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Clustering is one of the most common unsupervised learning tasks in machine learning and data mining. Clustering algorithms have been used in a plethora of applications across several scientific fields. However, there has been limited research in the clustering of point patterns - sets or multi-sets of unordered elements - that are found in numerous applications and data sources. In this paper, we propose two approaches for clustering point patterns. The first is a non-parametric method based on novel distances for sets. The second is a model-based approach, formulated via random finite set theory, and solved by the Expectation-Maximization algorithm. Numerical experiments show that the proposed methods perform well on both simulated and real data.
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Point patterns are sets or multi-sets of unordered elements that can be found in numerous data sources. However, in data analysis tasks such as classification and novelty detection, appropriate statistical models for point pattern data have not received much attention. This paper proposes the modelling of point pattern data via random finite sets (RFS). In particular, we propose appropriate likelihood functions, and a maximum likelihood estimator for learning a tractable family of RFS models. In novelty detection, we propose novel ranking functions based on RFS models, which substantially improve performance.
Most of existing clustering algorithms are proposed without considering the selection bias in data. In many real applications, however, one cannot guarantee the data is unbiased. Selection bias might bring the unexpected correlation between features and ignoring those unexpected correlations will hurt the performance of clustering algorithms. Therefore, how to remove those unexpected correlations induced by selection bias is extremely important yet largely unexplored for clustering. In this paper, we propose a novel Decorrelation regularized K-Means algorithm (DCKM) for clustering with data selection bias. Specifically, the decorrelation regularizer aims to learn the global sample weights which are capable of balancing the sample distribution, so as to remove unexpected correlations among features. Meanwhile, the learned weights are combined with k-means, which makes the reweighted k-means cluster on the inherent data distribution without unexpected correlation influence. Moreover, we derive the updating rules to effectively infer the parameters in DCKM. Extensive experiments results on real world datasets well demonstrate that our DCKM algorithm achieves significant performance gains, indicating the necessity of removing unexpected feature correlations induced by selection bias when clustering.
Safety is a top priority for civil aviation. Data mining in digital Flight Data Recorder (FDR) or Quick Access Recorder (QAR) data, commonly referred as black box data on aircraft, has gained interest from researchers, airlines, and aviation regulation agencies for safety management. New anomaly detection methods based on supervised or unsupervised learning have been developed to monitor pilot operations and detect any risks from onboard digital flight data recorder data. However, all existing anomaly detection methods are offline learning - the models are trained once using historical data and used for all future predictions. In practice, new QAR data are generated by every flight and collected by airlines whenever a datalink is available. Offline methods cannot respond to new data in time. Though these offline models can be updated by being re-trained after adding new data to the original training set, it is time-consuming and computational costly to train a new model every time new data come in. To address this problem, we propose a novel incremental anomaly detection method to identify common patterns and detect outliers in flight operations from FDR data. The proposed method is based on Gaussian Mixture Model (GMM). An initial GMM cluster model is trained on historical offline data. Then, it continuously adapts to new incoming data points via an expectation-maximization (EM) algorithm. To track changes in flight operation patterns, only model parameters need to be saved, not the raw flight data. The proposed method was tested on two sets of simulation data. Comparable results were found from the proposed online method and a classic offline model. A real-world application of the proposed method is demonstrated using FDR data from daily operations of an airline. Results are presented and future challenges of using online learning scheme for flight data analytics are discussed.
As one type of efficient unsupervised learning methods, clustering algorithms have been widely used in data mining and knowledge discovery with noticeable advantages. However, clustering algorithms based on density peak have limited clustering effect on data with varying density distribution (VDD), equilibrium distribution (ED), and multiple domain-density maximums (MDDM), leading to the problems of sparse cluster loss and cluster fragmentation. To address these problems, we propose a Domain-Adaptive Density Clustering (DADC) algorithm, which consists of three steps: domain-adaptive density measurement, cluster center self-identification, and cluster self-ensemble. For data with VDD features, clusters in sparse regions are often neglected by using uniform density peak thresholds, which results in the loss of sparse clusters. We define a domain-adaptive density measurement method based on K-Nearest Neighbors (KNN) to adaptively detect the density peaks of different density regions. We treat each data point and its KNN neighborhood as a subgroup to better reflect its density distribution in a domain view. In addition, for data with ED or MDDM features, a large number of density peaks with similar values can be identified, which results in cluster fragmentation. We propose a cluster center self-identification and cluster self-ensemble method to automatically extract the initial cluster centers and merge the fragmented clusters. Experimental results demonstrate that compared with other comparative algorithms, the proposed DADC algorithm can obtain more reasonable clustering results on data with VDD, ED and MDDM features. Benefitting from a few parameter requirements and non-iterative nature, DADC achieves low computational complexity and is suitable for large-scale data clustering.
This paper studies clustering of data sequences using the k-medoids algorithm. All the data sequences are assumed to be generated from emph{unknown} continuous distributions, which form clusters with each cluster containing a composite set of closely located distributions (based on a certain distance metric between distributions). The maximum intra-cluster distance is assumed to be smaller than the minimum inter-cluster distance, and both values are assumed to be known. The goal is to group the data sequences together if their underlying generative distributions (which are unknown) belong to one cluster. Distribution distance metrics based k-medoids algorithms are proposed for known and unknown number of distribution clusters. Upper bounds on the error probability and convergence results in the large sample regime are also provided. It is shown that the error probability decays exponentially fast as the number of samples in each data sequence goes to infinity. The error exponent has a simple form regardless of the distance metric applied when certain conditions are satisfied. In particular, the error exponent is characterized when either the Kolmogrov-Smirnov distance or the maximum mean discrepancy are used as the distance metric. Simulation results are provided to validate the analysis.
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