What are some extensions and variations of normalized cut clustering for different data types and structures?

1 Spectral clustering

One way to extend normalized cut clustering is to use spectral clustering, which applies dimensionality reduction techniques to the data before clustering. Spectral clustering transforms the data into a lower-dimensional space that preserves the pairwise relationships between the data points, and then applies a standard clustering algorithm, such as k-means, to the reduced data. Spectral clustering can capture complex cluster shapes, deal with noise and outliers, and avoid the bias of the Euclidean distance.

2 Multiscale normalized cut

Another variation of normalized cut clustering is multiscale normalized cut, which adapts the number of clusters to the local density and structure of the data. Multiscale normalized cut uses a hierarchical approach that recursively splits the data into smaller subsets based on the normalized cut criterion, until a stopping condition is met. The stopping condition can be based on a threshold, a minimum cluster size, or a stability measure. Multiscale normalized cut can discover clusters of different sizes and densities, and avoid overfitting or underfitting the data.

3 Graph-based normalized cut

A third extension of normalized cut clustering is graph-based normalized cut, which can handle data that are represented as graphs, such as images, social networks, or text documents. Graph-based normalized cut treats the data as nodes in a graph, and the similarity between the data as edges in the graph. It then partitions the graph into subgraphs that have high internal similarity and low external similarity, using the normalized cut criterion. Graph-based normalized cut can exploit the rich information contained in the graph structure, and cluster data that are not easily vectorized or measured by distance.

4 Kernelized normalized cut

A fourth variation of normalized cut clustering is kernelized normalized cut, which can handle data that are nonlinearly separable or have complex feature spaces. Kernelized normalized cut applies a kernel function to the data, which maps the data into a higher-dimensional space where they become more linearly separable. It then performs normalized cut clustering in the kernel space, using the kernel matrix as the similarity matrix. Kernelized normalized cut can capture nonlinear patterns and relationships in the data, and cluster data that are not well suited for linear methods.

5 Fuzzy normalized cut

A fifth extension of normalized cut clustering is fuzzy normalized cut, which can handle data that are ambiguous or uncertain. Fuzzy normalized cut assigns each data point to multiple clusters with different degrees of membership, rather than to a single cluster. It then optimizes the normalized cut criterion with respect to the membership matrix, using an iterative algorithm. Fuzzy normalized cut can account for the vagueness and overlap of the data, and cluster data that are not clearly defined or distinguished.

6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?