Chapter 16. Dimensionality Reduction

Dimensionality reduction transforms a data set from a high-dimensional space into a low-dimensional space, and can be a good choice when you suspect there are “too many” variables. An excess of variables, usually predictors, can be a problem because it is difficult to understand or visualize data in higher dimensions.

What Problems Can Dimensionality Reduction Solve?

Dimensionality reduction can be used either in feature engineering or in exploratory data analysis. For example, in high-dimensional biology experiments, one of the first tasks, before any modeling, is to determine if there are any unwanted trends in the data (e.g., effects not related to the question of interest, such as lab-to-lab differences). Debugging the data is difficult when there are hundreds of thousands of dimensions, and dimensionality reduction can be an aid for exploratory data analysis.

Another potential consequence of having a multitude of predictors is possible harm to a model. The simplest example is a method like ordinary linear regression where the number of predictors should be less than the number of data points used to fit the model. Another issue is multicollinearity, where between-predictor correlations can negatively impact the mathematical operations used to estimate a model. If there are an extremely large number of predictors, it is fairly unlikely that there are an equal number of real underlying effects. Predictors may be measuring the same latent ...

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