Model complexity is a fundamental problem in deep learning. In this paper, we conduct a systematic overview of the latest studies on model complexity in deep learning. Model complexity of deep learning can be categorized into expressive capacity and effective model complexity. We review the existing studies on those two categories along four important factors, including model framework, model size, optimization process, and data complexity. We also discuss the applications of deep learning model complexity including understanding model generalization, model optimization, and model selection and design. We conclude by proposing several interesting future directions.
In the past decade, human activity recognition (HAR) has grown in popularity due to its applications in security and entertainment. As recent years have witnessed the emergence of health care and exoskeleton robotics which make use of wearable suits, human–machine interaction based on action recognition performs an important role in multimedia applications. Considering the limitations of the application scenario, the surface electromyography (sEMG) signal stands out in many wearable data collection devices for HAR. That is because: (1) timely feedback; (2) no damage to the human body; and (3) the wide range of recognizable actions. However, existing public datasets of sEMG contained relatively few activities, and several large-scale datasets only collected the action of the hand. In addition, the processing of sEMG signals is a new field with no effective evaluation system for it. To tackle these problems, we establish a novel dataset for HAR on lower-limb sEMG named “HAR-sEMG,” using 6 sEMG signal sensors attached to the left leg. A benchmark summarizing experiments with many combinations of existing high-dimensional signal processing algorithms-based manifold learning on our dataset is also provided for a performance analysis.
Equivalence structure (ES) extraction enables us to determine correspondence relations within a dataset or between multiple datasets. Applications of ES extraction include the analysis of time series data, preprocessing of imitation learning, and preprocessing of transfer learning. Currently, pairwise incremental search (PIS) is the fastest method to extract ESs; however, a combinatorial explosion can occur when employing this method. In this paper, we show that combinatorial explosion is a problem that occurs in the PIS, and we propose a new method where this problem does not occur. We evaluate the proposed method via experiments; the results show that our proposed method is 39 times faster than the PIS for synthetic datasets where a 20-dimensional ES exists. For the experiment using video datasets, the proposed method enabled us to obtain a 29-dimensional ES, whereas the PIS did not because the memory usage reached its limit when the number of dimensions was 9. In this experiment, the total processing time for our proposed method up to 29 dimensions was 6.3 times shorter than that for PIS up to even 8 dimensions.
Stock market prediction is extremely important for investors because knowing the future trend of stock prices will reduce the risk of investing capital for profit. Therefore, seeking an accurate, fast, and effective approach to identify the stock market movement is of great practical significance. This study proposes a novel turning point prediction method for the time series analysis of stock price. Through the chaos theory analysis and application, we put forward a new modeling approach for the nonlinear dynamic system. The turning indicator of time series is computed firstly; then, by applying the RVFL-GMDH model, we perform the turning point prediction of the stock price, which is based on the fractal characteristic of a strange attractor with an infinite self-similar structure. The experimental findings confirm the efficacy of the proposed procedure and have become successful for the intelligent decision support of the stock trading strategy.
Support vector domain description (SVDD) is a data description method inspired by support vector machine (SVM). This classifier describes a set of data points with a sphere that encloses the majority of them and has a minimal volume. The boundary of this sphere is used to classify new samples. SVDD has been successfully applied to many challenging classification problems and has shown a good generalization capability. However, this classifier still has some major weaknesses. This paper focuses on two of them: The first regards the large amount of memory and computational time required by SVDD in the training step. This problem manifests most strongly when dealing with large-size datasets and can hinder or prevent its use. This paper presents an approximate solution to this problem that permits to apply SVDD to large-scale datasets. This new version is based on divide-and-conquer strategy and it processes in two steps: It begins by dividing the whole large-size dataset into random subsets that each can be described efficiently with a small sphere using SVDD. Then, it applies our new algorithm that can find the smallest sphere that encloses the minimal spheres built in the previous step. The second weak point of standard SVDD concerns its static learning process. This classifier must be re-trained with the whole dataset each time when new training samples are available. This paper proposes a new dynamic approach that only trains the new samples with SVDD and incorporates the resulting minimal sphere with the previous one (s) to construct the smallest sphere that encloses all the samples. Like Support Vector Domain Description, the proposed approach can be extended to non-linear classification cases by using kernel functions. Experimental results on artificial and real datasets have successfully validated the performance of our approach.
