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Principal Component Analysis
The document discusses Principal Component Analysis (PCA) as a feature engineering technique aimed at reducing dimensionality while preserving data variability. It highlights the challenges posed by high-dimensional data and how PCA helps in identifying correlations among variables to enhance classification tasks. The document also outlines the steps to perform PCA and emphasizes its utility in agile analytics for improving feature selection and extraction.
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Principal Component Analysis
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- 2. 2 Feature Engineering (Our motivation) Introductionto Principal Component Analysis (And some statistical concepts) Agile Analytics and PCA (Helping visualization…) Agenda
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- 4. 4 Given a classification problem… How dowe choose the right features?
- 5. 5 Intuition fails in high dimensions Buildinga 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 thinkthat gathering more features never hurts, right? At worst they provide no new information about the domain…
- 7. 7 The curse of dimensionality Manyalgorithms that work fine in low dimensions become intractable when the input is high-dimensional. Bellman, 1961
- 8. 8 How do we solveit? Feature Selection Feature Extraction
- 9. 9 Feature extraction “In most applications examplesare not spread uniformly throughout the examples space, but are concentrated on or near a lower-dimensional subspace.”
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- 11. 11 Objective of PCA To performdimensionality reduction while preserving as much of the randomness in the high-dimensional space as possible
- 12. 12 Principal Component Analysis It takes yourcloud 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 typeof 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
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- 15. 15 Beware: Correlation doesnot imply causation
- 16. 16 Correlation matrix It shows ata glance how variables correlate with each other
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- 18. 18 Steps for PCA1. 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 checkthe products of PCA…
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- 21. 21 Agile Analytics Machine learning anddata mining tools and techniques + Knowledge of the domain at hand + Short feedback cycles
- 22. 22 Agile Analytics We could usePCA 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 & NextSteps 23