What are some of the applications and benefits of multidimensional scaling for data visualization?

Multi-dimensional scaling (MDS) finds a more meaningful coordinate system for a set of data. The new coordinate system is guaranteed to have the first coordinate axis aligned with the one axis along which the data varies the most, then a second coordinate axis perpendicular to the first along which the data varies the most ignoring the first axis, and so on until no more axes are required to uniquely position every data point. This ordered sequence of axes allows you to choose a number N of axes, and be guaranteed that if you ignore all but the first N axes, you have captured as much of the variation in the data as is possible using N axes.

Several multivariate methods share the purpose of “mapping” the data : PCA, FA, MCA, DA, ... At the same time, the main goal of these methods is not mapping. As a consequence, it is not uncommon for these methods to retain more than 2 dimensions. This makes data visualization more difficult with 3+ dimensions If mapping is the primary objective, MDS improves the 2D data visualization.

MDS is often used in exploratory data analysis, where the objective is to identify the most important characteristics of a (new, unknown) dataset. For example, if the data contains two well-separated subsets, where each point is closer to every point in its subset than it is to any point in the other subset, the primary axis of variation (the first dimension found by MDS) must be aligned to the line between the centers of the two subsets. This also leads to maximizing the separation between points when plotting the data on the first few axes found by MDS, so these axes are a good choice for minimizing overplotted points.

Multidimensional scaling (MDS) may be used to visualise potential clusters in 2D especially when a large number of classification criteria are to be used. This visual data mapping helps identifying their presence, to get a rough idea on the number of groups and their shape. This info is needed to decide on which clustering method to use as some extract spherical clusters only.

Metric MDS is equivalent to principal components analysis, which is performed in R with the prcomp() function; the same results can be produced by a different algorithm in the princomp() function. Any two axes can be plotted against each other using biplot(). In this approach, both the data and the identified axes can be visualized. Each axis identified in metric MDS corresponds to an eigenvector of the data matrix.

When we map out the relationships between people, it helps us see hidden patterns. If our brains can make sense of groups, clusters, and subgroups based on how close or far apart they are on the MDS plot, then this understanding can help us figure out what we all have in common, and what sets us apart. By doing this, we can communicate better and understand each other a little bit better too.

Metric MDS is one of the most common ways for statisticians to visualize multidimensional datasets they have just acquired, regardless of what topic the data is about. In statistical genetics, it is common to use MDS to identify minor, but consistent differences between populations that are due to the history of human migrations across the world, not to medical or biological traits. Separating information about human migration from biological information is very helpful, whether your goal is to study human migration or to study human hereditary traits and inherited diseases. MDS is also used to simplify a set of related (correlated) features into a smaller set of independent features when training a machine learning (AI) tool.

Surveys and questionnaires in social sciences and psychology: ask people how different they perceive products, concepts, etc. Marketing: ask consumers about preferences (origin of preference mapping MDPREF) More generally, any situation where objects are compared instead of being measured individually.