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What is dimensionality reduction?
What is dimensionality reduction?
The process of reducing the number of input features in a dataset while preserving similar information.
Which of the following are fields of usage for dimensionality reduction? (Select all that apply)
Which of the following are fields of usage for dimensionality reduction? (Select all that apply)
What is Feature Extraction?
What is Feature Extraction?
What are the two types of Factor Analysis?
What are the two types of Factor Analysis?
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KMO measure is used to assess the appropriateness of using factor analysis on a dataset.
KMO measure is used to assess the appropriateness of using factor analysis on a dataset.
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What is a common application of Factor Analysis in marketing research?
What is a common application of Factor Analysis in marketing research?
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What does a KMO value below 0.6 indicate?
What does a KMO value below 0.6 indicate?
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Match the following terms with their definitions:
Match the following terms with their definitions:
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Study Notes
Dimensionality Reduction
- A process of converting a high-dimensional dataset into a lower dimensional dataset, preserving similar information.
- Used for training machine learning algorithms.
- Applied in various fields including speech recognition, signal processing, bioinformatics, data visualization, noise reduction, cluster analysis.
Dimensionality Reduction Techniques
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Feature Selection
- Filter Methods
- Wrapper Methods
- Intrinsic/ Embedded Methods
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Feature Extraction
- PCA (Principal Component Analysis)
- Factor Analysis
- Singular Value Decomposition
Feature Extraction
- A part of dimensionality reduction, where raw data is divided into manageable groups.
- Involves mapping original features into a lower dimensional space, expressing them as a function of the feature set.
- Lower dimensions should be uncorrelated.
- Features extracted from images, text, geospatial data, date and time, web data, sensor data.
Factor Analysis
- An interdependence technique that analyzes correlations between variables to reduce them into fewer factors, explaining much of the original data.
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Assumptions:
- Variables must be related, with sufficient correlations (Bartlett's test).
- A minimum sample size of 50, preferably 100, and a minimum of 5 observations per item, preferably 10 observations per item.
Types of Factor Analysis
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Exploratory Factor Analysis (EFA)
- Uses Principal Component Analysis (PCA/ Thurstone)
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Confirmatory Factor Analysis (CFA)
- Uses Structural Equations Modelling (SEM)
Issues with Factor Analysis
- Overloading: Identifies variables with the lowest communality and deletes them to address loading.
- Cross Loading: The proportion of variance in a single variable that is captured by extracted factors is known as communality.
Factor Analysis Explained
- Factor: A linear composite of variables.
- Factor Score: The score on a given factor.
- Eigen Value: Represents the sum of squares of variables for a factor loading. Eigen values less than 1 are usually omitted.
- Scree Plot: A graphical representation used in factor analysis that helps determine the optimal number of factors to retain.
- Factor Rotation: A technique used in factor analysis to improve the interpretability of the factors.
Steps of Factor Analysis
- Load data.
- Run the factor analysis.
Outputs of Factor Analysis
- Correlation Matrix.
- Bartlett's Test of Sphericity: Tests the null hypothesis that the variables in the population correlation matrix are uncorrelated.
- KMO (Kaiser-Meyer-Olkin): Measure of sampling adequacy; values between 0.8 and 1 indicate adequate sampling.
- Communalities: The proportion of variance in each original variable that is accounted for by the extracted factors.
- Total Variance.
- Scree Plot.
- Component Matrix.
- Rotated Component Matrix.
KMO and Bartlett's Test
- KMO values between 0.8 and 1 suggest adequate sampling.
- Values less than 0.6 (0.5 to 0.6) imply inadequate sampling.
- Values closer to 0 indicate more partial correlations than total correlations, which is not suitable for factor analysis.
Scree Plot
- A graphical representation of the eigenvalues, plotted against the factor number in descending order.
- Used to determine the appropriate number of factors to retain.
Applications of Factor Analysis
- In marketing research, to understand consumer motives for purchasing products or brands.
- To identify the most important attributes of products or services in the minds of customers.
- Example: A two-wheeler manufacturer uses factor analysis to determine variables potential customers consider when evaluating their product.
Example: Teacher Characteristics
- A school system surveyed 120 students to rate the importance of 9 teacher characteristics using a Likert scale (1-10).
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Characteristics rated
- Setting high expectations.
- Entertaining.
- Able to communicate effectively.
- Having expertise in their subject.
- Able to motivate.
- Caring.
- Charismatic.
- Having a passion for teaching.
- Friendly and easy-going.
Factor Analysis Application for Teacher Characteristics
- Identify the number of factors.
- Group variables into respective factors.
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Description
Explore the essential techniques of dimensionality reduction, focusing on feature selection and extraction methods. Learn about PCA, factor analysis, and their applications in various fields such as machine learning and data visualization. Test your knowledge with this quiz on critical concepts and methodologies used in managing high-dimensional datasets.
