Principal Component Analysis (PCA): Definition, History, and Characteristics
Principal Component Analysis (PCA) is a statistical technique used to reduce the dimensionality of high-dimensional datasets. It is a linear transformation method that uses orthogonal linear projection to convert a set of correlated variables into a set of uncorrelated variables called principal components (PCs). The PCs are orthogonal linear combinations of the original variables whose values represent the amount of variation in the data explained by each component. PCA is used in various fields, such as machine learning, signal processing, image processing, and bioinformatics.
History
The origins of Principal Component Analysis (PCA) can be traced back to the early 1900s. Karl Pearson, an English mathematician, is credited with introducing the concept of PCA in 1901. Pearson used the technique to reduce the dimensionality of data by projecting it onto a lower dimensional space. Pearson coined the term “factor analysis” to describe the technique. In the decades that followed, the technique was used in different disciplines, such as psychology, economics, and sociology.
In the 1950s, Harold Hotelling, a statistician, developed the modern-day version of PCA. Hotelling used the technique to reduce the dimensions of data for use in pattern recognition and classification. His work was further developed by J.J. Gaskett, who used PCA to reduce the dimensionality of data used to classify objects in images. In the decades that followed, PCA was used in different fields, such as machine learning, signal processing, image processing, and bioinformatics.
Characteristics
Principal Component Analysis (PCA) is a linear transformation technique used to reduce the dimensionality of high-dimensional datasets. It is an unsupervised learning technique, meaning it does not require labeled data. PCA is used to reduce the dimensionality of data, while preserving the maximum amount of information. This means that the data can be transformed into a lower-dimensional space while preserving the relationships between the variables.
PCA works by transforming the data into a set of PCs, which are linear combinations of the original variables. Each PC is orthogonal to the other PCs, meaning they are uncorrelated. PCs are ordered in terms of their variance, with the first PC explaining the most variance and the last PC explaining the least. PCA is used in various fields, such as machine learning, signal processing, image processing, and bioinformatics.
Conclusion
Principal Component Analysis (PCA) is a linear transformation technique used to reduce the dimensionality of high-dimensional datasets. The technique was developed by Karl Pearson in 1901 and further developed by Harold Hotelling in the 1950s. PCA works by transforming the data into a set of PCs, which are linear combinations of the original variables. Each PC is orthogonal to the other PCs, meaning they are uncorrelated. PCA is used in various fields, such as machine learning, signal processing, image processing, and bioinformatics.
References
Al-Anzi, B., & Al-Anzi, M. (2018). Principal Component Analysis: Review and Applications. International Journal of Computers and Technology, 16(4), 1020-1032.
Bishop, C. M. (2006). Pattern recognition and machine learning. Springer.
Hotelling, H. (1933). Analysis of a complex of statistical variables into principal components. Journal of educational psychology, 24(6), 417.
Pearson, K. (1901). On lines and planes of closest fit to systems of points in space. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 2(11), 559-572.