With the proliferation of the Semantic Web technologies, more and more spatial knowledge bases are being published on the Web. Discovering spatial links among spatial knowledge bases is crucial in achieving real-time applications such as reasoning and question answering over spatial linked data. However, existing approaches rely on numerous high-cost Dimensionally Extended Nine-Intersection Model (DE-9IM) computations which lead to inefficient spatial link discovery. To address this problem, we propose a novel approach for discovering topological relations based on the spatial link composition, namely DORIC. Different from conventional spatial link discovery methods, DORIC further reduces the required number of DE-9IM computations by composing existing spatial links. Specifically, we first propose a spatial link composition (SLC) model to infer new spatial links of topological relations from existing or intermediate links. We replace part of high-cost DE-9IM computations with relatively low-cost SLC, and it leads to reduced spatial link discovery time. Then to maximize the utility of SLC during the process of DORIC, we design two effective strategies for deciding the discovery and access orders. Experiments on three real-world datasets show that the proposed DORIC outperforms the state-of-the-art approaches in terms of the spatial link discovery time.
A business process model may be used as both a communication artefact for gathering and sharing knowledge of a business practice among stakeholders and as a specification for the automation of the process by a Business Process Management System (BPMS). For each of these uses, it is desirable to have an ability to visualise the process model from a range of different perspectives and at various levels of granularity. Such views are a common feature of enterprise architecture frameworks, but process modelling and management systems and tools generally have a limited number of available views to offer. This paper presents a taxonomy of process views that are presented in the literature and then proposes the definition and use of a common process model ontology, from which an extensible range of process views may be derived. The approach is illustrated through the realisation of a plug-in component for the YAWL BPMS, although it is by no means limited to that environment. The component illustrates that the process views frequently mentioned in the literature as desirable can be effectively implemented and extended using an ontology-based approach. It is envisaged that the accessibility of a repertoire of views that support business process development will lead to greater efficiencies through more accurate process definitions and improved change management support.
Question answering over knowledge graph (KGQA), which automatically answers natural language questions by querying the facts in knowledge graph (KG), has drawn significant attention in recent years. In this paper, we focus on single-relation questions, which can be answered through a single fact in KG. This task is a non-trivial problem since capturing the meaning of questions and selecting the golden fact from billions of facts in KG are both challengeable. We propose a pipeline framework for KGQA, which consists of three cascaded components: (1) an entity detection model, which can label the entity mention in the question; (2) a novel entity linking model, which considers the contextual information of candidate entities in KG and builds a question pattern classifier according to the correlations between question patterns and relation types to mitigate entity ambiguity problem; and (3) a simple yet effective relation detection model, which is used to match the semantic similarity between the question and relation candidates. Substantial experiments on the SimpleQuestions benchmark dataset show that our proposed method could achieve better performance than many existing state-of-the-art methods on accuracy, top-N recall and other evaluation metrics.
Uncertainty about data appears in many real-world applications and an important issue is how to manage, analyze and solve optimization problems over such data. An important tool for data analysis is clustering. When the data set is uncertain, we can model them as a set of probabilistic points each formalized as a probability distribution function which describes the possible locations of the points. In this paper, we study k-center problem for probabilistic points in a general metric space. First, we present a fast greedy approximation algorithm that builds k centers using a farthest-first traversal in k iterations. This algorithm improves the previous approximation factor of the unrestricted assigned k-center problem from 10 (see ) to 6. Next, we restrict the centers to be selected from all the probabilistic locations of the given points and we show that an optimal solution for this restricted setting is a 2-approximation factor solution for an optimal solution of the assigned k-center problem with expected distance assignment. Using this idea, we improve the approximation factor of the unrestricted assigned k-center problem to 4 by increasing the running time. The algorithm also runs in polynomial time when k is a constant. Additionally, we implement our algorithms on three real data sets. The experimental results show that in practice the approximation factors of our algorithms are better than in theory for these data sets. Also we compare the results of our algorithm with the previous works and discuss about the achieved results. At the end, we present our theoretical results for probabilistic k-median clustering.
