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# Machine Learning – Dimensionality Reduction Cognitive Class Exam Quiz Answers

## Machine Learning – Dimensionality Reduction Cognitive Class Certification Answers

Question 1: Which of the following techniques can be used to reduce the dimensions of the population?

• Exploratory Data Analysis
• Principal Component Analysis
• Exploratory Factor Analysis
• Cluster Analysis

Question 2: Cluster Analysis partitions the columns of the data, whereas principal component and exploratory factor analyses partition the rows of the data. True or false?

• False
• True

Question 3: Which of the following options are true? Select all that apply.

• PCA explains the total variance
• EFA explains the common variance
• EFA identifies measures that are sufficiently similar to each other to justify combination
• PCA captures latent constructs that are assumed to cause variance

Question 1: Which of the following options is true?

• A matrix of correlations describes all possible pairwise relationships
• Eigenvalues are the principal components
• Correlation does not explain the covariation between two vectors
• Eigenvectors are a measure of total variance, as explained by the principal components

Question 2: PCA is a method to reduce your data to the fewest ‘principal components’ while maximizing the variance explained. True or false?

• False
• True

Question 3: Which of the following techniques was NOT covered in this lesson?

• Parallel analysis
• Percentage of Common Variance
• Scree Test
• Kaiser-Guttman Rule

Question 1: EFA is commonly used in which of the following applications? Select all that apply.

• Customer satisfaction surveys
• Personality tests
• Performance evaluations
• Image analysis

Question 2: Which of the following options is an example of an Oblique Rotation?

• Regmax
• Varimax
• Softmax
• Promax

Question 3: An Orthogonal Rotation assumes that factors are correlated with each other. True or false?

• False
• True

Question 1: Why might you use cluster analysis as an analytic strategy?

• To identify higher-order dimensions
• To identify outliers
• To reduce the number of variables
• To segment the market
• None of the above

Question 2: Suppose you have 100,000 individuals in a dataset, and each individual varies along 60 dimensions. On average, the dimensions are correlated at r = .45. You want to group the variables together, so you decide to run principle component analysis. How many meaningful, higher-order components can you extract?

• 60
• 3
• 20
• 24
• The answer cannot be determined

Question 3: What technique should you use to identify the dimensions that hang together?

• Principal axis factoring
• Confirmatory factor analysis
• Exploratory factor analysis
• Two of the above
• None of the above

• Covariance between the two factors
• Correlations between each variable and its factor
• Correlations between each variable and its component
• Two of the above
• None of the above

Question 5: When would you use PCA over EFA?

• When you want to use an orthogonal rotation
• When you are interested in explaining the total variance in a variance-covariance matrix
• When you have too many variables
• When you are interested in a latent construct
• None of the above

Question 6: What is uniqueness?

• A measure of replicability of the factor
• The amount of variance not explained by the factor structure
• The amount of variance explained by the factor structure
• The amount of variance explained by the factor
• None of the above

Question 7: Suppose you are looking to extract the major dimensions of a parrot’s personality. Which technique would you use?

• Maximum likelihood
• Principal component analysis
• Cluster analysis
• Factor analysis
• None of the above

Question 8: Suppose you have 60 variables in a dataset, and you know that 2 components explain the data very well. How many components can you extract?

• 45
• 5
• 60
• 2
• None of the above

Question 9: When would you use an orthogonal rotation?

• When correlations between the variables are large
• When you observe small correlations between the variables in the dataset
• When you think that the factors are uncorrelated
• All of the above
• None of the above

Question 10: When would you use confirmatory factor analysis?

• When you want to validate the factor solution
• When you want to explain the variance in the matrix accounting for the measurement error
• When you want to identify the factors
• Two of the above
• None of the above

Question 11: Which of the following is NOT a rule when deciding on the number of factors?

• Newman-Frank Test
• Percentage of common variance explained
• Scree test
• Kaiser-Guttman
• None of the above

Question 12: What is one assumption of factor analysis?

