Graph pooling technique in GNNs for learning expressive graph-level representation is critical yet still chal-lenging. Existing pooling methods either struggle to capture local substructures or fail to utilize high-order dependency, thus diminishing the expression capability. To solve this problem, we propose HAP, a hierarchical graph-level representation learning framework adaptively sensitive to graph structures. Specifically, HAP utilizes a novel cross-level attention mechanism MOA to naturally focus more on the close neighborhood while effectively capturing higher-order dependency. It also learns a global graph content GCont that extracts the graph pattern properties to stabilize the pre- and post-coarsening graph content, thus providing global guidance in graph coarsening. Experiments show that HAP significantly outperforms the state-of-the-art graph pooling methods.

Time series anomaly detection is instrumental in maintaining system availability in various domains. Current work in this research line mainly focuses on learning data normality deeply and comprehensively by devising advanced neural network structures and new reconstruction/prediction learning objectives. However, their one-class learning process can be misled by latent anomalies in training data (i.e., anomaly contamination) under the unsupervised paradigm. Their learning process also lacks knowledge about the anomalies. Consequently, they often learn a biased, inaccurate normality boundary. To tackle these problems, this paper proposes calibrated one-class classification for anomaly detection, realizing contamination-tolerant, anomaly-informed learning of data normality via uncertainty modeling-based calibration and native anomaly-based calibration. Specifically, our approach adaptively penalizes uncertain predictions to restrain irregular samples in anomaly contamination during optimization, while simultaneously encouraging confident predictions on regular samples to ensure effective normality learning. This largely alleviates the negative impact of anomaly contamination. Our approach also creates native anomaly examples via perturbation to simulate time series abnormal behaviors. Through discriminating these dummy anomalies, our one-class learning is further calibrated to form a more precise normality boundary. Extensive experiments on ten real-world datasets show that our model achieves substantial improvement over sixteen state-of-the-art contenders.

Graph neural networks (GNN) have been proven to be mature enough for handling graph-structured data on node-level graph representation learning tasks. However, the graph pooling technique for learning expressive graph-level representation is critical yet still challenging. Existing pooling methods either struggle to capture the local substructure or fail to effectively utilize high-order dependency, thus diminishing the expression capability. In this paper we propose HAP, a hierarchical graph-level representation learning framework, which is adaptively sensitive to graph structures, i.e., HAP clusters local substructures incorporating with high-order dependencies. HAP utilizes a novel cross-level attention mechanism MOA to naturally focus more on close neighborhood while effectively capture higher-order dependency that may contain crucial information. It also learns a global graph content GCont that extracts the graph pattern properties to make the pre- and post-coarsening graph content maintain stable, thus providing global guidance in graph coarsening. This novel innovation also facilitates generalization across graphs with the same form of features. Extensive experiments on ten datasets show that HAP significantly outperforms twelve popular graph pooling methods on graph classification task with an maximum accuracy improvement of 20.18%, and exceeds the performance of state-of-the-art graph matching and graph similarity learning algorithms by over 3.42% and 16%.

Isolation forest (iForest) has been emerging as arguably the most popular anomaly detector in recent years due to its general effectiveness across different benchmarks and strong scalability. Nevertheless, its linear axis-parallel isolation method often leads to (i) failure in detecting hard anomalies that are difficult to isolate in high-dimensional/non-linear-separable data space, and (ii) notorious algorithmic bias that assigns unexpectedly lower anomaly scores to artefact regions. These issues contribute to high false negative errors. Several iForest extensions are introduced, but they essentially still employ shallow, linear data partition, restricting their power in isolating true anomalies. Therefore, this paper proposes deep isolation forest. We introduce a new representation scheme that utilises casually initialised neural networks to map original data into random representation ensembles, where random axis-parallel cuts are subsequently applied to perform the data partition. This representation scheme facilitates high freedom of the partition in the original data space (equivalent to non-linear partition on subspaces of varying sizes), encouraging a unique synergy between random representations and random partition-based isolation. Extensive experiments show that our model achieves significant improvement over state-of-the-art isolation-based methods and deep detectors on tabular, graph and time series datasets; our model also inherits desired scalability from iForest.

Graph pooling plays a vital role in learning graph embeddings. Due to the lack of label information, unsupervised graph pooling has received much attention, primarily via mutual information (MI). However, most existing MI-based pooling methods only preserve node features while overlooking the hierarchical substructural information. In this paper, we propose SMIP, a novel unsupervised hierarchical graph pooling method based on substructure-sensitive MI maximization. SMIP reconstructs a hard-style substructure encoder based on cluster-based pooling paradigm, and trains it with two substructure-sensitive MI-based objectives, i.e., node-substructure MI and node-node MI. The node-substructure MI guides to transfer maximum node feature information into corresponded substructures and the node-node MI guarantees a more accurate node allocation. Moreover, to avoid extra computation of augmented graphs and prevent noise information during MI estimation, we propose a local-scope contrastive MI estimation method, making SMIP more potent in capturing intrinsic features of the input graph. Experiments on six benchmark graph classification datasets demonstrate that our hierarchical deep learning approach outperforms all state-of-the-art unsupervised GNN-based methods and even surpasses the performance of nine supervised ones. Generalization study shows that the proposed substructure-sensitive MI objective can be successfully embedded into other cluster-based pooling methods to improve their performance.