Dominance-based rough set approach is successfully applied to analyze multicriteria decision problems. For the incomplete ordered decision system, its various extensions have been proposed. The valued dominance relation is such an extension. However, the general calculation of dominance degree between objects depends on a prior distribution of incomplete ordered decision system, and how to choose a suitable threshold is also difficult. To solve these problems, a data-driven valued dominance relation is proposed in this paper. First of all, an objective calculation method of dominance degree between objects is designed, which is based on probability statistics. Moreover, this method is more effective for big data sets with a large quantity of objects. Secondly, an automatic threshold calculation method is presented, which does not depend on any prior knowledge except data sets. Finally, some properties of this method are investigated. Experimental results show that this method is superior to other generalized dominance relations in dealing with incomplete information.
How can we transfer the knowledge from a source domain to a target domain when each side cannot observe the data in the other side? Recent transfer learning methods show significant performance in classification tasks by leveraging both source and target data simultaneously at training time. However, leveraging both source and target data simultaneously is often impossible due to privacy reasons. In this paper, we define the problem of unsupervised domain adaptation under blind constraint, where each of the source and the target domains cannot observe the data in the other domain, but data from both domains are used for training. We propose TAN (Transfer Alignment Network for Blind Domain Adaptation), an effective method for the problem by aligning source and target domain features in the blind setting. TAN maps the target feature into source feature space so that the classifier learned from the labeled data in the source domain is readily used in the target domain. Extensive experiments show that TAN (1) provides the state-of-the-art accuracy for blind domain adaptation outperforming the standard supervised learning by up to 9.0% and (2) performs well regardless of the proportion of target domain data in the training data.
Similarity-preserving hashing is a core technique for fast similarity searches, and it randomly maps data points in a metric space to strings of discrete symbols (i.e., sketches) in the Hamming space. While traditional hashing techniques produce binary sketches, recent ones produce integer sketches for preserving various similarity measures. However, most similarity search methods are designed for binary sketches and inefficient for integer sketches. Moreover, most methods are either inapplicable or inefficient for dynamic datasets, although modern real-world datasets are updated over time. We propose dynamic filter trie (DyFT), a dynamic similarity search method for both binary and integer sketches. An extensive experimental analysis using large real-world datasets shows that DyFT performs superiorly with respect to scalability, time performance, and memory efficiency. For example, on a huge dataset of 216 million data points, DyFT performs a similarity search 6000 times faster than a state-of-the-art method while reducing to one-thirteenth in memory.
Graph attention networks are effective graph neural networks that perform graph embedding for semi-supervised learning, which considers the neighbors of a node when learning its features. This paper presents a novel attention-based graph neural network that introduces an attention mechanism in the word-represented features of a node together incorporating the neighbors’ attention in the embedding process. Instead of using a vector as the feature of a node in the traditional graph attention networks, the proposed method uses a 2D matrix to represent a node, where each row in the matrix stands for a different attention distribution against the original word-represented features of a node. Then, the compressed features are fed into a graph attention layer that aggregates the matrix representation of the node and its neighbor nodes with different attention weights as a new representation. By stacking several graph attention layers, it obtains the final representation of nodes as matrices, which considers both that the neighbors of a node have different importance and that the words also have different importance in their original features. Experimental results on three citation network datasets show that the proposed method significantly outperforms eight state-of-the-art methods in semi-supervised classification tasks.
Decision-making in our everyday lives is surrounded by visually important information. Fashion, housing, dating, food or travel are just a few examples. At the same time, most commonly used tools for information retrieval operate on relational and text-based search models which are well understood by end users, but unable to directly cover visual information contained in images or videos. Researcher communities have been trying to reveal the semantics of multimedia in the last decades with ever-improving results, dominated by the success of deep learning. However, this does not close the gap to relational retrieval model on its own and often rather solves a very specialized task like assigning one of pre-defined classes to each object within a closed application ecosystem. Retrieval models based on these novel techniques are difficult to integrate in existing application-agnostic environments built around relational databases, and therefore, they are not so widely used in the industry. In this paper, we address the problem of closing the gap between visual information retrieval and relational database model. We propose and formalize a model for discovering candidates for new relational attributes by analysis of available visual content. We design and implement a system architecture supporting the attribute extraction, suggestion and acceptance processes. We apply the solution in the context of e-commerce and show how it can be seamlessly integrated with SQL environments widely used in the industry. At last, we evaluate the system in a user study and discuss the obtained results.
