Unsupervised Learning - Preliminaries

Distance Calculation

Distance is either calculated between:

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Distance Properties:

• Should be non-negative (distance > 0)
• Distance between a record to itself is equal to 0
• Satisfies Symmetry (Distance between records 'i' & 'j' is equal to the distance between records 'j' & 'i')

If the variables scale or have different units, standardise or normalise the variables before computing the distance.

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Distance Calculations

Distance Metrics for Continuous Data

• Mahalanobis Distance which is calculated using Correlation Matrix
• Manhattan Distance, is also called as L1 norm
• Euclidean Distance, is also called as L2 norm

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Distance Metrics for Binary Categorical Data

• Binary Euclidean Distance
• Simple Matching Coefficient
• Jaccard's Coefficient

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Distance Metrics for Categorical Data (> 2 categories)

• Distance is 0, if both items have same category
• Distance is 1 otherwise

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Distance Metrics when both Quantitative Data & Categorical Data exists in a dataset

• Gower's General Dissimilarity Coefficient

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Linkages

Linkages - Distance between a record & a cluster, or between two clusters.

• Single Linkage - This is the closest a record may be to a cluster or to another cluster.

  • Single Linkage is also called as Nearest Neighbor
  • Emphasis is on close records or regions and not on overall structure of Data
  • Capable of clustering non-elliptical shaped regions
  • Gets influenced greatly by outliers or noisy data

   

• Complete Linkage - The diameter between a record and a cluster, or between two clusters, is the greatest.

  • Complete Linkage is also called as Farthest Neighbor
  • Complete Linkage is also sensitive to outliers
  

   

• Average Linkage - This is the mean distance between any two clusters or between any two records.

  • Average Linkage is also called Group Average
  • Very expensive because computation takes a lot of time

   

• Centroid Linkage - This is the separation between two clusters' centroids, or between a cluster's record and centroid.

  • Centroid Linkage is also called Centroid Similarity

   

• Ward's Criterion - By combining them into a single cluster, the SSE criteria for clustering's value increased.

  • This is also called Ward's Minimum Variance and it minimizes the total within cluster variance

   

• Group Averaged Agglomerative Clustering (GAAC)

  • Two clusters are merged based on cardinality of the clusters and centroid of clusters
  • Cardinality is the number of elements in the cluster