What does PCA retain while reducing dimensions of data?

Principal Component Analysis (PCA) is a statistical technique primarily used for dimensionality reduction while preserving as much of the data's variability as possible. When PCA transforms a high-dimensional dataset to a lower-dimensional space, it focuses on maintaining the variance present in the original dataset. This means PCA tries to capture the directions (or principal components) along which the data varies the most. By projecting the data onto these principal components, PCA effectively reduces the number of features while retaining the most significant patterns and structure in the data.

The emphasis on variance is crucial because it allows the reduced dataset to reflect the underlying relationships and trends present in the original data. This characteristic makes PCA particularly useful when dealing with high-dimensional data where visualization or understanding the data's structure becomes challenging.

While striving to reduce dimensionality, PCA does not account for label accuracy directly or maintain all data points. Instead, it seeks to summarize the original variables into fewer dimensions, leading to a loss of some original structure, but the goal remains to keep the variance intact. Thus, preserving variance is the key aspect that makes PCA effective for dimensionality reduction.