarize
the dataset.
You are given:
A principal component analysis is performed on a dataset with 20 features and 500 observations.
All features in the dataset are continuous variables, which have been standardized.
ϕj,m is the mth principal component loading for the jth feature.
Determine which of the following statements is true.
I. There are at most 20 distinct principal components.
II. The sum of squares of the principal component loadings for the first feature is one.
III. The sample covariance of the first principal component scores and the sixth principal component
scores is one. - Only I is true.
I is true. With a dataset with p features and n observations, a maximum of min(n−1,p) principal
components can be created. Hence, we can create a maximum of min(500−1,20)=20 principal
components.
II is false. In fact, it is the sum of squares of the first principal component loadings across ALL features
that is equal to one.
III is false. All principal components are uncorrelated with one another. This means that the sample
covariance between the principal component scores is zero.
https://www.stuvia.com/
, Maximum number of principal components - Max of min(n-1,p).
p features and n observations
T/F: Principal components are not correlated with one another. - True.
T/F: The first principal component explains the largest portion of variability in a dataset - True.
Therefore, its variance will be greater than all of the following components.
Sum of squares of principal loading components must be equal to: - 1
What is the shortest distance from the observation to the sample mean? - The first principal
component score is the z1-distance from the observation to the sample mean of the first feature.
This distance is also the shortest (perpendicular) distance from the observation to the second
principal component in a two-dimensional setting.
Scree plot - Shows the proportion of variance explained by each principal component
-Can be used to determine the number of components to use
How to find amount of variance explained by each principle component: - Square the component's
standard deviation
Derived principal components are orthogonal, which means: - that they are uncorrelated. PCA, in
essence, transforms correlated features into uncorrelated principal components.
Uses of PCA - PCA provides a low-dimensional representation of a dataset. This further serves as a
dimension reduction technique in regression — principal component regression.
PCA can be used as a data visualization tool.
https://www.stuvia.com/
Unsupervised learning - Analyzes data without a response variable
Principal components analysis (PCA) - A statistical tool that finds a low-dimensional representation of
a dataset that contains as much information from the dataset as possible.
In other words, it aims to reduce the number of variables (features) in a dataset by finding the first
few principal components that explain a sufficient amount of variability in the dataset. Principal
components are new variables calculated using the original features in an attempt to best summarize
the dataset.
You are given:
A principal component analysis is performed on a dataset with 20 features and 500 observations.
All features in the dataset are continuous variables, which have been standardized.
ϕj,m is the mth principal component loading for the jth feature.
Determine which of the following statements is true.
I. There are at most 20 distinct principal components.
II. The sum of squares of the principal component loadings for the first feature is one.
III. The sample covariance of the first principal component scores and the sixth principal component
scores is one. - Only I is true.
I is true. With a dataset with p features and n observations, a maximum of min(n−1,p) principal
components can be created. Hence, we can create a maximum of min(500−1,20)=20 principal
components.
II is false. In fact, it is the sum of squares of the first principal component loadings across ALL features
that is equal to one.
III is false. All principal components are uncorrelated with one another. This means that the sample
covariance between the principal component scores is zero.
https://www.stuvia.com/
, Maximum number of principal components - Max of min(n-1,p).
p features and n observations
T/F: Principal components are not correlated with one another. - True.
T/F: The first principal component explains the largest portion of variability in a dataset - True.
Therefore, its variance will be greater than all of the following components.
Sum of squares of principal loading components must be equal to: - 1
What is the shortest distance from the observation to the sample mean? - The first principal
component score is the z1-distance from the observation to the sample mean of the first feature.
This distance is also the shortest (perpendicular) distance from the observation to the second
principal component in a two-dimensional setting.
Scree plot - Shows the proportion of variance explained by each principal component
-Can be used to determine the number of components to use
How to find amount of variance explained by each principle component: - Square the component's
standard deviation
Derived principal components are orthogonal, which means: - that they are uncorrelated. PCA, in
essence, transforms correlated features into uncorrelated principal components.
Uses of PCA - PCA provides a low-dimensional representation of a dataset. This further serves as a
dimension reduction technique in regression — principal component regression.
PCA can be used as a data visualization tool.
https://www.stuvia.com/
