Clustering/Subspace Clustering Algorithms on MATLAB

This repo is no longer in active development. However, any problem on implementations of existing algorithms is welcomed. [Oct, 2020]

1. Clustering Algorithms

• K-means
• K-means++
  • Generally speaking, this algorithm is similar to K-means;
  • Unlike classic K-means randomly choosing initial centroids, a better initialization procedure is integrated into K-means++, where observations far from existing centroids have higher probabilities of being chosen as the next centroid.
  • The initializeation procedure can be achieved using Fitness Proportionate Selection.
• ISODATA (Iterative Self-Organizing Data Analysis)
  • To be brief, ISODATA introduces two additional operations: Splitting and Merging;
  • When the number of observations within one class is less than one pre-defined threshold, ISODATA merges two classes with minimum between-class distance;
  • When the within-class variance of one class exceeds one pre-defined threshold, ISODATA splits this class into two different sub-classes.
• Mean Shift
  • For each point x, find neighbors, calculate mean vector m, update x = m, until x == m;
  • Non-parametric model, no need to specify the number of classes;
  • No structure priori.
• DBSCAN (Density-Based Spatial Clustering of Application with Noise)
  • Starting with pre-selected core objects, DBSCAN extends each cluster based on the connectivity between data points;
  • DBSCAN takes noisy data into consideration, hence robust to outliers;
  • Choosing good parameters can be hard without prior knowledge;
• Gaussian Mixture Model (GMM)
• LVQ (Learning Vector Quantization)

2. Subspace Clustering Algorithms

• Subspace K-means
  • This algorithm directly extends K-means to Subspace Clustering through multiplying each dimension d_j by one weight m_j (s.t. sum(m_j)=1, j=1,2,...,p);
  • It can be efficiently sovled in an Expectation-Maximization (EM) fashion. In each E-step, it updates weights, centroids using Lagrange Multiplier;
  • This rough algorithm suffers from the problem on its favor of using just a few dimensions when clustering sparse data;
• Entropy-Weighting Subspace K-means
  • Generally speaking, this algorithm is similar to Subspace K-means;
  • In addition, it introduces one regularization item related to weight entropy into the objective function, in order to mitigate the aforementioned problem in Subspace K-means.
  • Apart from its succinctness and efficiency, it works well on a broad range of real-world datasets.