Are the First Principal Component and Principal Component Scores Equivalent in Principal Component Analysis?
The first principal component and the principal component scores are not equivalent:
First Principal Component (FPC)
The first principal component refers to the direction in which the variance of the projected data is maximized during Principal Component Analysis (PCA). It serves as the primary axis in the transformed coordinate system and captures the most significant source of variation in the original dataset. This direction is determined by maximizing the variance among all possible linear combinations of the original variables and is considered the most informative in representing the underlying structure of the data.
Principal Component Scores
Principal component scores are the numerical values obtained by projecting the original data onto the principal component axes. In PCA, each sample is assigned a score for each principal component, resulting in a new data matrix where each column corresponds to a specific principal component. These scores quantify the position of each sample along each principal component and are commonly used to assess the contribution of samples to different components, as well as to evaluate similarities or differences among samples.
The first principal component in PCA identifies the direction of greatest variance in the original dataset, whereas the principal component scores represent the coordinates of the samples along these directions, serving as a basis for interpreting sample variation and structure in the reduced space.
MtoZ Biolabs, an integrated chromatography and mass spectrometry (MS) services provider.
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