  Semi-supervised active clustering (SSAC) utilizes the knowledge of a domain
expert to cluster data points by interactively making pairwise "same-cluster"
queries. However, it is impractical to ask human oracles to answer every
pairwise query. In this paper, we study the influence of allowing "not-sure"
answers from a weak oracle and propose algorithms to efficiently handle
uncertainties. Different types of model assumptions are analyzed to cover
realistic scenarios of oracle abstraction. In the first model, random-weak
oracle, an oracle randomly abstains with a certain probability. We also
proposed two distance-weak oracle models which simulate the case of getting
confused based on the distance between two points in a pairwise query. For each
weak oracle model, we show that a small query complexity is adequate for the
effective $k$ means clustering with high probability. Sufficient conditions for
the guarantee include a $\gamma$-margin property of the data, and an existence
of a point close to each cluster center. Furthermore, we provide a sample
complexity with a reduced effect of the cluster's margin and only a logarithmic
dependency on the data dimension. Our results allow significantly less number
of same-cluster queries if the margin of the clusters is tight, i.e. $\gamma
\approx 1$. Experimental results on synthetic data show the effective
performance of our approach in overcoming uncertainties.