Outlier detection is an important task in many domains and is intensively studied in the past decade. Further, how to explain outliers, i.e., outlier interpretation, is more significant, which can provide valuable insights for analysts to better understand, solve, and prevent these detected outliers. However, only limited studies consider this problem. Most of the existing methods are based on the score-and-search manner. They select a feature subspace as interpretation per queried outlier by estimating outlying scores of the outlier in searched subspaces. Due to the tremendous searching space, they have to utilize pruning strategies and set a maximum subspace length, often resulting in suboptimal interpretation results. Accordingly, this paper proposes a novel Attention-guided Triplet deviation network for Outlier interpretatioN (ATON). Instead of searching a subspace, ATON directly learns an embedding space and learns how to attach attention to each embedding dimension (i.e., capturing the contribution of each dimension to the outlierness of the queried outlier). Specifically, ATON consists of a feature embedding module and a customized self-attention learning module, which are optimized by a triplet deviation-based loss function. We obtain an optimal attention-guided embedding space with expanded high-level information and rich semantics, and thus outlying behaviors of the queried outlier can be better unfolded. ATON finally distills a subspace of original features from the embedding module and the attention coefficient. With the good generality, ATON can be employed as an additional step of any black-box outlier detector. A comprehensive suite of experiments is conducted to evaluate the effectiveness and efficiency of ATON. The proposed ATON significantly outperforms state-of-the-art competitors on 12 real-world datasets and obtains good scalability w.r.t. both data dimensionality and data size.

Mixed-type data are pervasive in real life, but very limited outlier detection methods are available for these data. Some existing methods handle mixed-type data by feature converting, whereas their performance is downgraded by information loss and noise caused by the transformation. Another kind of approaches separately evaluates outlierness in numerical and categorical features. However, they fail to adequately consider the behaviours of data objects in different feature spaces, often leading to suboptimal results. As for outlier form, both clustered outliers and scattered outliers are contained in many real-world data, but a number of outlier detectors are inherently restricted by their outlier definitions to simultaneously detect both of them. To address these issues, an unsupervised outlier detection method MIX is proposed. MIX constructs a joint learning framework to establish a cooperation mechanism to make separate outlier scoring constantly communicate and sufficiently grasp the behaviours of data objects in another feature space. Specifically, MIX iteratively performs outlier scoring in numerical and categorical space. Each outlier scoring phase can be iteratively and cooperatively enhanced by the prior knowledge given by another feature space. To target both clustered and scattered outliers, the outlier scoring phases capture the essential characteristic of outliers, i.e., evaluating outlierness via the deviation from the normal model. We show that MIX significantly outperforms eight state-of-the-art outlier detectors on twelve real-world datasets and obtains good scalability.

Unavoidable noise in real-world categorical data presents significant challenges to existing outlier detection methods because they normally fail to separate noisy values from outlying values. Feature subspace-based methods inevitably mix noisy values when retaining an entire feature because a feature may contain both outlying values and noisy values. Pattern-based methods are normally based on frequency and are easily misled by noisy values, resulting in many faulty patterns. This paper introduces a novel unsupervised framework termed OUVAS, and its parameter-free instantiation RHAC to explore a high-quality outlying value set for detecting outliers in noisy categorical data. Based on the observation that the relations between values reflect their essence, OUVAS investigates value similarities to cluster values into different groups and combines cluster-level analysis and value-level refinement to identify an outlying value set. RHAC instantiates OUVAS by three successive modules (i.e., the combination of Ochiai coefficient and LOUVAIN algorithm to cluster values, hierarchical value coupling learning to perform cluster-level analysis, and a threshold to divide fake and real outlying values in value-level refinement). We show that (i) RHAC-based outlier detector significantly outperforms five state-of-the-art outlier detection methods; (ii) Extended RHAC-based feature selection method successfully improves the performance of existing outlier detectors and performs better than two latest outlying feature selection methods.

This paper introduces a novel framework, namely SelectVC and its instance POP, for learning selective value couplings (i.e., interactions between the full value set and a set of outlying values) to identify outliers in high-dimensional categorical data. Existing outlier detection methods work on a full data space or feature subspaces that are identified independently from subsequent outlier scoring. As a result, they are significantly challenged by overwhelming irrelevant features in high-dimensional data due to the noise brought by the irrelevant features and its huge search space. In contrast, SelectVC works on a clean and condensed data space spanned by selective value couplings by jointly optimizing outlying value selection and value outlierness scoring. Its instance POP defines a value outlierness scoring function by modeling a partial outlierness propagation process to capture the selective value couplings. POP further defines a top-k outlying value selection method to ensure its scalability to the huge search space. We show that POP (i) significantly outperforms five state-of-the-art full space- or subspace-based outlier detectors and their combinations with three feature selection methods on 12 real-world high-dimensional data sets with different levels of irrelevant features; and (ii) obtains good scalability, stable performance w.r.t. k, and fast convergence rate.