  \textbf{A}ccuracy, \textbf{R}obustness to noises and scales,
\textbf{I}nterpretability, \textbf{S}peed, and \textbf{E}asy to use (ARISE) are
crucial requirements of a good clustering algorithm. However, achieving these
goals simultaneously is challenging, and most advanced approaches only focus on
parts of them. Towards an overall consideration of these aspects, we propose a
novel clustering algorithm, namely GIT (Clustering Based on \textbf{G}raph of
\textbf{I}ntensity \textbf{T}opology). GIT considers both local and global data
structures: firstly forming local clusters based on intensity peaks of samples,
and then estimating the global topological graph (topo-graph) between these
local clusters. We use the Wasserstein Distance between the predicted and prior
class proportions to automatically cut noisy edges in the topo-graph and merge
connected local clusters as final clusters. Then, we compare GIT with seven
competing algorithms on five synthetic datasets and nine real-world datasets.
With fast local cluster detection, robust topo-graph construction and accurate
edge-cutting, GIT shows attractive ARISE performance and significantly exceeds
other non-convex clustering methods. For example, GIT outperforms its
counterparts about $10\%$ (F1-score) on MNIST and FashionMNIST. Code is
available at \color{red}{https://github.com/gaozhangyang/GIT}.
