How to Understand Principal Component Scores in Principal Component Analysis?
Principal component scores represent the coordinates of each sample in the principal component space. They provide insights into the sample’s position and its relative contribution to each principal component. A higher principal component score indicates a stronger projection of the sample onto that principal component, signifying greater alignment with the corresponding variance direction.
Interpretation as New Coordinates
Principal component scores can be interpreted as the coordinates of each data point in the transformed principal component space. For instance, the first principal component score indicates the position of each data point along the first principal component, which captures the largest variance in the data.
Revealing Data Structure and Patterns
Principal component scores facilitate the analysis of data structure by enabling visualization of patterns, clusters, and outliers. By plotting the scores of the first two principal components in a two-dimensional space, one can observe groupings and deviations within the dataset.
Linear Transformation of Original Data
Principal component scores result from a linear transformation of the original data. Each score is a weighted sum of the original variables, where the weights are determined by the principal component loadings. Although expressed in a new coordinate system, these scores retain key information from the original dataset.
Dimensionality Reduction and Feature Selection
In many cases, only the top-ranked principal component scores are retained for further analysis, as they capture the majority of variance in the data while significantly reducing dimensionality. These scores can serve as new features in predictive modeling and other machine learning applications.
Principal component scores offer a transformed representation of the dataset in a new coordinate system defined by the principal components. They are widely used for visualization, exploratory data analysis, and as features in subsequent computational models.
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