Aiming at the problem that the existing privacy protection histogram publishing methods based on grouping to suppress differential noise errors cannot effectively balance the group approximation error and the Differential Privacy (DP) Laplacian error, resulting in the lack of histogram availability, a High-Precision Histogram Publishing method (HPHP) was proposed. First, the constraint inference method was used to achieve the histogram ordering under the premise of satisfying the DP constraints. Then, based on the ordered histogram, the dynamic programming grouping method was used to generate groups with the smallest total error on the noise-added histogram. Finally, the Laplacian noise was added to each group mean. For the convenience of comparative analysis, the privacy protection histogram publishing method with the theoretical minimum error (Optimal) was proposed. Experimental analysis results between HPHP, DP method with noise added directly, AHP (Accurate Histogram Publication) method and Optimal show that the Kullback-Leibler Divergence (KLD) of the histogram published by HPHP is reduced by 90% compared to that of AHP method and is close to the effect of Optimal. In conclusion, under the same pre-conditions, HPHP can publish higher-precision histograms on the premise of ensuring DP.

Mining outliers is to find exceptional objects that deviate from the most rest of the data set. Outlier detection based on density has attracted lots of attention, but the density-based algorithm named Local Outlier Factor (LOF) is not suitable for the data set with abnormal distribution, and the algorithm named INFLuenced Outlierness (INFLO) solves this problem by analyzing both k nearest neighbors and reverse k nearest neighbors of each data point at cost of inferior efficiency. To solve this problem, a local density-based algorithm named Local Density Based Outlier detection (LDBO) was proposed, which can improve outlier detection efficiency and effectiveness simultaneously. LDBO introduced definitions of strong k nearest neighbors and weak k nearest neighbors to realize outlier relation analysis of those data points located nearby. Furthermore, to improve the outlier detection efficiency, prejudgement was applied to avoid unnecessary reverse k nearest neighbor analysis as far as possible. Theoretical analysis and experimental results Indicate that LDBO outperforms INFLO in efficiency, and it is effective and feasible.