The social media technologies are open to users who are intended in creating a community and publishing their opinions of recent incidents. The participants of the online social networking sites remain ignorant of the criticality of disclosing personal data to the public audience. The private data of users are at high risk leading to many adverse effects like cyberbullying, identity theft, and job loss. This research work aims to define the user entities or data like phone number, email address, family details, health-related information as user’s sensitive private data (SPD) in a social media platform. The proposed system, Tweet-Scan-Post (TSP), is mainly focused on identifying the presence of SPD in user’s posts under personal, professional, and health domains. The TSP framework is built based on the standards and privacy regulations established by social networking sites and organizations like NIST, DHS, GDPR. The proposed approach of TSP addresses the prevailing challenges in determining the presence of sensitive PII, user privacy within the bounds of confidentiality and trustworthiness. A novel layered classification approach with various state-of-art machine learning models is used by the TSP framework to classify tweets as sensitive and insensitive. The findings of TSP systems include 201 Sensitive Privacy Keywords using a boosting strategy, sensitivity scaling that measures the degree of sensitivity allied with a tweet. The experimental results revealed that personal tweets were highly related to mother and children, professional tweets with apology, and health tweets with concern over the father’s health condition.
The minibatching technique has been extensively adopted to facilitate stochastic first-order methods because of their computational efficiency in parallel computing for large-scale machine learning and data mining. Indeed, increasing the minibatch size decreases the iteration complexity (number of minibatch queries) to converge, resulting in the decrease of the running time by processing a minibatch in parallel. However, this gain is usually saturated for too large minibatch sizes and the total computational complexity (number of access to an example) is deteriorated. Hence, the determination of an appropriate minibatch size which controls the trade-off between the iteration and total computational complexities is important to maximize performance of the method with as few computational resources as possible. In this study, we define the optimal minibatch size as the minimum minibatch size with which there exists a stochastic first-order method that achieves the optimal iteration complexity and we call such a method the optimal minibatch method. Moreover, we show that Katyusha (in: Proceedings of annual ACM SIGACT symposium on theory of computing vol 49, pp 1200–1205, ACM, 2017), DASVRDA (Murata and Suzuki, in: Advances in neural information processing systems vol 30, pp 608–617, 2017), and the proposed method which is a combination of Acc-SVRG (Nitanda, in: Advances in neural information processing systems vol 27, pp 1574–1582, 2014) with APPA (Cotter et al. in: Advances in neural information processing systems vol 27, pp 3059–3067, 2014) are optimal minibatch methods. In experiments, we compare optimal minibatch methods with several competitors on \(L_1\) -and \(L_2\) -regularized logistic regression problems and observe that iteration complexities of optimal minibatch methods linearly decrease as minibatch sizes increase up to reasonable minibatch sizes and finally attain the best iteration complexities. This confirms the computational efficiency of optimal minibatch methods suggested by the theory.
Querying a search engine is one of the most frequent activities performed by Internet users. As queries are submitted, the server collects and aggregates them to build detailed user profiles. While user profiles are used to offer personalized search services, they may also be employed in behavioral targeting or, even worse, be transferred to third parties. Proactive protection of users' privacy in front of search engines has been tackled by submitting fake queries that aim at distorting the users' real profile. However, most approaches submit either random queries (which do not allow controlling the profile distortion) or queries constructed by following deterministic algorithms (which may be detected by aware search engines). In this paper, we propose a semantically grounded method to generate fake queries that (i) is driven by the privacy requirements of the user, (ii) submits the least number of fake queries needed to fulfill the requirements and (iii) creates queries in a non-deterministic way. Unlike related works, we accurately analyze and exploit the semantics underlying to user queries and their influence in the resulting profile. As a result, our approach offers more control—because users can tailor how their profile should be protected—and greater efficiency—because the desired protection is achieved with fewer fake queries. The experimental results on real query logs illustrate the benefits of our approach.
With the access devices that are densely deployed in multi-access edge computing environments, users frequently switch access devices when moving, which causes the imbalance of network load and the decline of service quality. To solve the problems above, a seamless handover scheme for wireless access points based on perception is proposed. First, a seamless handover model based on load perception is proposed to solve the unbalanced network load, in which a seamless handover algorithm for wireless access points is used to calculate the access point with the highest weight, and a software-defined network controller controls the switching process. A joint allocation method of communication and computing resources based on deep reinforcement learning is proposed to minimize the terminal energy consumption and the system delay. A resource allocation model is based on minimizing terminal energy consumption, and system delay is built. The optimal value of task offloading decision and resource allocation vector are calculated with deep reinforcement learning. Experimental results show that the proposed method can reduce the network load and the task execution cost.
