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What Is Constrained Clustering In Data Mining?


Data mining is the process of extracting useful information from large datasets. One of the most popular techniques used in data mining is clustering with constraints, which involves grouping similar objects based on reconsidering traditional clustering, making any external knowledge or constraints that may be available about the data. This can lead to suboptimal results and make it difficult to interpret the clusters. Researchers have developed constrained clustering algorithms that incorporate domain-specific knowledge or user-defined constraints into the clustering process to address this issue. Furthermore, clustering with constraints is a vital concept of data science. So to know more about the topic, keep reading. 

What is Constraint Based Clustering?

Constraint based clustering (CBC) is a constrained clustering algorithm that uses additional information or constraints to guide the cluster formation process. The goal of constraint based clustering is to produce clusters consistent with these constraints while still being as homogeneous as possible within each cluster.

CBC is a popular clustering technique in various fields, including biology, social sciences, and computer science. It provides a flexible framework for incorporating prior knowledge or domain-specific information into the clustering process.In constraint based clustering, constraints can take different forms depending on the application domain. For example, genes may be constrained to belong to specific biological pathways or co-expression modules in gene expression analysis. In image segmentation tasks, pixels may be constrained to have similar color intensities or spatial proximity. In text mining applications, documents may be constrained to belong to predefined topics or categories.

CBC algorithms typically consist of two main steps: 

(1) Constraint Modeling: The constraints are encoded as mathematical expressions that define the allowable configurations of clusters. This can involve defining similarity measures between data points based on their attributes and relationships with other data points.

(2) Cluster Formation: In the second step of constraint based clustering algorithms, clusters are formed by optimizing an objective function that balances adherence to constraints with homogeneity within each cluster. This optimization process involves the iterative refinement of cluster assignments until convergence criteria are met.

Types of Constraints Used in Clustering 

Several constraints can be used in constraint based clustering, including pairwise similarity/dissimilarity constraints, must-link and cannot-link constraints, attribute-value equality/inequality constraints, and hierarchical structure constraints. Let’s learn about these methods in details: 

  • Pairwise Similarity/Dissimilarity Constraints: Pairwise similarity/dissimilarity constraints are often used in constraint based clustering to ensure that objects with similar characteristics or attributes are grouped. For example, suppose a survey asks respondents to rate different types of cars based on their fuel efficiency, size, and price. In that case, pairwise similarity/dissimilarity constraints can be used to group cars with similar ratings for these attributes. This helps create more meaningful clusters and ensures that the results accurately reflect respondent preferences.
  • Must-Link and Cannot-Link Constraints: Must-link and cannot-link constraints are also commonly used in constraint based clustering studies. Must-link constraints require grouping particular objects because they share common characteristics or attributes.For example, if a survey asks respondents about their favorite sports teams, must-link constraints can group all responses related to a specific team into one cluster. On the other hand, cannot-link constraints prevent particular objects from being grouped because they have significant differences or conflicts in terms of characteristics or attributes.
  • Attribute-Value Equality/Inequality Constraints: Attribute-value equality/inequality constraints require specific attribute values for objects within a cluster. For instance, if respondents were asked about their preferred type of pizza toppings (e.g., meat lovers vs. vegetarians), attribute-value equality/inequality constraints could be applied so that only those who selected the same topping preferences would belong in the same cluster.
  • Hierarchical Structure Constraint: Finally, the hierarchical structure constraint specifies how many levels should be between different groups when forming clusters. This is particularly useful when studying complex topics such as brand loyalty, where multiple layers of preference may influence consumer behavior.Overall, using various constraints allows researchers conducting constraint based clustering studies to obtain more accurate results by ensuring better grouping and clustering while also considering respondent preferences and behaviors.

Popular Algorithms For Constraint Based Clustering

Several popular algorithms have been developed for constraint based clusterings each algorithm has its strengths and weaknesses, depending on the type of constraints used and the nature of the data:

  • Constrained Optimization Problem K-Means(COP-KMeans): COP-KMeans is a popular algorithm for constraint based clustering that aims to minimize the sum of distances between data points and their respective cluster centers while satisfying a set of constraints. These constraints can be used to ensure that certain data points are assigned to specific clusters or that clusters have a minimum or maximum size.
  • Clustering by Constraints: COBWEB-CLUSTER is another widely used algorithm for constraint based clustering, which uses an incremental approach to build hierarchical clusters. The algorithm starts with a single cluster containing all the data points and then splits it recursively into smaller sub-clusters until no further splitting is possible. Constraints can be added at each step of the process to guide the formation of clusters.
  • Constrained Spectral Partitioning Algorithm: CSPA is an algorithm that combines spectral partitioning techniques with constraints to create high-quality partitions in large datasets. It works by constructing a similarity matrix from the input data and then using spectral methods to identify groups of highly similar objects. Constraints are incorporated into this process by penalizing any solutions that do not satisfy them.
  • Complete Neighborhood Graph Algorithm: CONGA, on the other hand, relies on complete neighborhood graphs (CNGs) to identify densely connected regions within high-dimensional spaces. It achieves this by first constructing CNGs from the input data and then partitioning them into smaller subgraphs using agglomerative clustering techniques. Constraints can be applied during both stages of this process, allowing users to control how tightly connected objects should be grouped together.
  • Clustering Objects on Labeled Categorical Attributes: COOLCAT (Clustering Objects On Labeled Categorical Attributes), which focuses specifically on categorical data. 
  • Constraint-Based Clustering: CONCLUS (CONstraint-based CLUStering), which allows users to specify complex logical expressions as constraints.
  • Probabilistic Constrained K-Means: PCK-Means (Probabilistic Constrained K-Means), which uses probability distributions instead of distance measures when assigning objects to clusters.
Advantages of Constraint Based Clustering

