Sampling random graph homomorphisms and applications to network data analysis

A graph homomorphism is a map between two graphs that preserves adjacency relations. We consider the problem of sampling a random graph homomorphism from a graph $F$ into a large network $\mathcal{G}$. We propose two complementary MCMC algorithms for sampling a random graph homomorphisms and establish bounds on their mixing times and concentration of their time averages. Based on our sampling algorithms, we propose a novel framework for network data analysis that circumvents some of the drawbacks in methods based on independent and neigborhood sampling. Various time averages of the MCMC trajectory give us various computable observables, including well-known ones such as homomorphism density and average clustering coefficient and their generalizations. Furthermore, we show that these network observables are stable with respect to a suitably renormalized cut distance between networks. We provide various examples and simulations demonstrating our framework through synthetic networks. We also apply our framework for network clustering and classification problems using the Facebook100 dataset and Word Adjacency Networks of a set of classic novels.Comment: 51 pages, 33 figures, 2 table

Time-aware Sub-Trajectory Clustering in Hermes@PostgreSQL

In this paper, we present an efficient in-DBMS framework for progressive time-aware sub-trajectory cluster analysis. In particular, we address two variants of the problem: (a) spatiotemporal sub-trajectory clustering and (b) index-based time-aware clustering at querying environment. Our approach for (a) relies on a two-phase process: a voting-and-segmentation phase followed by a sampling-and-clustering phase. Regarding (b), we organize data into partitions that correspond to groups of sub-trajectories, which are incrementally maintained in a hierarchical structure. Both approaches have been implemented in Hermes@PostgreSQL, a real Moving Object Database engine built on top of PostgreSQL, enabling users to perform progressive cluster analysis via simple SQL. The framework is also extended with a Visual Analytics (VA) tool to facilitate real world analysis

Identification of centroids of Mohammed V airport arrivals.

This paper presents a flight trajectory data analytics framework for identifying spatial and temporal patterns in aircraft movement and providing a high-fidelity characterization of air traffic flows. The framework includes three modules : Collecting Data, Resampling trajectories, and Clustering air traffic flows at temporal and spacial scale. Different machine learning techniques are especially incorporated into the three modules to process aircraft trajectory data and enable the characterization of traffic flows

Trajectory based video analysis in multi-camera setups

PhDThis thesis presents an automated framework for activity analysis in multi-camera setups. We start with the calibration of cameras particularly without overlapping views. An algorithm is presented that exploits trajectory observations in each view and works iteratively on camera pairs. First outliers are identified and removed from observations of each camera. Next, spatio-temporal information derived from the available trajectory is used to estimate unobserved trajectory segments in areas uncovered by the cameras. The unobserved trajectory estimates are used to estimate the relative position of each camera pair, whereas the exit-entrance direction of each object is used to estimate their relative orientation. The process continues and iteratively approximates the configuration of all cameras with respect to each other. Finally, we refi ne the initial configuration estimates with bundle adjustment, based on the observed and estimated trajectory segments. For cameras with overlapping views, state-of-the-art homography based approaches are used for calibration. Next we establish object correspondence across multiple views. Our algorithm consists of three steps, namely association, fusion and linkage. For association, local trajectory pairs corresponding to the same physical object are estimated using multiple spatio-temporal features on a common ground plane. To disambiguate spurious associations, we employ a hybrid approach that utilises the matching results on the image plane and ground plane. The trajectory segments after association are fused by adaptive averaging. Trajectory linkage then integrates segments and generates a single trajectory of an object across the entire observed area. Finally, for activities analysis clustering is applied on complete trajectories. Our clustering algorithm is based on four main steps, namely the extraction of a set of representative trajectory features, non-parametric clustering, cluster merging and information fusion for the identification of normal and rare object motion patterns. First we transform the trajectories into a set of feature spaces on which Meanshift identi es the modes and the corresponding clusters. Furthermore, a merging procedure is devised to re fine these results by combining similar adjacent clusters. The fi nal common patterns are estimated by fusing the clustering results across all feature spaces. Clusters corresponding to reoccurring trajectories are considered as normal, whereas sparse trajectories are associated to abnormal and rare events. The performance of the proposed framework is evaluated on standard data-sets and compared with state-of-the-art techniques. Experimental results show that the proposed framework outperforms state-of-the-art algorithms both in terms of accuracy and robustness

Adaptive Douglas-Peucker Algorithm With Automatic Thresholding for AIS-Based Vessel Trajectory Compression

