Handling incomplete and heterogeneous data remains a central challenge in real-world machine learning, where missing values may follow complex mechanisms (MCAR, MAR, MNAR) and features can be of mixed types (numerical and categorical). Existing methods often rely on imputation, which may introduce bias or privacy risks, or fail to jointly address data heterogeneity and structured missingness. We propose the Heterogeneous Incomplete Probability Mass Kernel (HI-PMK), a novel data-dependent representation learning approach that eliminates the need for imputation. HI-PMK introduces two key innovations: (1) a probability mass-based dissimilarity measure that adapts to local data distributions across heterogeneous features (numerical, ordinal, nominal), and (2) a missingness-aware uncertainty strategy (MaxU) that conservatively handles all three missingness mechanisms by assigning maximal plausible dissimilarity to unobserved entries. Our approach is privacy-preserving, scalable, and readily applicable to downstream tasks such as classification and clustering. Extensive experiments on over 15 benchmark datasets demonstrate that HI-PMK consistently outperforms traditional imputation-based pipelines and kernel methods across a wide range of missing data settings. Code is available at: github.com/echoid/Incomplete-Heter-Kernel

Measuring similarity between two objects is the core operation in existing clustering algorithms in grouping similar objects into clusters. This paper introduces a new similarity measure called point-set kernel which computes the similarity between an object and a set of objects. The proposed clustering procedure utilizes this new measure to characterize every cluster grown from a seed object. We show that the new clustering procedure is both effective and efficient that enables it to deal with large scale datasets. In contrast, existing clustering algorithms are either efficient or effective. In comparison with the state-of-the-art density-peak clustering and scalable kernel k-means clustering, we show that the proposed algorithm is more effective and runs orders of magnitude faster when applying to datasets of millions of data points, on a commonly used computing machine.

This paper shows that adaptive kernel density estimator (KDE) can be derived effectively from Isolation Kernel. Existing adaptive KDEs often employ a data independent kernel such as Gaussian kernel. Therefore, it requires an additional means to adapt its bandwidth locally in a given dataset. Because Isolation Kernel is a data dependent kernel which is derived directly from data, no additional adaptive operation is required. The resultant estimator called IKDE is the only KDE that is fast and adaptive. Existing KDEs are either fast but non-adaptive or adaptive but slow. In addition, using IKDE for anomaly detection, we identify two advantages of IKDE over LOF (Local Outlier Factor), contributing to significantly faster runtime.

Abstract The first successful isolation‐based anomaly detector, ie, iForest, uses trees as a means to perform isolation. Although it has been shown to have advantages over existing anomaly detectors, we have identified 4 weaknesses, ie, its inability to detect local anomalies, anomalies with a high percentage of irrelevant attributes, anomalies that are masked by axis‐parallel clusters, and anomalies in multimodal data sets. To overcome these weaknesses, this paper shows that an alternative isolation mechanism is required and thus presents iNNE or isolation using Nearest Neighbor Ensemble. Although relying on nearest neighbors, iNNE runs significantly faster than the existing nearest neighbor–based methods such as the local outlier factor, especially in data sets having thousands of dimensions or millions of instances. This is because the proposed method has linear time complexity and constant space complexity.

Boosting has been shown to improve the predictive performance of unstable learners such as decision trees, but not of stable learners like Support Vector Machines (SVM), k‐nearest neighbors and Naive Bayes classifiers. In addition to the model stability problem, the high time complexity of some stable learners such as SVM prohibits them from generating multiple models to form an ensemble for large data sets. This paper introduces a simple method that not only enables Boosting to improve the predictive performance of stable learners, but also significantly reduces the computational time to generate an ensemble of stable learners such as SVM for large data sets that would otherwise be infeasible. The method proposes to build local models, instead of global models; and it is the first method, to the best of our knowledge, to solve the two problems in Boosting stable learners at the same time. We implement the method by using a decision tree to define local regions and build a local model for each local region. We show that this implementation of the proposed method enables successful Boosting of three types of stable learners: SVM, k‐nearest neighbors and Naive Bayes classifiers.

Density estimation is the ubiquitous base modelling mechanism employed for many tasks such as clustering, classification, anomaly detection and information retrieval. Commonly used density estimation methods such as kernel density estimator and k-nearest neighbour density estimator have high time and space complexities which render them inapplicable in problems with large data size and even a moderate number of dimensions. This weakness sets the fundamental limit in existing algorithms for all these tasks. We propose the first density estimation method which stretches this fundamental limit to an extent that dealing with millions of data can now be done easily and quickly. We analyze the error of the new estimation (from the true density) using a bias-variance analysis. We then perform an empirical evaluation of the proposed method by replacing existing density estimators with the new one in two current density-based algorithms, namely, DBSCAN and LOF. The results show that the new density estimation method significantly improves the runtime of DBSCAN and LOF, while maintaining or improving their task-specific performances in clustering and anomaly detection, respectively. The new method empowers these algorithms, currently limited to small data size only, to process very large databases - setting a new benchmark for what density-based algorithms can achieve.

This paper introduces a new ensemble approach, Feature-Subspace Aggregating (Feating), which builds local models instead of global models. Feating is a generic ensemble approach that can enhance the predictive performance of both stable and unstable learners. In contrast, most existing ensemble approaches can improve the predictive performance of unstable learners only. Our analysis shows that the new approach reduces the execution time to generate a model in an ensemble through an increased level of localisation in Feating. Our empirical evaluation shows that Feating performs significantly better than Boosting, Random Subspace and Bagging in terms of predictive accuracy, when a stable learner SVM is used as the base learner. The speed up achieved by Feating makes feasible SVM ensembles that would otherwise be infeasible for large data sets. When SVM is the preferred base learner, we show that Feating SVM performs better than Boosting decision trees and Random Forests. We further demonstrate that Feating also substantially reduces the error of another stable learner, k-nearest neighbour, and an unstable learner, decision tree.

Mass estimation, an alternative to density estimation, has been shown recently to be an effective base modelling mechanism for three data mining tasks of regression, information retrieval and anomaly detection. This paper advances this work in two directions. First, we generalise the previously proposed one-dimensional mass estimation to multidimensional mass estimation, and significantly reduce the time complexity to O(ψh) from O(ψh)-making it feasible for a full range of generic problems. Second, we introduce the first clustering method based on mass-it is unique because it does not employ any distance or density measure. The structure of the new mass model enables different parts of a cluster to be identified and merged without expensive evaluations. The characteristics of the new clustering method are: (i) it can identify arbitrary-shape clusters; (ii) it is significantly faster than existing density-based or distance-based methods; and (iii) it is noise-tolerant.