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Hierarchical Clustering
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Table of Content
Agglomerative technique (top-down hierarchy of clusters) or Divisive technique (bottom-up hierarchy of clusters) are other names for hierarchical clustering.
Agglomerative:
When merging records or clusters, start by treating each data point as a separate cluster and proceed until all records have been combined into a single large cluster.
Steps:
- Start with 'n' number of clusters where 'n' is the number of data points
- Merge two records, or a record and a cluster, or two clusters at each step based on the distance criteria and linkage functions.
Divisive:
- Start by considering that all data points belong to one single cluster and keep splitting into two groups each time, until we reach a stage where each data point is a single cluster.
- Divisive Clustering is more efficient than Agglomerative Clustering.
- Split the clusters with the largest SSE value.
- Splitting criterion can be Ward's criterion or Gini-index in case of categorical data.
- Stopping criterion can be used to determine the termination criterion
After executing the algorithm and examining the Dendrogram, a selection of clusters is made. A dendrogram is a collection of data points that resembles a multi-level nested partitioned tree of clusters.
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Disadvantages of Hierarchical Clustering
Work done previously cannot be undone and cannot work well on large datasets.
Types of Hierarchical Clustering
- BIRCH - Balanced Iterative Reducing and Clustering using Hierarchies
- CURE - Clustering Using REpresentatives
- CHAMELEON - Hierarchical Clustering using Dynamic Modeling. This is a graph partitioning approach used in clustering complex structures.
- Probabilistic Hierarchical Clustering
- Generative Clustering Model
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Density-Based Clustering: DBSCAN
- Clustering based on a local cluster criterion
- Can discover clusters of random shapes and can handle outliers
- Density parameters should be provided for stopping condition
DBSCAN - Density-Based Spatial Clustering of Applications with Noise
Works on the basis of two parameters:
Eps - Maximum Radius of the neighbourhood
MinPts - Minimum number of points in the Eps-neighbourhood of a point
It works on the principle of density
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OPTICS
Ordering of Points to Identify Cluster Structure
Works on the principle of varying density of clusters
2 Aspects for Optics
“Plot the number of clusters for the image if it was subject to Optics clustering”.
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Grid-Based Clustering Methods
Create a grid structure by dividing the data space into a fixed number of cells.
From the grid's cells, identify clusters.
Challenges:
uneven data distribution is challenging to handle.
is plagued by dimensionality, making it challenging to cluster high-dimensional data.
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Methods:
STING - STatistical INformation Grid approach.
CLIQUE - CLustering in QUEst - This is both density-based as well as grid-based subspace clustering algorithm.
Three broad categories of measurement in clustering:
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External
Used to compare the clustering output against subject matter expertise (ground truth)
Four criteria for External Methods are:
-
Cluster Homogeneity - More the purity, better is the cluster formation.
-
Cluster Completeness - Ground truth of objects and cluster assigned objects to belong to the same cluster.
-
Ragbag better than Alien - Assigning heterogeneous object is very different from the remaining points of a cluster to a cluster will be penalized more than assigning it into a rag bag/miscellaneous/other category
-
Small cluster preservation - Splitting a large cluster into smaller clusters is much better than splitting a small cluster into smaller clusters.
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Most Common External Measures
- Matching-based measures
- Purity
- Maximum Matching
- F-measure (Precision & Recall)
- Entropy-based measures
- Entropy of Clustering
- Entropy of Partitioning
- Conditional Entropy
- Mutual Information
- Normalized Mutual Information (NMI)
- Pairwise measures
- True Positive
- False Negative
- False Positive
- True Negative
- Jaccard Coefficient
- Rand Statistic
- Fowlkes - Mallow Measure
- Correlation measures
- Discretized Huber Static
- Normalized Discretized Huber Static
Internal
Goodness of clustering and an example of same is Silhouette coefficient
Most common internal measures:
- Beta-CV measure
- Normalized Cut
- Modularity
- Relative measure - Silhouette Coefficient
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Relative
Compare the results of clustering obtained by different parameter settings of the same algorithm.
Clustering Assessment Methods
- Spatial Histogram
- Distance Distribution
- Hopkins Statistic
Finding K value in clustering
- Bootstrapping Approach
- Empirical Method
- Elbow Method
- Cross-Validation Method
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