Define factor analysis. Differentiate between cluster analysis and factor analysis.

Factor analysis is a statistical method used to identify underlying relationships or patterns among a set of observed variables. It aims to reduce the complexity of data by grouping correlated variables into fewer unobserved variables, called factors, that can explain the correlations. These factors are essentially latent constructs that capture the shared variance among the variables. Factor analysis is widely used in fields like psychology, social sciences, market research, and scientometrics to analyze large datasets and uncover hidden structures.

In factor analysis, the data matrix is decomposed into two primary components: the factor loadings and the unique variances. The factor loadings represent how strongly each observed variable is associated with a particular factor, while the unique variances represent the portion ______ ____ ______ ________ _______ __________ ______ ______ ___ ________.
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