  We consider a non-stochastic privacy-preserving problem in which an adversary
aims to infer sensitive information $S$ from publicly accessible data $X$
without using statistics. We consider the problem of generating and releasing a
quantization $\hat{X}$ of $X$ to minimize the privacy leakage of $S$ to
$\hat{X}$ while maintaining a certain level of utility (or, inversely, the
quantization loss). The variables $S$ and $S$ are treated as bounded and
non-probabilistic, but are otherwise general. We consider two existing
non-stochastic privacy measures, namely the maximum uncertainty reduction
$L_0(S \rightarrow \hat{X})$ and the refined information $I_*(S; \hat{X})$
(also called the maximin information) of $S$. For each privacy measure, we
propose a corresponding agglomerative clustering algorithm that converges to a
locally optimal quantization solution $\hat{X}$ by iteratively merging elements
in the alphabet of $X$. To instantiate the solution to this problem, we
consider two specific utility measures, the worst-case resolution of $X$ by
observing $\hat{X}$ and the maximal distortion of the released data $\hat{X}$.
We show that the value of the maximin information $I_*(S; \hat{X})$ can be
determined by dividing the confusability graph into connected subgraphs. Hence,
$I_*(S; \hat{X})$ can be reduced by merging nodes connecting subgraphs. The
relation to the probabilistic information-theoretic privacy is also studied by
noting that the G{\'a}cs-K{\"o}rner common information is the stochastic
version of $I_*$ and indicates the attainability of statistical
indistinguishability.
