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1/6/2024
Dimensionality reduction is a method used to reduce the number of variables in a dataset, also known as dimensionality, while retaining its most meaningful properties. In other words, it aims to transform data from a high-dimensional space (i.e. data with a high number of variables) into a low-dimensional space (i.e. by reducing the number of variables) so that the low-dimensional representation retains the local and global properties of the original data1. Dimensionality reduction, like cluster analysis, refers to a series of methods that can be used to reach this objective.
This method is primarily used to simplify the data and make it easier to analyze. One of the main problems with high-dimensional data is that the model’s performance generally deteriorates as the number of variables increases. This is because the complexity of the model increases with the number of variables, making it more difficult to determine an optimal solution, especially when the sample size is limited. In addition, dimensionality reduction can also help to eliminate redundant and potentially collinear variables that can affect the performance of certain models. Where there is a large volume of data, dimensionality reduction can also help to optimize computing time.
In addition to simplifying the data, reducing dimensionality can be useful for visualizing the data by projecting it onto two or three-dimensional space. This can provide a better understanding of the relationships between variables and facilitate the identification of underlying structures in the data. We use these methods here at Polygon to visualize emerging themes in concept mapping.
For reviews of dimensionality reduction, as well as comparative reviews, see the following articles by Wang et al., (2021) and Anowar et al., (2023).
For more information on concept mapping and Polygon’s CM* tool, see the following links: What is concept mapping? and CM*
Note:
Local data property is used here to refer to groups of points that are close in high-dimensional space and remain so in lower-dimensional space. Global properties refers to larger-scale relationships, i.e. patterns that characterize the dataset.
Concept Mapping Tool
Dimensionality reduction
