It refers to mathematical procedure that needs to transform a number of possibly correlated variables into small number of uncorrelated variables:

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Accepted Answer

The correct option is (2):
**Principle component analysis** (PCA) is precisely the mathematical and statistical procedure defined in the question. PCA is the most common and widely used technique for **dimensionality reduction**. Its core function is to transform a large set of original, potentially highly correlated variables into a much smaller set of **uncorrelated variables**, called *principal components*. This transformation is achieved by finding orthogonal linear combinations of the original features, ordered so that the first few components retain the maximum variance—or most of the information—present in the original data set, thereby simplifying the data structure while minimizing information loss.

The incorrect option is (1):
**Natural language analysis** (NLA) is a broad field, typically falling under Natural Language Processing (NLP), whose goal is to enable computers to understand, interpret, and manipulate human language. While NLA might be a *use case* where dimensionality reduction is applied (for instance, on a document's feature set), NLA itself is not the mathematical procedure for transforming correlated variables. It is the overall task or domain of study, focusing on linguistic and semantic interpretation, rather than the core statistical method of de-correlation and variable compression.

The incorrect option is (3):
A **Hidden Markov Model** (HMM) is a probabilistic statistical model used primarily for modeling sequential data. It assumes that a system's observable outputs depend on unobservable (hidden) states, and the system transitions between these hidden states probabilistically. HMMs are fundamentally used for sequence classification, tagging, and pattern recognition in applications like speech recognition and bioinformatics, not for the general mathematical transformation of a dataset's feature space to reduce dimensionality and eliminate variable correlation.

The incorrect option is (4):
A **Support Vector Machine** (SVM) is a powerful, supervised machine learning algorithm. Its primary purpose is **classification** (and regression) by finding the optimal hyperplane that distinctly separates data points belonging to different classes in a high-dimensional feature space. The process involves maximizing the margin between the decision boundary and the closest training data points (support vectors). While it works with variables, its function is classification/separation, not the general-purpose mathematical procedure of transforming and condensing a correlated variable set into a smaller, uncorrelated one.