Towards Scalable Spectral Embedding and Data Visualization via Spectral Coarsening

Boosting Graph Embedding on a Single GPU

“…Most recently, Gilbert et al presented CPU and GPU optimizations on many graph coarsening algorithms and demonstrated significant performance improvements on graph partitioning [27]. There have been recent attempts to use coarsening for embedding [5], [6], [28], [29], [30], however, they do not utilize specialized processing units such as GPUs, and they employ computationally expensive coarsening algorithms. Distributed embedding approaches are also proposed to make the embedding faster [10], [31], [32].…”

Improving Spectral Clustering Using Spectrum-Preserving Node Aggregation

“…[8] introduced a graph coarsening method for dividing the graph topology into random number of partitions. However, [8] mixed up and garbled spectral clustering and graph partitioning. All the data used for graph partitioning in [8] are without cluster membership (labels), so their claim that it works for clustering is wrong.…”

“…However, [8] mixed up and garbled spectral clustering and graph partitioning. All the data used for graph partitioning in [8] are without cluster membership (labels), so their claim that it works for clustering is wrong. Clustering aims to group similar samples together, however, the graphs used in [8] are pure topologies, rather than data graphs.…”

“…So, there is no "similarity" between their nodes, how comes clustering? [8] is not applicable to spectral clustering due to the following reasons: 1) spectral clustering aims to discover clusters for all the samples in the data set. However, original samples are missing in the coarsened graph.…”

“…Merits such as quotient-style metrics, edge-cut metric and expansion or conductance are all needed to be considered. Only using the normalized cut as in [8] cannot demonstrate its effectiveness.…”