MATLAB Implementation of Hierarchical Clustering Algorithm

Hierarchical clustering is a popular unsupervised learning method that progressively merges data points into hierarchical cluster structures. When implementing hierarchical clustering algorithms in MATLAB, different distance metrics can be employed to determine cluster merging strategies. ### Algorithm Approach Initialization: Treat each data point as an individual cluster. Implementation note: In MATLAB, this can be represented by creating a separate cluster index for each data point using a vector or cell array. Distance Matrix Calculation: Compute distances between all clusters, with options including Euclidean distance, Manhattan distance, or other metrics based on requirements. Code implementation: Use MATLAB functions like pdist() to calculate pairwise distances and squareform() to convert them into a square distance matrix. Merge Closest Clusters: Apply the "minimum inter-cluster distance" (single linkage method) to identify and merge the two closest clusters. Programming approach: Implement a function that scans the distance matrix to find the minimum non-diagonal value, recording the indices of clusters to merge. Update Distance Matrix: After merging clusters, recalculate distances between the new cluster and remaining clusters. The "maximum intra-cluster distance" (complete linkage method concept) can be used to ensure internal consistency of merged clusters. Algorithm optimization: Use dynamic programming to update only affected portions of the distance matrix rather than recalculating the entire matrix, improving computational efficiency. Repeat Merging Until Termination: Continuously merge the closest clusters until meeting termination criteria (such as reaching a specified number of clusters or merging all points into one cluster). Control structure: Implement a while-loop that continues until the stopping condition is met, with cluster count tracking through each iteration. ### Key Implementation Details Maximum Intra-cluster Distance (for cluster consistency): Calculate the maximum distance between points within merged clusters to ensure tightness of new clusters. MATLAB function suggestion: Implement max(pdist(cluster_points)) to compute the maximum distance within each cluster. Minimum Inter-cluster Distance (for cluster dissimilarity): When merging clusters, prioritize the minimum distance between two clusters to maintain distinctiveness after merging. Code technique: Maintain a priority queue or use min() function with appropriate indexing to efficiently find the smallest inter-cluster distance. Dynamic Update Strategy: After each merge, use recursive methods to update the distance matrix, enhancing computational efficiency. Programming optimization: Implement a function that updates only the row and column corresponding to the new cluster while preserving other unchanged distances. ### Application Scenarios This method is suitable for tasks requiring clear cluster structures, such as biological classification, market segmentation, or social network analysis, where cluster boundaries and hierarchical relationships are crucial. (Note: Since specific code was not provided by the user, this article focuses on explaining the algorithmic logic and implementation approaches.)