Consensus Clustering

In this article, we’ll begin by providing a concise overview of clustering and its prevalent challenges. Subsequently, we’ll explore how consensus clustering serves as a solution to mitigate these challenges and delve into interpreting its results. Before learning Consensus Clustering, we must know what Clustering is.

In Machine Learning, Clustering is a technique used for grouping different objects in separated clusters according to their similarity, i.e. similar objects will be in the same clusters, separated from other clusters of similar objects. It is an Unsupervised learning method. Few frequently used Clustering algorithms are K-means, K-prototype, DBSCAN etc.

Clustering

Issues with the existing clustering Methods

• Modern clustering techniques might not be able to satisfy all needs. Time complexity makes managing multiple dimensions and large datasets difficult.
• The accuracy of the definition of “distance,” particularly in distance-based clustering, determines how effective these methods are. There may be difficulties with this definition, especially in multidimensional spaces.
• In the absence of a simple distance measure, one must “define” it intricately, which is a difficult task, especially in high-dimensional settings.
• There are various ways to interpret the results of clustering algorithms, which in some cases can be interpreted arbitrarily. This variability in interpretation adds another level of complexity to the analysis.

Proof for using Consensus Clustering

Existing clustering techniques have inherent limitations, making the interpretation of results challenging, particularly when the number of clusters is unknown. Clustering methods are highly sensitive to the initial settings, leading to the amplification of non-significant data in non-reiterative methods.

It is very difficult to validate clustering results in the absence of an external objective criterion (such as known class labels in supervised analysis). Without these standards, this validation becomes elusive. Certain drawbacks of hierarchical clustering are addressed by techniques like SOM and k-means, which offer clearly defined boundaries and clusters.

Consensus clustering provides a way to visualize cluster details, calculate cluster numbers, evaluate stability, and represent consensus across multiple clustering runs. Nevertheless, the number of clusters needs to be selected in advance, and it does not have the same intuitive appeal as hierarchical dendrograms.

Consensus Clustering

Consensus clustering is an approach that combines data from several clustering algorithm runs to increase the robustness of clustering analyses. It helps identify the optimal number of clusters in the data and assesses the stability of clusters that have been identified by comparing the consensus between various runs. This method is useful for overcoming the initial condition sensitivity of clustering algorithms. Users can also examine and comprehend the features of the recognized clusters thanks to its visual depiction of cluster-related insights. In the difficult field of cluster analysis, consensus clustering helps produce results that are more stable and dependable.

Consensus Clustering Process

Working of Consensus Clustering

The Consensus Clustering is based on two phases-

1. Partition Generation:  In this stage, different partitions of data objects are created using different subsets of data attributes, applying different clustering algorithms with different bias, taking different parameters for clustering and using a different random subsample of the whole dataset. Once we generate the initial partition, we move forward towards generating consensus among the partitions and further generating the new partitions based on the previous consensus.
2. Consensus Generation: The consensus among the data partitions is generated using the Consensus Function, which is obtained generally in these approaches –
   • Median Partitioning based approach: Here the data points of different partitions are grouped together by their similarity index. We form new partitions based on the medians of the data points of previous partitions. The Similarity index depends on the agreement & disagreement of the data points, which is measured by F-measures, Rand index etc.
   • Co-occurrence based approach: In this approach, there are 3 methods we can use: 1. Relabeling/Voting based method, 2. Co-association matrix-based method, 3. Graph-based method. Relabeling/Voting based method generates the new clusters by determining the correspondence with the current consensus. Each instance gains a certain vote from their cluster assignments and updates the consensus and the cluster assignments accordingly. The Co-association matrix-based method generates the new clusters based on the co-association matrix by the similarity of data points and the Graph-based method generates a weighted graph to represent multiple clusters and finds the optimal partitions by minimizing the graph cut.

Workflow of Consensus Clustering

There are many different Consensus Clustering algorithms based on different approaches of generating consensus function and there are many research works still going on improving the existing models.

Summary Statistics

We can calculate two summary statistics to assess the stability of a cluster and the importance of specific observations within it. The first statistic, cluster consensus that calculates the average consensus value for every pair of observations within the clusters.

Cluster Consensus =

The next statistic is item consensus which centers on a specific item or observation. It calculates the average consensus value of that item with respect to all other items within its cluster.

Item Consensus =

The stability and dependability of clusters as well as individual data points in consensus clustering can be assessed quantitatively using these formulas. They are usually applied in the analysis of the consensus matrix that is produced after several iterations of clustering.

Advantages of Consensus Clustering

The advantages of Consensus clustering include:

• Robustness: Consensus Clustering enhances the robustness of clustering results by aggregating information from multiple runs, reducing sensitivity to initialization.
• Stability Assessment: It helps to identify clusters that are consistently present across various iterations by providing a quantitative measure of cluster stability.
• Cluster Validation: Consensus Clustering aids in the validation of clusters by offering insights into the reliability and significance of identified clusters.
• Noise Reduction: It assists in filtering out noise or less stable clusters by capturing consensus patterns, producing clustering results that are more dependable.

Disadvantages of Consensus Clustering

Consensus clustering has a number of benefits, but it may also have some drawbacks:

• Computational Intensity: Consensus Clustering involves running the clustering algorithm multiple times, which can be computationally intensive and time-consuming, especially for large datasets.
• Parameter Sensitivity: Consensus clustering is sensitive to parameter selection, as its efficacy can be influenced by the selection of the clustering algorithm or the number of runs.
• Interpretability: Consensus results can be difficult to interpret because they produce a consensus matrix that needs more examination in order to yield useful information.
• Dependency on Initial Clustering Algorithm: The first clustering algorithm used determines the quality of consensus results, and the method may not work well if the base algorithm has trouble with a particular kind of data.

Frequently Asked Questions on Consensus Clustering

Q. What is Consensus Clustering?

Consensus Clustering is a technique that combines multiple clustering results to improve the stability, robustness, and reliability of the overall clustering outcome.

Q. Why is Consensus Clustering used?

In order to provide more reliable and validated clusters, it is used to address the unpredictability and sensitivity to initialization in conventional clustering methods.

Q. How does Consensus Clustering work?

It involves running a base clustering algorithm multiple times, creating a consensus matrix, and extracting stable clusters based on the agreement among different runs.

Q. In what scenarios is Consensus Clustering beneficial?

It helps with datasets where more robustness is needed, where validation metrics are unclear, or where traditional clustering techniques exhibit sensitivity to initialization.

Q. How to choose the number of clusters in Consensus Clustering?

In order to find a stable and meaningful partitioning, the consensus matrix’s stability and consensus values are frequently used to calculate the ideal number of clusters.