One way that constraint based clustering can specific external knowledge is by using constraints. Constraints are conditions or rules that specify how specific data points should be assigned to clusters based on prior knowledge or domain expertise. For example, a constraint might state that two data points must belong to the same cluster if they have similar values for a particular feature. By incorporating these constraints into the clustering process, constraint based clustering can produce more accurate and meaningful clusters.

  • The main advantage of constraint based clustering is that it allows for external knowledge or user-defined constraints to be incorporated into the clustering process. This can lead to more meaningful clusters that are easier to interpret and use in downstream analysis tasks such as classification or anomaly detection. 
  • Constraint based clustering can help overcome some limitations of traditional clustering algorithms, such as sensitivity to outliers or noise in the data.
  • Another advantage of constraint based clustering is its ability to handle complex data structures and relationships between variables. Traditional clustering algorithms often rely on assumptions about the distribution and scale of features in the data, which may only hold for some datasets. CBC can overcome these limitations by using non-linear transformations or distance metrics that capture more nuanced relationships between variables.
  • The constraint based clustering has been applied successfully in various domains, including biology, finance, and social science research. In one study, researchers used constraint based clustering to identify subgroups of breast cancer patients with different prognoses based on gene expression patterns. In another study, financial analysts used constraint based clustering to segment customers based on their spending habits and preferences. 
  • One advantage of constraint based clustering over traditional unsupervised clustering methods is its ability to handle noisy or incomplete data by incorporating external information sources such as expert knowledge or ontologies. Additionally, constraint based clustering allows for fine-grained control over how constraints influence cluster formation by adjusting parameters such as penalty weights and threshold values.

Overall, constraint based clustering is a powerful tool for exploratory data analysis and pattern recognition that leverages additional information beyond just raw input features during the clustering process resulting in more accurate results than standard techniques when dealing with complex datasets with some form of prior knowledge about groupings within its contents.

Challenges with Constraint Based Clustering

Despite its advantages, several challenges are associated with constraint based clustering. 

  • One major challenge is determining which constraints should be used and how they should be defined. 
  • Another challenge of constraint based clustering is dealing with conflicting or inconsistent constraints that may arise due to errors in the essential input differences in expert opinions.


Constraint based clustering has become essential for data mining researchers who want to incorporate external knowledge or user-defined constraints into their analyses. By using these algorithms, analysts can produce more meaningful clusters that better reflect domain-specific information about their datasets while still being as homogeneous as possible within each cluster. However, the continuing challenges associated with constraint based clustering must be addressed if this technique continues growing in popularity among practitioners across different domains. Finally, if you are keen to become a data scientist, then you must have mastery over programming languages like R, Python, and Hadoop. Proficiency in these languages and proper communication skills will help you attain your dream job as a Data scientist. 

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Q.1. What is The Benefit of Clustering with Constraints?

Ans. The significant advantage of clustering with constraints is that it helps you make the clustering job more precise and definite by uniting user constraints, which can be instance-level or cluster-level constraints. 

Q.2. What is The Need For Clustering with Constraints in Data Mining?

Ans. It is implemented in marketing to know about customer demographics. Having a deeper insight into various market divisions helps you target buyers accurately with promotional advertisements. It provides the scope for various practical applications for clustering with constraints in data mining. 

Q.3. Give Some Examples of Clustering with Constraints.

Ans. Some examples of clustering with constraints are as follows: 

  • Detecting fake news
  • Spam filter
  • Sales and marketing campaigns
  • Categorizing web traffic
  • Detecting deceptive activity
  • Document analysis

Q.4. When Should We Not Use Clustering?

Ans. Clustering must not be utilized when there is data. Still, there is no method to arrange it into definite groups/ If there is a proper class label in the data set, then the labels made by a clustering analysis may not work properly like the natural class label.

Q.5. Mention The Types of Clustering with Constraints.

Ans. The types of clustering with constraints include centroid-based clustering, density-based clustering, distribution-based clustering, and hierarchical clustering, 

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