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    Interpretation of Universities Using Multidimensional Scaling and Principal Component Analysis

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    Joshua chirchir
    This document discusses using multidimensional scaling (MDS) and principal component analysis (PCA) to analyze similarity data from universities. It first loads university data and calculates Euclidean distances between them. MDS is performed using classical and non-metric approaches. Classical MDS plots certain universities with strong correlations closer together. Non-metric MDS yields a high stress value, indicating dissimilarity. PCA is also applied, showing the first principal component explains most variance and separates some universities. Key differences between MDS and PCA are discussed.

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    Interpretation of Universities Using Multidimensional Scaling and Principal Component Analysis

    Uploaded by

    Joshua chirchir
    39 views4 pages
    This document discusses using multidimensional scaling (MDS) and principal component analysis (PCA) to analyze similarity data from universities. It first loads university data and calculates Euclidean distances between them. MDS is performed using classical and non-metric approaches. Classical MDS plots certain universities with strong correlations closer together. Non-metric MDS yields a high stress value, indicating dissimilarity. PCA is also applied, showing the first principal component explains most variance and separates some universities. Key differences between MDS and PCA are discussed.

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    Business analytics

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    4_5886332904862124665

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    This document discusses using multidimensional scaling (MDS) and principal component analysis (PCA) to analyze similarity data from universities. It first loads university data and calculates Euclidean distances between them. MDS is performed using classical and non-metric approaches. Classical MDS plots certain universities with strong correlations closer together. Non-metric MDS yields a high stress value, indicating dissimilarity. PCA is also applied, showing the first principal component explains most variance and separates some universities. Key differences between MDS and PCA are discussed.

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    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    39 views4 pages

    Interpretation of Universities Using Multidimensional Scaling and Principal Component Analysis

    Uploaded by

    Joshua chirchir
    This document discusses using multidimensional scaling (MDS) and principal component analysis (PCA) to analyze similarity data from universities. It first loads university data and calculates Euclidean distances between them. MDS is performed using classical and non-metric approaches. Classical MDS plots certain universities with strong correlations closer together. Non-metric MDS yields a high stress value, indicating dissimilarity. PCA is also applied, showing the first principal component explains most variance and separates some universities. Key differences between MDS and PCA are discussed.

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    © All Rights Reserved
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    of 4

    Interpretation of Universities Using Multidimensional

    Scaling and Principal Component Analysis


    Multidimensional scaling is a type of multivariate analysis that involves visualization of similarity
    or dissimilarity of data points by displaying the points in two-dimensional plots. There are two
    types of multidimensional scaling i.e. Classical multidimensional scaling and Non-metric
    multidimensional scaling. The data provided is first loaded and the first six columns are viewed
    using the head() method. The data contains seven columns where the six of the columns are
    numerical while the column university contains character names. The data has no missing
    values or any duplicated rows. Using the summary() to get a brief statistical summary of the
    data.

    In order to perform multidimensional scaling in R, the data has to be converted into an array or
    matrix. This involves first removing the first column from the data set and assigning the same to
    as the row values. The Euclidean distance is then calculated between the various universities.
    Euclidean distance is used to measure the similarity between the variables. Displaying the
    Euclidean distances in a heat map to explain the similarity. Basing on the heatmap, the
    universities Havard, Yale, Stanford and MIT are seen to have a strong correlation hence more
    similarities in term of variables provide while there is huge dissimilarity in universities such as
    Havard and TexaxA&m while a less dissimilarity between Georgetown and yale.
    For Classical multidimensional scaling, the compute classical (metric) multidimensional scaling
    (cmdscale()) stats package is used. This works by preserving the original distance metric
    between points. The output contains the preserved distances, the eigenvalues returned, the
    doubly centred distance matrix, the additive constant and the numeric vectors. From the plot,
    the distance between the universities Havard, Standford, Yale, MIT, Duke, Columbia is less
    hence shows the similarities. The distance to from the same university to Pennstate, Umchigan
    and TexasA&M is largely showing the dissimilarities between these universities. CalTech and
    JohnsHopkins have high negative points showing their dissimilarities to the other universities.

    The Kruskal’s Non-metric multidimensional scaling provides a stress value of 4.48976. This
    represents the goodness of fit of the regression based on the sum of squared differences. This
    is a high value the dissimilarities in the universities.

    Finally, deploying the principal component analysis to the data using the prcomp() function of
    the numerical column and factoextra package for visualisation. Screeplot displays a graph of
    inertia against principal components. Principal components are created in order of the amount
    of variation they cover. PC1 covers the most variation, PC2 the second-most while PC6 covers
    the least variation. Fviz_eig() displays an elbow-shaped which is the ideal cutting off point after
    which it flattens out.

    PC1 explains 76.8% of the total variance, which means that nearly two-thirds (four variables)
    can be encapsulated by just that once principal component. Grad, Top10, SAT, and Expense all
    contribute to pca1. From the biplot of individuals and variables, CalTech and JohnsHopkins
    universities are observed at a distance in pca1 compared to Havard, MIT, Duke, Yale which
    shows the dissimilarities.
    Some of the advantages of multidimensional scaling over principal component analysis include;
    ● MDS is more focused on relations among the scaled objects while PCA is focused on
    the dimension seeking to maximize explained variance.
    ● MDS projects data point in 2-dimensional space such that similar objects are closer
    together while PCA projects a multidimensional space to the direction of maximum
    variability using correlation matrix for analyzing the correlation between data points.

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