Principal Component Analysis
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Slides used to present an overview on Principal Component Analysis during a analytics group meeting at TWBR.
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Principal Component Analysis
- 2. 2 Feature Engineering (Our motivation) Introduction to Principal Component Analysis (And some statistical concepts) Agile Analytics and PCA (Helping visualization…) Agenda
- 4. 4 Given a classification problem… How do we choose the right features?
- 5. 5 Intuition fails in high dimensions Building a classifier in two or three dimensions is relatively easy… It’s usually possible to find a reasonable frontier between examples of different classes just by visual inspection.
- 6. 6 Feature engineering Intuitively, one might think that gathering more features never hurts, right? At worst they provide no new information about the domain…
- 7. 7 The curse of dimensionality Many algorithms that work fine in low dimensions become intractable when the input is high-dimensional. Bellman, 1961
- 8. 8 How do we solve it? Feature Selection Feature Extraction
- 9. 9 Feature extraction “In most applications examples are not spread uniformly throughout the examples space, but are concentrated on or near a lower-dimensional subspace.”
- 11. 11 Objective of PCA To perform dimensionality reduction while preserving as much of the randomness in the high-dimensional space as possible
- 12. 12 Principal Component Analysis It takes your cloud of data points, and rotates it such that the maximum variability is visible. PCA is mainly concerned with identifying correlations in the data.
- 13. 13 Measuring Correlation Degree and type of relationship between any two or more quantities (variables) in which they vary together over a period Correlation can vary from +1 to -1. Values close to +1 indicate a high- degree of positive correlation, and values close to -1 indicate a high degree of negative correlation. Values close to zero indicate poor correlation of either kind, and 0 indicates no correlation at all
- 15. 15 Beware: Correlation does not imply causation
- 16. 16 Correlation matrix It shows at a glance how variables correlate with each other
- 18. 18 Steps for PCA 1. Standardize the data 2. Calculate the covariance matrix 3. Find the eigenvalues and eingenvectors of the covariance matrix 4. Plot the eigenvectors / principal components over the scaled data
- 19. 19 Demo with R Let’s check the products of PCA…
- 21. 21 Agile Analytics Machine learning and data mining tools and techniques + Knowledge of the domain at hand + Short feedback cycles
- 22. 22 Agile Analytics We could use PCA as a tool to quickly identify correlation between features, helping feature extraction and selection. Reducing dimensionality using PCA or other similar technique can help us achieve better and quicker results.
- 23. 23 QA & Next Steps 23