In-class Exercise 7

Author

Eugene Toh

Cluster analysis

  • Data preparation and exploration

    • Make sure that we normalise the data (e.g., based on population as for instance drug abuse cases is affected by population)

      • Multiply it by a number to not see too many decimals to make it clearer

  • Data analysis and selecting clustering variables

    • Checking the distribution of the cluster variables

    • If numbers have too large a range, use standardisation techniques

      • Z-score (if your data is normally distributed)

        • Positive and negative, centre is 0

      • Min-max (highly skewed)

        • Outputs numbers between 0 to 1

      • Decimal scaling

        • The same as the normalisation method shown above

    • Create correlation matrix to visualise linear relationship data

      • Ellipses that look like a forward slash has a positive correlation and vice versa

      • 0 means no linear relationship

      • Ranges from -1 to 1

      • When ellipse is very narrow, there is very strong relationship

  • Decide on the clustering technique

    • Agglomerative (more common)

    • Divisive

  • Perform cluster analysis

    • Hierarchical clustering is done with aspatial data

    • For each two pairs of variable, we calculate the similarity

      • Euclidean distance

      • City-block formula

      • Chebychev distance

    • All of them use square roots as the result of clustering have to be the same sign

    • Visualising it

      • Nested clusters

      • Dendrogram

        • The closer each item is grouped together, the more similar they are

    • Since we are using hierarchical agglomerative clustering, each iteration subsumes the previous clusters

    • Doing comparisons between agglomerative clustering methods

      • Methods

        • Average

        • Single

        • Complete

        • Ward

      • The method with the highest agglomerative coefficient is typically the best method

  • Decide on the number of clusters

    • Gap statistic method

      • Input called B that uses permutation to do simulation

      • K.max restricts the number of clusters (feel free to use any value depending on how many items you have)

        • Feel free to experiment with the value

        • Use gap statistics to figure out the best number of clusters

          • Only analyse values after 3 clusters

          • Then get the k that has the max gap statistic

  • Validate and interpret the clusters

    • Check if there are any clusters which have only one member

      • Data errors

      • One extreme outlier (unlikely)

        • You should exclude it out

    • Methods

      • Parallel coordinates

        • You can try to make it interactive with Plotly

        • You can also split them up into separate graphs for each cluster using facets with GGally

        • You can then try and identify how each facets differ to reach a conclusion

      • Dendrogram

      • If at the end you find that there is only one variable that is highly correlated, you can use LISA instead.