LC4_2023 - Unsupervised learning

The goals of PCA are…

• • …to identify underlying dimensions that explain correlations among variables.

• …to identify multiplicative effects in a linear regression.

• …to identify a smaller set of uncorrelated variables.

• …to identify interaction terms in a linear regression.

• None of these

What are typical hypotheses in PCA concerning how many factors will emerge?

• A reduction greater than 50% of the input variables

• Between a third and a fourth of the input variables

• A reduction smaller than 50% of the input variables

• None of these

What assumptions have to be fulfilled for using PCA?

• Variables must be in interval or ratio scale

• • Existence of some underlying factor structure

• The correlation matrix must have sufficient number of correlations

• Variables must be measured using ordinal scales

• None of these

• Regression coefficients

• Correlations between the variables

• • Weights of a variable on a factor

• • Factor loadings

• None of these

What is communality?

• Proportion of common variance in a variable

• Variance that is unique to a particular variable

• • Proportion of unique variance in a variable

• • Covariance between two factors

• None of these

Orthogonal factor rotation assumes:

• • Inter-correlated factors

• Uncorrelated factors

• • Outer-correlated factors

• None of these

Which of the following statements regarding cluster analysis are TRUE?

• • The goal is to reduce the number of columns in a data set

• The goal is to reduce the number of rows in a data set

• • H-Means is a popular clustering method

• • The goal is to establish a relationship between a dependent variable and an independent variable

• The goal is to group observations into clusters such that those in the same cluster are more “similar” than those of other clusters

What is the main objective of k-means clustering in data analysis?

• To find the best-fitting linear regression model

• To identify underlying factors that explain correlations among variables

• To partition data into clusters based on similarity

• To calculate the correlation between variables

• None of these

In the k-means algorithm, what does “k” represent?

• • The number of variables in the dataset

• The number of clusters to be formed

• The number of iterations to converge

• The number of outliers in the data

• None of these

What is the primary limitation of the k-means clustering algorithm?

• It is computationally expensive

• It requires specifying the number of clusters in advance

• It cannot handle categorical data

• It always produces spherical clusters

• None of these