Dimensionality Reduction of Liver Function Indicators based on Factor Analysis (FA)

Factor analysis (FA) is a statistical method used to reduce dimensionality by condensing a large number of observed variables into a smaller set of latent factors. In this study, FA is employed to reduce dimensionality of liver function indicators. Four test indicators, alanine transaminase (ALT) level, hepatomegaly index, zinc sulfate turbidity, and alpha-fetoprotein (AFP) level, are the observed variables. Datasets from twenty collected samples are exploited. The four observed variables are represented by linear combination of two latent factors. Factor loadings are calculated and illustrated using an arrow graph. These results indicate that the first two indicators correlate strongly with factor 1, the third indicator correlate strongly with factor 2, and the fourth indicator exhibits weak relationships with each factor. The first two indicators are assumed to be primarily influenced by one latent factor and are independent of the other two indicators. The third and fourth indicators are independent variables. These findings help physicians better understand the intrinsic structures of liver function indicators and offer guidance for clinical practice. This study highlights the potential of FA in medical applications.