Factor Analysis Vs. Principle Component Analysis PCA components explain the maximum amount of variance while factor analysis explains the covariance in data. PCA components are fully orthogonal to each other whereas factor analysis does not require factors to be orthogonal. PCA component is a linear combination of the observed variable while in FA, the observed variables are linear combinations of the unobserved variable or factor. PCA components are uninterpretable. In FA, underlying factors are labelable and interpretable. PCA is a kind of dimensionality reduction method whereas factor analysis is the latent variable method. PCA is a type of factor analysis. PCA is observational whereas FA is a modeling technique. 3.3 Multidimensional Scaling Multidimensional scaling is a visual representation of distances or dissimilarities between sets of objects. “Objects” can be colors, faces, map coordinates etc.
Objects that are more similar (or have shorter distances) are closer together on the graph than objects that are less similar (or have longer distances). As well as interpreting dissimilarities as distances on a graph, MDS can also serve as a dimension reduction technique for high-dimensional data. MDS is now used over a wide variety of disciplines. When to use MDS? :- For example you were give a list of city location and task is to make a map that includes distances between cities. For this procedure is quite simple i.e taking ruler and measuring distance of both city end (Location). But what If you were given distance between cities (Similarity) and not location. This could need a fair amount of geometric knowledge to complete it. Hence this type of problem is suitable for multidimensional scaling. You’re basically given a set of differences, and the goal is to create a map that will also tell you what the original distances where and where they were located. Pitfalls of MDS: - 2d graph is easiest graph to figure out but it might get distorted because of poor representation of distances. If this happens you can switch to 3d graph, but 3d graph is difficult to plot on sheet of paper in addition to it is difficult to comprehend Multidimensional scaling is similar to Principal Components Analysis (PCA) and dendrograms. All are tools to visualize relationships, but they differ in how the data is presented. In some cases, MDS can be used as an alternative to a dendrogram. However, unlike dendrograms, MDS is not plotted in “clusters,” nor are they hierarchical structures. PCA is another similar tool, but while MDS uses a similarity matrix to plot the graph, PCA uses the original data. Multidimensional scaling vs factor analysis Both Multidimensional scaling (MDS) and Factor Analysis (FA) uncover hidden patterns or relationships in data. Both techniques require a matrix of measures of associations.
- Winter '17
- Multivariate statistics