Is Data Scale Important When Applying PCA? — Science and Data

2023-08-15 02:39:22

PCA (Principal Component Analysis) is a dimensionality reduction technique that transforms data into a new coordinate system, where axes are the principal components of the data. These components are linear combinations of the original features and are selected to capture the greatest possible amount of variance in the data.

When using PCA the scale of the data can be important and here are some considerations:

Normalization before PCA: It is usually good practice to standardize (normalize) the data before applying PCA. This is because the PCA is sensitive to the scale of the variables. If one variable has a much larger scale than another, it may dominate the principal components and the PCA may not provide a meaningful representation of the structure of the data. Using a normalization such as the StandardScaler (which subtracts the mean and divides by the standard deviation) is common in this context.

MinMaxScaler before PCA: Using the MinMaxScaler is another option to place all features on the same scale (e.g. in the range [0, 1]). This can also be useful before applying PCA, depending on the nature of the data and what you want to capture.

Variation in Principal Components: The fact that the principal components vary greatly is not necessarily a problem. In fact, the purpose of the PCA is to capture this variation. The first principal component is the direction in which the data varies the most, the second principal component captures most of the remaining variation, and so on.

Dimensionality and Information: Reducing dimensionality through PCA keeps the directions of greatest variation in the data, which often corresponds to the most important information. However, if the data are not standardized, this information can be distorted by the scale of the original variables.

Conclusion:

It is generally safe to say that standardizing or applying the MinMaxScaler prior to the PCA is a best practice. This helps ensure that the PCA captures the structure of the data in a balanced way, without being unduly influenced by the scale of the original variables.

David Matos

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