  In this paper, we develop a series of differential privacy (DP) algorithms
from a family of random projections (RP) for general applications in machine
learning, data mining, and information retrieval. Among the presented
algorithms, iDP-SignRP is remarkably effective under the setting of
``individual differential privacy'' (iDP), based on sign random projections
(SignRP). Also, DP-SignOPORP considerably improves existing algorithms in the
literature under the standard DP setting, using ``one permutation + one random
projection'' (OPORP), where OPORP is a variant of the celebrated count-sketch
method with fixed-length binning and normalization. Without taking signs, among
the DP-RP family, DP-OPORP achieves the best performance.
  Our key idea for improving DP-RP is to take only the signs, i.e., $sign(x_j)
= sign\left(\sum_{i=1}^p u_i w_{ij}\right)$, of the projected data. The
intuition is that the signs often remain unchanged when the original data ($u$)
exhibit small changes (according to the ``neighbor'' definition in DP). In
other words, the aggregation and quantization operations themselves provide
good privacy protections. We develop a technique called ``smooth flipping
probability'' that incorporates this intuitive privacy benefit of SignRPs and
improves the standard DP bit flipping strategy. Based on this technique, we
propose DP-SignOPORP which satisfies strict DP and outperforms other DP
variants based on SignRP (and RP), especially when $\epsilon$ is not very large
(e.g., $\epsilon = 5\sim10$). Moreover, if an application scenario accepts
individual DP, then we immediately obtain an algorithm named iDP-SignRP which
achieves excellent utilities even at small~$\epsilon$ (e.g., $\epsilon<0.5$).