Graph learning, such as node classification, is typically carried out in a closed-world setting. A number of nodes are labeled, and the learning goal is to correctly classify remaining (unlabeled) nodes into classes, represented by the labeled nodes. In reality, due to limited labeling capability or dynamic evolving nature of networks, some nodes in the networks may not belong to any existing/seen classes and therefore cannot be correctly classified by closed-world learning algorithms. In this paper, we propose a new open-world graph learning paradigm, where the learning goal is to correctly classify nodes belonging to labeled classes into correct categories and also classify nodes not belonging to labeled classes to an unseen class. Open-world graph learning has three major challenges: (1) Graphs do not have features to represent nodes for learning; (2) unseen class nodes do not have labels and may exist in an arbitrary form different from labeled classes; and (3) graph learning should differentiate whether a node belongs to an existing/seen class or an unseen class. To tackle the challenges, we propose an uncertain node representation learning principle to use multiple versions of node feature representation to test a classifier’s response on a node, through which we can differentiate whether a node belongs to the unseen class. Technical wise, we propose constrained variational graph autoencoder, using label loss and class uncertainty loss constraints, to ensure that node representation learning is sensitive to the unseen class. As a result, node embedding features are denoted by distributions, instead of deterministic feature vectors. In order to test the certainty of a node belonging to seen classes, a sampling process is proposed to generate multiple versions of feature vectors to represent each node, using automatic thresholding to reject nodes not belonging to seen classes as unseen class nodes. Experiments, using graph convolutional networks and graph attention networks on four real-world networks, demonstrate the algorithm performance. Case studies and ablation analysis also show the advantage of the uncertain representation learning and automatic threshold selection for open-world graph learning.
Developing effective and efficient data stream classifiers is challenging for the machine learning community because of the dynamic nature of data streams. As a result, many data stream learning algorithms have been proposed during the past decades and achieve great success in various fields. This paper aims to explore a specific type of challenge in learning evolving data streams, called concept evolution (emergence of novel classes). Concept evolution indicates that the underlying patterns evolve over time, and new patterns (classes) may emerge at any time in streaming data. Therefore, data stream classifiers with emerging class detection have received increasing attention in recent years due to the practical values in many real-world applications. In this article, we provide a comprehensive overview of the existing works in this line of research. We discuss and analyze various aspects of the proposed algorithms for data stream classification with concept evolution detection and adaptation. Additionally, we discuss the potential application areas in which these techniques can be used. We also provide a detailed overview of evaluation measures and datasets used in these studies. Finally, we describe the current research challenges and future directions for data stream classification with novel class detection.
In text categorization, Vector Space Model (VSM) has been widely used for representing documents, in which a document is represented by a vector of terms. Since different terms contribute to a document’s semantics in various degrees, a number of term weighting schemes have been proposed for VSM to improve text categorization performance. Much evidence shows that the performance of a term weighting scheme often varies across different text categorization tasks, while the mechanism underlying variability in a scheme’s performance remains unclear. Moreover, existing schemes often weight a term with respect to a category locally, without considering the global distribution of a term’s occurrences across all categories in a corpus. In this paper, we first systematically examine pros and cons of existing term weighting schemes in text categorization and explore the reasons why some schemes with sound theoretical bases, such as chi-square test and information gain, perform poorly in empirical evaluations. By measuring the concentration that a term distributes across all categories in a corpus, we then propose a series of entropy-based term weighting schemes to measure the distinguishing power of a term in text categorization. Through extensive experiments on five different datasets, the proposed term weighting schemes consistently outperform the state-of-the-art schemes. Moreover, our findings shed new light on how to choose and develop an effective term weighting scheme for a specific text categorization task.
