Outlier Mining Methods Based on Graph Structure Analysis

Outlier detection in high-dimensional datasets is a fundamental and challenging problem across disciplines that has also practical implications, as removing outliers from the training set improves the performance of machine learning algorithms. While many outlier mining algorithms have been proposed in the literature, they tend to be valid or efficient for specific types of datasets (time series, images, videos, etc.). Here we propose two methods that can be applied to generic datasets, as long as there is a meaningful measure of distance between pairs of elements of the dataset. Both methods start by defining a graph, where the nodes are the elements of the dataset, and the links have associated weights that are the distances between the nodes. Then, the first method assigns an outlier score based on the percolation (i.e., the fragmentation) of the graph. The second method uses the popular IsoMap non-linear dimensionality reduction algorithm, and assigns an outlier score by comparing the geodesic distances with the distances in the reduced space. We test these algorithms on real and synthetic datasets and show that they either outperform, or perform on par with other popular outlier detection methods. A main advantage of the percolation method is that is parameter free and therefore, it does not require any training; on the other hand, the IsoMap method has two integer number parameters, and when they are appropriately selected, the method performs similar to or better than all the other methods tested.Peer ReviewedPostprint (published version

Finding an unknown number of multivariate outliers

We use the forward search to provide robust Mahalanobis distances to detect the presence of outliers in a sample of multivariate normal data. Theoretical results on order statistics and on estimation in truncated samples provide the distribution of our test statistic. We also introduce several new robust distances with associated distributional results. Comparisons of our procedure with tests using other robust Mahalanobis distances show the good size and high power of our procedure. We also provide a unification of results on correction factors for estimation from truncated samples

Local Subspace-Based Outlier Detection using Global Neighbourhoods

Outlier detection in high-dimensional data is a challenging yet important task, as it has applications in, e.g., fraud detection and quality control. State-of-the-art density-based algorithms perform well because they 1) take the local neighbourhoods of data points into account and 2) consider feature subspaces. In highly complex and high-dimensional data, however, existing methods are likely to overlook important outliers because they do not explicitly take into account that the data is often a mixture distribution of multiple components. We therefore introduce GLOSS, an algorithm that performs local subspace outlier detection using global neighbourhoods. Experiments on synthetic data demonstrate that GLOSS more accurately detects local outliers in mixed data than its competitors. Moreover, experiments on real-world data show that our approach identifies relevant outliers overlooked by existing methods, confirming that one should keep an eye on the global perspective even when doing local outlier detection.Comment: Short version accepted at IEEE BigData 201

Detecting outlying subspaces for high-dimensional data: the new task, algorithms and performance

[Abstract]: In this paper, we identify a new task for studying the outlying degree (OD) of high-dimensional data, i.e. finding the subspaces (subsets of features) in which the given points are outliers, which are called their outlying subspaces. Since the state-of-the-art outlier detection techniques fail to handle this new problem, we propose a novel detection algorithm, called High-Dimension Outlying subspace Detection (HighDOD), to detect the outlying subspaces of high-dimensional data efficiently. The intuitive idea of HighDOD is that we measure the OD of the point using the sum of distances between this point and its k nearest neighbors. Two heuristic pruning strategies are proposed to realize fast pruning in the subspace search and an efficient dynamic subspace search method with a sample-based learning process has been implemented. Experimental results show that HighDOD is efficient and outperforms other searching alternatives such as the naive top–down, bottom–up and random search methods, and the existing outlier detection methods cannot fulfill this new task effectively

A survey of outlier detection methodologies

Outlier detection has been used for centuries to detect and, where appropriate, remove anomalous observations from data. Outliers arise due to mechanical faults, changes in system behaviour, fraudulent behaviour, human error, instrument error or simply through natural deviations in populations. Their detection can identify system faults and fraud before they escalate with potentially catastrophic consequences. It can identify errors and remove their contaminating effect on the data set and as such to purify the data for processing. The original outlier detection methods were arbitrary but now, principled and systematic techniques are used, drawn from the full gamut of Computer Science and Statistics. In this paper, we introduce a survey of contemporary techniques for outlier detection. We identify their respective motivations and distinguish their advantages and disadvantages in a comparative review