Applying Predictive Analytics by Richard V. McCarthy & Mary M. McCarthy & Wendy Ceccucci & Leila Halawi

Author:Richard V. McCarthy & Mary M. McCarthy & Wendy Ceccucci & Leila Halawi
Language: eng
Format: epub
ISBN: 9783030140380
Publisher: Springer International Publishing

4.5 Principal Component Regression

4.5.1 Principal Component Analysis Revisited

When there are many input variables, it may be necessary to reduce the number of input variables to permit more meaningfully interpretation of the data. In Chap. 3, principal component analysis (PCA), a nonparametric analysis, was described as another variable reduction strategy and used when there are many redundant variables or variables that are possibly correlated. PCA is frequently used in exploratory data analysis but can also be used to build predictive models.

PCA applies a method referred to as feature extraction. Feature extraction creates “new” input variables. The “new” input variables are a combination of each of the “old” input variables. The new input variables are created through a process known as orthogonal transformation (a linear transformation process). The new input variables (referred to as principal components) are now linearly uncorrelated variables. Orthogonal transformation orders the new input variables such that the first principal component explains the largest amount of variability in the data set as possible and each subsequent principal component in sequence has the highest variance possible under the limitation that it is orthogonal (perpendicular) to the preceding components. Since the new input variables are ordered from highest variance to smallest variance (least important), a decision can be made which variables to exclude from the prediction model. The results of PCA are normally defined as component scores or factor scores.

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