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Graph Clustering: Challenges of Finding Good Cuts
- High computational cost
- Many graph cut problems are computationally expensive
- The sparsest cut problem is NP-hard
- Need to tradeoff between efficiency/scalability and quality
- Sophisticated graphs
- May involve weights and/or cycles.
- High dimensionality
- A graph can have many vertices. In a similarity matrix, a vertex is represented as a vector (a row in the matrix) whose dimensionality is the number of vertices in the graph
- Sparsity
- A large graph is often sparse, meaning each vertex on average connects to only a small number of other vertices
- A similarity matrix from a large sparse graph can also be sparse
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