• A number of factors can be determined via the Scree test
• Factor analysis will extract only unique factors
• A latent variable causes the variance in observed variables
• There is no measurement error
• None of the above

Question 13: What is an eigenvector?

• The proportion of the variance explained in the matrix
• A higher-order dimension that subsumes all of the lower-order errors
• A higher-order dimension that subsumes similar lower-order dimensions
• A higher-order dimension that subsumes all lower-order dimensions
• None of the above

Question 14: What is a promax rotation?

• A rotation method that minimizes the square loadings on each factor
• A rotation method that maximizes the variance explained
• A rotation method that maximizes the square loadings on each factor
• A rotation method that minimizes the variance explained
• None of the above

Question 15: What is the cut-off point for the Common Variance Explained rule?

• 80% of variance explained
• 50% of variance explained
• 3 variables
• 1 unit
• None of the above

Question 16: Why would you try to reduce dimensions?

• Individuals need to be placed into groups
• Variables are highly-correlated
• Many variables are likely assessing the same thing
• Two of the above
• All of the above

Question 17: If you have 20 variables in a dataset, how many dimensions are there?

• At most 20
• At least 20
• As many as the number of factors you can extract
• Not enough information
• None of the above

Question 18: What term describes the amount of variance of each variable explained by the factor structure?

• Eigenvector
• Commonality
• Similarity
• Communality
• None of the above

Question 19: What package contains the necessary functions to perform PCA and EFA?

• ggplot2
• FA
• psych
• factAnalis
• None of the above

Question 20: What is the best method for identifying the number of factors to extract?

• Parallel Analysis
• Scree test
• Newman-Frank Test
• Percentage of common variance explained
• All of the above

## Introduction to Machine Learning – Dimensionality Reduction

Dimensionality reduction is a crucial technique in the field of machine learning, particularly when dealing with high-dimensional data. In essence, it’s about simplifying data by reducing its dimensionality while retaining its most important features. This process not only helps in visualizing and understanding complex data but also aids in improving the performance of machine learning algorithms by mitigating the curse of dimensionality.

Here are some key points to understand about dimensionality reduction:

1. Curse of Dimensionality: As the number of features or dimensions in the dataset increases, the amount of data required to generalize accurately grows exponentially. This phenomenon, known as the curse of dimensionality, leads to increased computational complexity and can cause machine learning algorithms to overfit or perform poorly.
2. Motivation for Dimensionality Reduction: Dimensionality reduction addresses the challenges posed by the curse of dimensionality by transforming high-dimensional data into a lower-dimensional space. This not only reduces computational complexity but also helps in visualizing data and removing redundant or irrelevant features, which can improve the performance of machine learning models.
3. Types of Dimensionality Reduction Techniques:
• Feature Selection: Involves selecting a subset of the original features while discarding the rest based on certain criteria such as relevance, importance, or correlation with the target variable.
• Feature Extraction: Involves transforming the original features into a lower-dimensional space using techniques like Principal Component Analysis (PCA), Singular Value Decomposition (SVD), or t-distributed Stochastic Neighbor Embedding (t-SNE). These techniques aim to capture the most important information in the data while discarding less relevant or noisy features.
4. Principal Component Analysis (PCA): PCA is one of the most widely used techniques for dimensionality reduction. It works by transforming the data into a new coordinate system such that the greatest variance lies along the first axis (principal component), the second greatest variance along the second axis, and so on. By retaining only the top principal components, PCA effectively reduces the dimensionality of the data while preserving as much variance as possible.
5. Applications of Dimensionality Reduction: Dimensionality reduction finds applications in various domains such as image and signal processing, natural language processing, bioinformatics, and more. It is particularly useful in tasks such as classification, clustering, visualization, and feature engineering.

In summary, dimensionality reduction is a fundamental technique in machine learning for simplifying high-dimensional data, mitigating the curse of dimensionality, and improving the performance of models. By selecting or extracting the most informative features, it enables more efficient computation, better visualization, and enhanced model generalization.