Detecting Communities under Differential Privacy

Complex networks usually expose community structure with groups of nodes sharing many links with the other nodes in the same group and relatively few with the nodes of the rest. This feature captures valuable information about the organization and even the evolution of the network. Over the last decade, a great number of algorithms for community detection have been proposed to deal with the increasingly complex networks. However, the problem of doing this in a private manner is rarely considered. In this paper, we solve this problem under differential privacy, a prominent privacy concept for releasing private data. We analyze the major challenges behind the problem and propose several schemes to tackle them from two perspectives: input perturbation and algorithm perturbation. We choose Louvain method as the back-end community detection for input perturbation schemes and propose the method LouvainDP which runs Louvain algorithm on a noisy super-graph. For algorithm perturbation, we design ModDivisive using exponential mechanism with the modularity as the score. We have thoroughly evaluated our techniques on real graphs of different sizes and verified their outperformance over the state-of-the-art

Efficient Computation of Multiple Density-Based Clustering Hierarchies

HDBSCAN*, a state-of-the-art density-based hierarchical clustering method, produces a hierarchical organization of clusters in a dataset w.r.t. a parameter mpts. While the performance of HDBSCAN* is robust w.r.t. mpts in the sense that a small change in mpts typically leads to only a small or no change in the clustering structure, choosing a "good" mpts value can be challenging: depending on the data distribution, a high or low value for mpts may be more appropriate, and certain data clusters may reveal themselves at different values of mpts. To explore results for a range of mpts values, however, one has to run HDBSCAN* for each value in the range independently, which is computationally inefficient. In this paper, we propose an efficient approach to compute all HDBSCAN* hierarchies for a range of mpts values by replacing the graph used by HDBSCAN* with a much smaller graph that is guaranteed to contain the required information. An extensive experimental evaluation shows that with our approach one can obtain over one hundred hierarchies for the computational cost equivalent to running HDBSCAN* about 2 times.Comment: A short version of this paper appears at IEEE ICDM 2017. Corrected typos. Revised abstrac

Localization in Unstructured Environments: Towards Autonomous Robots in Forests with Delaunay Triangulation

Autonomous harvesting and transportation is a long-term goal of the forest industry. One of the main challenges is the accurate localization of both vehicles and trees in a forest. Forests are unstructured environments where it is difficult to find a group of significant landmarks for current fast feature-based place recognition algorithms. This paper proposes a novel approach where local observations are matched to a general tree map using the Delaunay triangularization as the representation format. Instead of point cloud based matching methods, we utilize a topology-based method. First, tree trunk positions are registered at a prior run done by a forest harvester. Second, the resulting map is Delaunay triangularized. Third, a local submap of the autonomous robot is registered, triangularized and matched using triangular similarity maximization to estimate the position of the robot. We test our method on a dataset accumulated from a forestry site at Lieksa, Finland. A total length of 2100\,m of harvester path was recorded by an industrial harvester with a 3D laser scanner and a geolocation unit fixed to the frame. Our experiments show a 12\,cm s.t.d. in the location accuracy and with real-time data processing for speeds not exceeding 0.5\,m/s. The accuracy and speed limit is realistic during forest operations

Training Gaussian Mixture Models at Scale via Coresets

How can we train a statistical mixture model on a massive data set? In this work we show how to construct coresets for mixtures of Gaussians. A coreset is a weighted subset of the data, which guarantees that models fitting the coreset also provide a good fit for the original data set. We show that, perhaps surprisingly, Gaussian mixtures admit coresets of size polynomial in dimension and the number of mixture components, while being independent of the data set size. Hence, one can harness computationally intensive algorithms to compute a good approximation on a significantly smaller data set. More importantly, such coresets can be efficiently constructed both in distributed and streaming settings and do not impose restrictions on the data generating process. Our results rely on a novel reduction of statistical estimation to problems in computational geometry and new combinatorial complexity results for mixtures of Gaussians. Empirical evaluation on several real-world datasets suggests that our coreset-based approach enables significant reduction in training-time with negligible approximation error