Standardization vs. Normalization of PCA Data (2 Examples)

On this page, we’ll compare standardization and normalization in the Principal Component Analysis (PCA) context.

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Let’s dive into it!

Standardization vs. Normalization

In the context of Principal Component Analysis (PCA), the choice between standardization and normalization is crucial. Let’s first understand standardization and normalization individually!

Standardization

Standardization, also known as z-score normalization, involves rescaling the features of your data to have a mean of zero and a standard deviation of one. See the formula, here. This process is achieved by subtracting the mean of each feature and then dividing by the standard deviation. This means that after standardization, one unit on the new scale corresponds to one standard deviation in the original data, regardless of the original scale of the data.

Normalization

Normalization, particularly min-max scaling, adjusts data to fit within a specific range, typically between 0 and 1. This process involves subtracting the minimum value of each feature and dividing by the range (maximum – minimum). See here for the formula. Normalization is particularly useful when the data contains predefined boundaries, like image processing data. Making the highest value 1 and the lowest value 0, or other selected values, all other values proportionally adjusted within this range.

Appropriateness for PCA

PCA assumes that the importance of a feature is determined by its variance. Features with higher variance contribute more in principal component construction. This assumption is critical in determining whether to standardize or normalize.

Standardization is typically favored in PCA as it ensures that each feature’s contribution to the analysis is based on a standardized scale, where variability is expressed in terms of standard deviation. This approach mitigates the effects of the original scales and units, preventing variables with inherently larger variances due to their larger scales, from disproportionately influencing the identification of principal components. See our tutorial, PCA Using Correlation & Covariance Matrix, to observe the difference between the results when the data is standardized and unstandardized.

Normalization may not be as suitable for PCA since it changes the range of the data but doesn’t necessarily align the features based on their variability. While normalization is about scaling data within a particular range, PCA is more focused on how much each feature varies, regardless of their range.

In summary, standardization aligns with the objectives of PCA due to its focus on feature variability and equal contribution, whereas normalization is more concerned with scaling data to a specific range.

Video, Further Resources & Summary

I have recently released a video on the Statistics Globe YouTube channel, which explains PCA and the importance of standardization. Please find the video below:

In addition, you may want to read the other articles on my website. Some tutorials can be found below.

• PCA Using Correlation & Covariance Matrix
• What are Loadings in PCA?
• Advantages & Disadvantages of Principal Component Analysis
• Factor Analysis vs Principal Component Analysis
• Datasets for PCA

In this article, we have analyzed the differences between standardization and normalization within the scope of PCA. In case you have any further questions, tell me about it in the comments.

This page was created in collaboration with Cansu Kebabci. Have a look at Cansu’s author page to get more information about her professional background, a list of all her tutorials, as well as an overview on her other tasks on Statistics Globe.