Cluster Analysis and Its
Significance to Business

Cluster Analysis Overview

One of the most popular techniques in data science, clustering is the method of identifying similar groups of data in a dataset. One of the most common uses of clustering is segmenting a customer base by transaction behavior, demographics, or other behavioral attributes.

Types of Clustering

In broad terms, clustering can be divided into two subgroups.

• Hard Clustering
• Soft Clustering

In the case of hard clustering, each data point completely belongs to a cluster, or it doesn’t. However, in soft clustering, instead of each data point being assigned to a cluster, the probability of that data point being in a certain cluster is assigned.

Different Types of Clustering Algorithms and Their Applicability in Real-World Scenarios

Clustering is subjective, and there are multiple means for achieving it. Each methodology has a different set of rules for defining similarity, and there are more than 100 clustering algorithms. There are a few algorithms, though, which are popularly used.

• Connectivity Models

  Connectivity models are based on the idea that data points closer in data space show more similarity to each other than data points farther away. These models can follow two approaches. The first approach involves starting with the classification of all data points into clusters and aggregating them as distance decreases. The second involves all data points being identified as a single cluster and partitioned as the distance increases. The choice of distance function is also subjective. Connectivity models are easy to interpret, but lack scalability for handling large datasets. Hierarchical clustering algorithms and its variants are an example of connectivity models.

• Centroid Model

  Iterative clustering algorithms in which similarity is derived by the closeness of a data point to the centroid of the clusters, centroid models include K-Means clustering. In centroid models, the number of clusters required at the end must be identified in the beginning, making it important to have prior knowledge of the dataset. Centroid Models also run iteratively to find the local optima.

• Distribution Model

  This type of clustering model is based on the probability of all data points in the cluster belonging to the same distribution (Normal, Gaussian, etc.) Distribution models often suffer from overfitting. Expectation-maximization algorithm is a popular example of a distribution model, using multivariate normal distributions.

• Density Model

  Density models search data space for areas of varied density of data points, isolating various different density regions and assigning the data points within these regions in the same cluster. DBSCAN and OPTICS are popular examples of density models.

• K Means Clustering

  An iterative clustering algorithm, K means aims to find local maxima in each iteration, working in five steps:

  1. Specify the desired number of clusters K. For example, we’ll choose k=2 for these 5 data points in 2-D space.
  
  2. Specify the desired number of clusters K. For example, we’ll choose k=2 for these 5 data points in 2-D space.
  
  3. Cluster centroids must then be computer: The centroid of data points in the grey cluster using grey cross and those in the red cluster is shown using red cross.
  
  4. Each point must then be reassigned to the closest cluster centroid. Note that only the data point that is at the bottom is assigned to the red cluster even though it is closer to the centroid of grey cluster. Therefore, that data point must be assigned into the grey cluster
  
  5. The cluster centroids must then be recomputed, now re-computing the centroids for both the clusters.
  
  6. Repeat steps 4 and 5 until there are no more improvements are to make. When there are no further switching of data points between two clusters for two successive repeats, it marks the termination of the algorithm if not explicitly mentioned.
  

• Hierarchical Clustering

  As the name suggests, Hierarchical Clustering is an algorithm which builds a hierarchy of clusters. Starting with all the data points assigned to a cluster of their own, the algorithm then merges the two nearest clusters into the same cluster. This algorithm will only terminate only when a single cluster left.

  The results of hierarchical clustering can be shown using dendrogram, which can be interpreted as:

  

  At the bottom, we begin with 25 data points assigned to separate clusters. The two closest clusters are merged until one cluster remains at the top. The height at which two clusters are merged in the dendrogram represents the distance between two clusters in the data space. The number of clusters that best depict different groups can be chosen by observing the dendrogram. The best choice for the number of clusters is the number of vertical lines in the dendrogram cut by a horizontal line which can transverse the maximum vertical distance without intersecting a cluster.

  In the example above, the best number of clusters will be four, as the horizontal red line in the dendrogram below covers maximum vertical distance AB.

  

There are two important things to know about hierarchical clustering:

• The algorithm has been implemented in the above examples using a bottom-up approach, though it is possible to follow a top-down approach, beginning with all data points assigned to the same cluster and recursively performing splits until each data point is assigned a separate cluster.
• The decision to merge two clusters is made based on the closeness of the clusters:
  1. Squared Euclidean distance: ||a-b||22 = Σ((ai-bi)2)
  2. Mahalanobis distance: √((a-b)T S-1 (-b)) {where, s : covariance matrix}
  3. Euclidean distance: ||a-b||2 = √(Σ(ai-bi))
  4. Manhattan distance: ||a-b||1 = Σ|ai-bi|
  5. Maximum distance:||a-b||INFINITY = maxi|ai-bi|

Need Help? – Consult the Cluster Analysis Experts at Research Optimus

Though clustering is easy to implement, there are important aspects to take care of, such as treating outliers in your data and making sure each cluster has enough population so that the inferred information gives the right directive. It has many uses, including planning or strategizing marketing campaigns, identifying test markets for new product development as well as in the field of biology and medical science like human genetic clustering, etc.

Research Optimus (ROP) as a knowledge process outsourcing service provider has been assisting businesses achieving their business objectives. With a pool of experienced analysts, the ROP team can certainly add value to you decision-making process utilizing the power of statistics in the form of cluster analysis, PESTEL analysis, data modeling, performance analysis, and more.