Automatic identification system (AIS) is an important part of perfecting terrestrial networks, radar systems and satellite constellations. It has been widely used in vessel traffic service system to improve navigational safety. Following the explosion in vessel AIS data, the issues of data storing, processing, and analysis arise as emerging research topics in recent years. Vessel trajectory compression is used to eliminate the redundant information, preserve the key features, and simplify information for further data mining, thus correspondingly improving data quality and guaranteeing accurate measurement for ensuring navigational safety. It is well known that trajectory compression quality significantly depends on the threshold selection. We propose an Adaptive Douglas-Peucker (ADP) algorithm with automatic thresholding for AIS-based vessel trajectory compression. In particular, the optimal threshold is adaptively calculated using a novel automatic threshold selection method for each trajectory, as an improvement and complement of original Douglas-Peucker (DP) algorithm. It is developed based on the channel and trajectory characteristics, segmentation framework, and mean distance. The proposed method is able to simplify vessel trajectory data and extract useful information effectively. The time series trajectory classification and clustering are discussed and analysed based on ADP algorithm in this paper. To verify the reasonability and effectiveness of the proposed method, experiments are conducted on two different trajectory data sets in inland waterway of Yangtze River for trajectory classification based on the nearest neighbor classifier, and for trajectory clustering based on the spectral clustering. Comprehensive results demonstrate that the proposed algorithm can reduce the computational cost while ensuring the clustering and classification accuracy

Amortized Global Search for Efficient Preliminary Trajectory Design with Deep Generative Models

Preliminary trajectory design is a global search problem that seeks multiple qualitatively different solutions to a trajectory optimization problem. Due to its high dimensionality and non-convexity, and the frequent adjustment of problem parameters, the global search becomes computationally demanding. In this paper, we exploit the clustering structure in the solutions and propose an amortized global search (AmorGS) framework. We use deep generative models to predict trajectory solutions that share similar structures with previously solved problems, which accelerates the global search for unseen parameter values. Our method is evaluated using De Jong's 5th function and a low-thrust circular restricted three-body problem

A multiple k-means cluster ensemble framework for clustering citation trajectories

Citation maturity time varies for different articles. However, the impact of all articles is measured in a fixed window. Clustering their citation trajectories helps understand the knowledge diffusion process and reveals that not all articles gain immediate success after publication. Moreover, clustering trajectories is necessary for paper impact recommendation algorithms. It is a challenging problem because citation time series exhibit significant variability due to non linear and non stationary characteristics. Prior works propose a set of arbitrary thresholds and a fixed rule based approach. All methods are primarily parameter dependent. Consequently, it leads to inconsistencies while defining similar trajectories and ambiguities regarding their specific number. Most studies only capture extreme trajectories. Thus, a generalised clustering framework is required. This paper proposes a feature based multiple k means cluster ensemble framework. 1,95,783 and 41,732 well cited articles from the Microsoft Academic Graph data are considered for clustering short term (10 year) and long term (30 year) trajectories, respectively. It has linear run time. Four distinct trajectories are obtained Early Rise Rapid Decline (2.2%), Early Rise Slow Decline (45%), Delayed Rise No Decline (53%), and Delayed Rise Slow Decline (0.8%). Individual trajectory differences for two different spans are studied. Most papers exhibit Early Rise Slow Decline and Delayed Rise No Decline patterns. The growth and decay times, cumulative citation distribution, and peak characteristics of individual trajectories are redefined empirically. A detailed comparative study reveals our proposed methodology can detect all distinct trajectory classes.Comment: 29 page

Multi-body Non-rigid Structure-from-Motion

Conventional structure-from-motion (SFM) research is primarily concerned with the 3D reconstruction of a single, rigidly moving object seen by a static camera, or a static and rigid scene observed by a moving camera --in both cases there are only one relative rigid motion involved. Recent progress have extended SFM to the areas of {multi-body SFM} (where there are {multiple rigid} relative motions in the scene), as well as {non-rigid SFM} (where there is a single non-rigid, deformable object or scene). Along this line of thinking, there is apparently a missing gap of "multi-body non-rigid SFM", in which the task would be to jointly reconstruct and segment multiple 3D structures of the multiple, non-rigid objects or deformable scenes from images. Such a multi-body non-rigid scenario is common in reality (e.g. two persons shaking hands, multi-person social event), and how to solve it represents a natural {next-step} in SFM research. By leveraging recent results of subspace clustering, this paper proposes, for the first time, an effective framework for multi-body NRSFM, which simultaneously reconstructs and segments each 3D trajectory into their respective low-dimensional subspace. Under our formulation, 3D trajectories for each non-rigid structure can be well approximated with a sparse affine combination of other 3D trajectories from the same structure (self-expressiveness). We solve the resultant optimization with the alternating direction method of multipliers (ADMM). We demonstrate the efficacy of the proposed framework through extensive experiments on both synthetic and real data sequences. Our method clearly outperforms other alternative methods, such as first clustering the 2D feature tracks to groups and then doing non-rigid reconstruction in each group or first conducting 3D reconstruction by using single subspace assumption and then clustering the 3D trajectories into groups.Comment: 21 pages, 16 figure