How do you update and maintain a PCA for visualization when new data is added or changed?

1 Why update PCA?

PCA is based on finding the directions of maximum variance in the data and projecting it onto a lower-dimensional space. These directions, called principal components, are linear combinations of the original variables and capture most of the information in the data. However, if your data changes, the principal components may not reflect the current variance and structure of the data. For example, if you add new observations or variables, the mean and covariance of the data may change, affecting the eigenvalues and eigenvectors that determine the principal components. Similarly, if you remove or modify some observations or variables, the principal components may become less representative or meaningful. Therefore, updating your PCA is important to ensure that your visualizations are accurate and informative.

2 How to update PCA?

There are different methods for updating your PCA depending on the type and extent of the data changes. For example, if you add new observations to your data, you can use out-of-sample prediction with libraries and packages such as scikit-learn in Python or prcomp in R. However, this assumes that the new observations do not change the mean and covariance of the data significantly. If you add new variables to your data, you can use incremental PCA with scikit-learn in Python or bigpca in R. Alternatively, if you remove or modify some observations or variables from your data, deflation PCA with deflatr in R can be used. Both incremental and deflation PCA may introduce some errors and instability in the principal components, particularly when the new variables or deleted/modified data have large variance/correlation/influence/leverage.

3 How to visualize PCA?

Once you have updated your PCA, you can visualize it using various tools and techniques. For example, plotting the scores of the principal components can show how the data points are distributed and clustered along the principal components. You can also color or label the data points by some categorical variable to see how they differ by groups. Similarly, plotting the loadings of the principal components can indicate how the original variables contribute to the variance and structure of the data along the principal components. Additionally, biplots of the principal components combine both scores and loadings in one plot, allowing you to see how the data points and original variables are related to the principal components. Libraries and packages such as matplotlib or seaborn in Python or ggplot2 or factoextra in R can be used to create these plots.

4 How to interpret PCA?

Interpreting your PCA involves looking at various metrics and indicators. Explained variance ratio of the principal components can tell you how much of the total variance in the data is captured by each principal component, which can help you select the optimal number of principal components. You can also plot a scree plot or cumulative explained variance plot to observe how the explained variance ratio changes with the number of principal components. The correlation matrix of the principal components can tell you how correlated the principal components are with each other and with the original variables. You can also look at outliers and leverage points to detect any anomalies or errors in your data and assess their impact on your PCA results. Libraries and packages such as scikit-learn in Python or prcomp or factoextra in R can help you calculate and plot these metrics.

5 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?