This post a summary of clustering methods I learned from Data Mining course at UMN.

Basically, clustering methods can be divided into two types: hierarchical and partitional.

Type of Clusters

Well-Separated Clusters

A cluster is a set of points such that any point in a cluster is closer (or more similar) to every other point in the cluster than to any point not in the cluster.

Well separated

Center-based clusters

A cluster is a set of objects such that an object in a cluster is closer (moresimilar) to the “center” of a cluster, than to the center of any other cluster.

The center of a cluster is often a centroid, the average of all the points in the cluster, or a medoid, the most “representative” point of a cluster.

Center based

Contiguity-based clusters

Contiguity based

A cluster is a set of points such that a point in a cluster is closer (or more similar) to one or more other points in the cluster than to any point not in the cluster.

Density-based clusters

Density based

A cluster is a dense region of points, which is separated by low-density regions, from other regions of high density. Used when the clusters are irregular or intertwined, and when noise and outliers are present.

Clusters Algorithms

More about K-meanas and Hierarchical clustering can be found in another post.

K-means Clustering

Sum of Squared Error (SSE) is usually used to evaluate K-means.

\[SSE=\sum_{i=1}^K\sum_{x\in C_i}\text{dist}^2(m_i,x)\]

K-means has problems when clusters are of differing sizes, densities and non-globular shapes.

K-means has problems when the data contains outliers.

Choosing initial centroids is very important for K-means.

Hierarchical Clustering

Strengths of Hierarchical Clustering:

  • Do not have to assume any particular number of clusters.
  • They may correspond to meaningful taxonomies.

Key operation is the computation of the proximity of two clusters.

We have the following ways to define the inter-cluster distances: MIN, MAX, Group Average, Distance Between Centroids

MIN: Single link, can handle non-elliptical shapes.

Single link strength

However, single link is sensitive to noise and outliers

Single link weakness

MAX: Complete link, less susceptible to noise and outliers.

Complete link strength

The limitations of MAX is:

  • Tends to break large clusters
  • Biased towards globular clusters

Complete link weakness

Group Average: is a compromis between single and complete Link.

Ward’s Method: Similarity of two clusters is based on the increase in squared error when two clusters are merged.


lDBSCAN is a density-based algorithm.

  • Density = number of points within a specified radius (Eps)
  • A point is a core point if it has at least a specified number of points (MinPts) within Eps
  • A border point is not a core point, but is in the neighborhood of a core point
  • A noise point is any point that is not a core point or a border point


The DBSCAN algorithm is resisitant to noise, and can handle clusters of different shapes and sizes.

DBSCAN Algorithm

DBSCAN can fail when the data has varying densities and high-dimensional data.

Cluster Validity

Entropy and SSE can be used to evaluate the performance of clustering.