Spectral Cluster Analysis

Spectral clustering is an unsupervised method that builds a similarity graph of the observations, embeds them using eigenvectors of the graph Laplacian, and then clusters the embedded points, typically with k-means.

스펙트럴 군집분석은 관측치 간 유사도 그래프를 만들고 그래프 라플라시안의 고유벡터로 관측치를 임베딩한 뒤 보통 k-평균으로 군집화하는 비지도 학습 방법이다.

How do I find clusters that are not round or convex in shape?

둥글지 않거나 볼록하지 않은 모양의 군집은 어떻게 찾나요?

Spectral clustering represents the data as a similarity graph and clusters points using the leading eigenvectors of its Laplacian, so it can separate connected but non-convex groups. It fits when clusters are defined by connectivity, such as rings or elongated shapes, where k-means fails.

When to use Spectral Cluster Analysis

• Clusters with non-convex shapes such as rings or crescents
• Data naturally expressed as a similarity or affinity matrix
• Moderate sample sizes where an n-by-n similarity matrix is feasible

When to use something else

• Clusters are roughly spherical and the dataset is large: use k-means clustering
• The number of clusters is unknown and noise points should be flagged: use DBSCAN or HDBSCAN

Assumptions and requirements

• Number of clusters is specified in advance
• A sensible similarity kernel and scale parameter (or nearest-neighbor graph) are chosen
• Features are scaled comparably
• Computation grows quickly with sample size

What the analysis reports

• Cluster membership for each observation
• Eigenvalues of the graph Laplacian (eigengap to guide number of clusters)
• Low-dimensional spectral embedding plot
• Validity indices such as silhouette width

How to report it

Spectral clustering with a [kernel] affinity identified [k] clusters, with an average silhouette width of [value].

Related methods

• K-Means Clustering
• Hierarchical Cluster Analysis
• DBSCAN

Run Spectral Cluster Analysis on Quorant