The standard machine learning tasks often assume that the training (source domain) and test (target domain) data follow the same distribution and feature space. However, many real-world applications suffer from the limited number of training labeled data and benefit from the related available labeled datasets to train the model. In this way, since there is the distribution difference across the source and target domains (i.e., domain shift problem), the learned classifier on the training set might perform poorly on the test set. To address the shift problem, domain adaptation provides variety of solutions to learn robust classifiers to deal with distribution mismatch across the source and target domains. In this paper, we put forward a novel domain adaptation approach, referred to as cross- and multiple-domains visual transfer learning via iterative Fischer linear discriminant analysis (CIDA) to tackle shift problem across domains. CIDA transfers the source and target domains into a shared low-dimensional Fischer linear discriminant analysis (FLDA)-based subspace in an unsupervised manner. CIDA benefits joint FLDA and domain adaptation criterions to reduce the distribution mismatch across the training and test sets. Moreover, CIDA employs an adaptive classifier to build a robust model against data drift across different domains. Also, CIDA generates the intermediate pseudotarget labels to utilize the target data in training process. In this way, CIDA refines the pseudolabels using an iterative manner to converge the model. Our extensive experiments illustrate that CIDA significantly outperforms the baseline machine learning and other state-of-the-art transfer learning methods on nine visual benchmark datasets under different difficulties.
The location selection is a strategic decision that significantly influences revenue, level of competition, and success of companies and countries. This study aims to propose a hybrid approach for the location selection, to evaluate the potential location for the automotive manufacturing plant of Turkey, and to reveal a comprehensive analysis of weighting and multiple criteria decision-making (MCDM) methods. The proposed approach integrates different objective and subjective weighting, MCDM, and Copeland methods. Turkey has recently introduced its first automobile prototypes and has announced that the manufacturing plant will be located in Bursa. This decision is thoroughly examined via four objective weighting methods—entropy, criteria importance through inter-criteria correlation, standard deviation, and mean weight and a subjective method—analytic hierarchy process. Besides, the alternatives are evaluated based on six MCDM methods—technique for order preference by similarity to ideal solution, preference ranking organization method for enrichment evaluations, vise kriterijumska optimizacija i kompromisno resenje, organization, rangement et synthese de donnes relationnelles, elimination and choice translating reality, and the weighted sum method. The outcomes of the weighting methods and MCDM methods, the impact of the attribute weights provided by each method on rankings, the outcome of each method pair, and selection of the best location (Bursa) are thoroughly evaluated considering a real-world case with a potential outcome that makes evaluations more realistic and tangible unlike most of the other studies in the literature. In this regard, Spearman's rank correlation coefficients are considered. Also, sensitivity analysis is conducted to reveal the robustness of the methods and the impact of each weight on outcomes. Some considerable results, including the most robust method and optimal method pairs for the case, are presented.
In this paper, we propose a generic boosting framework for multiple object tracking (MOT). Unlike other works tracking objects from zero, our framework uses their results (tracklets) and makes further optimizations. The motivation of us derives from the observation that most modern MOT trackers have been acceptable performance and can yield relatively reliable tracklets; accordingly, we straight focus on the tracklet-level re-identification, which is the most challenging issue in this case. To achieve that goal, we simultaneously utilize the techniques of single object tracking, tracking fragment (tracklets) and re-identification mechanism through casting them into a multi-label energy optimization and then innovatively solving it using the \(\alpha -\) expansion with label costs algorithm. All these techniques inspire recent MOT a lot to mitigate the occlusion problem, but to our knowledge, by far few works explore to reasonably combine them all like us. Furthermore, we introduce a spatial attention to improve the appearance model and a hierarchical clustering as post-process to progressively improve the tracking consistency. Finally, testing results on the most used benchmarks demonstrate the significant effectiveness and generality of our framework, and the importance of each contribution is also verified through ablative studies.
Most existing algorithms of anomaly detection are suitable for static data where all data are available during detection but are incapable of handling dynamic data streams. In this study, we proposed an improved iLOF (incremental local outlier factor) algorithm based on the landmark window model, which provides an efficient method for anomaly detection in data streams and outperforms conventional methods. What is more, data windows as updating units are introduced to reduce the false alarm rate, and multiple tests are taken here to identify candidate anomalies and real anomalies. The improved iLOF shows its obvious advantage with its false positive rate. Furthermore, the proposed algorithm instantly deletes data points of identified real anomalies. We analyzed the performance of the improved algorithm and the sensitivity of certain parameters via empirical experiments using synthetic and real data sets. The experimental results demonstrate that the proposed improved algorithm achieved better performance on the higher detection rate and the lower false alarm rate compared with the original iLOF algorithm and its improvements.