In-Depth Notes on Clustering Algorithms, K-Means and Hierarchical Clustering

Overview of Clustering Algorithms

• Clustering is a way to group data points in such a way that similar data points are grouped together.
• K-means and hierarchical clustering are two popular methods of clustering.

K-Means Clustering

• K-means is particularly good for datasets that form globular clusters:

  • Clusters must match expectations for them to be effective.
  • If clusters do not appear as expected, it may require recalibrating the clustering approach (e.g., adjusting the algorithm parameters).

• Choosing the number of clusters (k):

  • Elbow Method: Involves plotting the variance explained as a function of the number of clusters and looking for a "knee" point where the rate of variance explained drops off.
  • Silhouette Method: Provides a way to assess the appropriateness of clusters by measuring how similar an object is to its own cluster versus other clusters. Better for datasets lacking a defined elbow.

Hierarchical Clustering

• Hierarchical clustering uses a bottom-up approach:

  • Starts with each observation as its own cluster and merges them into larger clusters as the algorithm progresses.
  • Flexibility to select the number of clusters at any point based on user needs.

• Dendrograms:

  • A visual representation of the hierarchical clustering that shows the distance or dissimilarity between clusters.
  • Observations can be grouped according to the tallest links (representing dissimilarities) in the dendrogram.

Dendrogram Interpretation

• Vertical distance indicates dissimilarity; the larger the distance, the more dissimilar the clusters are.
• Cutting the dendrogram at a certain height allows selecting the number of clusters:
  • Example: Cutting high results in fewer clusters, cutting low results in more clusters.

Considerations for Clustering

• Unsupervised Learning:
  • Clustering does not rely on pre-labeled categories. It identifies inherent relationships based on feature similarities.
  • Important to understand that features selected for clustering significantly influence results.
  • Results may not always align with known categories or labels since clustering algorithms operate independently.

Challenges of Clustering

• Curse of Dimensionality:
  • In high-dimensional space, data points become sparse and varied. More data is needed for similar statistical power.
  • More features result in exponentially larger combinatorial space, necessitating more observations to fill that space adequately.
• Distance Measures in Clustering:
  • Different distance metrics can continually affect clustering performance:
  • Euclidean distance: Commonly used but can mislead in high dimensionality.
  • Other metrics include Manhattan, cosine similarity, etc.

Dissimilarity Metrics in Hierarchical Clustering

1. Single Linkage: Takes minimum distance from elements in different groups.
2. Complete Linkage: Takes maximum distance from elements in different groups.
3. Average Linkage: Considers the average distance from all elements in the cluster.
4. Ward's Linkage: Seeks to minimize the total within-cluster variance.

Key Takeaways in Clustering Algorithms

• Clustering can reveal hidden patterns in data but needs careful selection of features and metrics to be effective.
• It’s crucial to interpret results within the context of the data and intended task, as clustering is unsupervised and may not directly correspond to expected outcomes.
• Strong statistical and domain knowledge is necessary to select the most appropriate methods and evaluate traffic between clusters effectively.