Description: Partial Least Squares (PLS) is a statistical method that seeks to identify the fundamental relationships between two data matrices. This approach is particularly useful in situations where there are many predictor variables and one wishes to reduce the dimensionality of the data while preserving relevant information. Through matrix decomposition, PLS allows for the identification of latent components that explain variability in both input and output matrices. This method combines features of regression and principal component analysis, making it versatile for analyzing complex data. In the context of unsupervised learning, PLS is used to explore and model relationships in datasets without the need for predefined labels or categories, facilitating the identification of underlying patterns and structures. Its ability to handle collinear data and its focus on maximizing covariance between matrices make it a valuable tool across various disciplines, from chemistry to economics and biology, where data is often multidimensional and complex.
History: The Partial Least Squares method was developed in the 1960s by Herman Wold, a Swedish statistician. Wold introduced PLS as a technique to address regression problems in situations where predictor variables were numerous and highly correlated. Over the years, the method has evolved and adapted to various applications in fields such as chemistry, psychology, and economics. In the 1990s, PLS gained popularity in the field of multivariate data analysis, especially with the rise of analytical chemistry and spectroscopy data analysis.
Uses: Partial Least Squares is used in a variety of fields, including chemistry, where it is applied for the analysis of spectroscopic data and the calibration of predictive models. It is also common in market research, where it helps identify relationships between consumer behavior variables. In biology, PLS is used to analyze genomic and proteomic data, allowing for the identification of patterns in large biological datasets. Additionally, in the field of economics, it is applied to model complex relationships between economic variables.
Examples: A practical example of Partial Least Squares is its use in analytical chemistry, where it is applied to develop calibration models that relate the concentrations of chemical substances to their spectra. Another example can be found in market research, where it is used to analyze consumer surveys and determine factors influencing purchasing decisions. In the field of biology, PLS has been used to identify biomarkers in gene expression studies, helping to uncover relationships between genes and diseases.
