Finding and tracking multi-density clusters in an online dynamic data stream

The file attached to this record is the author's final peer reviewed version.Change is one of the biggest challenges in dynamic stream mining. From a data-mining perspective, adapting and tracking change is desirable in order to understand how and why change has occurred. Clustering, a form of unsupervised learning, can be used to identify the underlying patterns in a stream. Density-based clustering identifies clusters as areas of high density separated by areas of low density. This paper proposes a Multi-Density Stream Clustering (MDSC) algorithm to address these two problems; the multi-density problem and the problem of discovering and tracking changes in a dynamic stream. MDSC consists of two on-line components; discovered, labelled clusters and an outlier buffer. Incoming points are assigned to a live cluster or passed to the outlier buffer. New clusters are discovered in the buffer using an ant-inspired swarm intelligence approach. The newly discovered cluster is uniquely labelled and added to the set of live clusters. Processed data is subject to an ageing function and will disappear when it is no longer relevant. MDSC is shown to perform favourably to state-of-the-art peer stream-clustering algorithms on a range of real and synthetic data-streams. Experimental results suggest that MDSC can discover qualitatively useful patterns while being scalable and robust to noise

AMANDA : density-based adaptive model for nonstationary data under extreme verification latency scenarios

Gradual concept-drift refers to a smooth and gradual change in the relations between input and output data in the underlying distribution over time. The problem generates a model obsolescence and consequently a quality decrease in predictions. Besides, there is a challenging task during the stream: The extreme verification latency (EVL) to verify the labels. For batch scenarios, state-of-the-art methods propose an adaptation of a supervised model by using an unconstrained least squares importance fitting (uLSIF) algorithm or a semi-supervised approach along with a core support extraction (CSE) method. However, these methods do not properly tackle the mentioned problems due to their high computational time for large data volumes, lack in representing the right samples of the drift or even for having several parameters for tuning. Therefore, we propose a density-based adaptive model for nonstationary data (AMANDA), which uses a semi-supervised classifier along with a CSE method. AMANDA has two variations: AMANDA with a fixed cutting percentage (AMANDA-FCP); and AMANDA with a dynamic cutting percentage (AMANDADCP). Our results indicate that the two variations of AMANDA outperform the state-of-the-art methods for almost all synthetic datasets and real ones with an improvement up to 27.98% regarding the average error. We have found that the use of AMANDA-FCP improved the results for a gradual concept-drift even with a small size of initial labeled data. Moreover, our results indicate that SSL classifiers are improved when they work along with our static or dynamic CSE methods. Therefore, we emphasize the importance of research directions based on this approach.Concept-drift gradual refere-se à mudança suave e gradual na distribuição dos dados conforme o tempo passa. Este problema causa obsolescência no modelo de aprendizado e queda na qualidade das previsões. Além disso, existe um complicador durante o processamento dos dados: a latência de verificação extrema (LVE) para se verificar os rótulos. Métodos do estado da arte propõem uma adaptação do modelo supervisionado usando uma abordagem de estimação de importância baseado em mínimos quadrados ou usando uma abordagem semi-supervisionada em conjunto com a extração de instâncias centrais, na sigla em inglês (CSE). Entretanto, estes métodos não tratam adequadamente os problemas mencionados devido ao fato de requererem alto tempo computacional para processar grandes volumes de dados, falta de correta seleção das instâncias que representam a mudança da distribuição, ou ainda por demandarem o ajuste de grande quantidade de parâmetros. Portanto, propomos um modelo adaptativo baseado em densidades para dados não-estacionários (AMANDA), que tem como base um classificador semi-supervisionado e um método CSE baseado em densidade. AMANDA tem duas variações: percentual de corte fixo (AMANDAFCP); e percentual de corte dinâmico (AMANDA-DCP). Nossos resultados indicam que as duas variações da proposta superam o estado da arte em quase todas as bases de dados sintéticas e reais em até 27,98% em relação ao erro médio. Concluímos que a aplicação do método AMANDA-FCP faz com que a classificação melhore mesmo quando há uma pequena porção inicial de dados rotulados. Mais ainda, os classificadores semi-supervisionados são melhorados quando trabalham em conjunto com nossos métodos de CSE, estático ou dinâmico

Adaptive estimation and change detection of correlation and quantiles for evolving data streams

Streaming data processing is increasingly playing a central role in enterprise data architectures due to an abundance of available measurement data from a wide variety of sources and advances in data capture and infrastructure technology. Data streams arrive, with high frequency, as never-ending sequences of events, where the underlying data generating process always has the potential to evolve. Business operations often demand real-time processing of data streams for keeping models up-to-date and timely decision-making. For example in cybersecurity contexts, analysing streams of network data can aid the detection of potentially malicious behaviour. Many tools for statistical inference cannot meet the challenging demands of streaming data, where the computational cost of updates to models must be constant to ensure continuous processing as data scales. Moreover, these tools are often not capable of adapting to changes, or drift, in the data. Thus, new tools for modelling data streams with efficient data processing and model updating capabilities, referred to as streaming analytics, are required. Regular intervention for control parameter configuration is prohibitive to the truly continuous processing constraints of streaming data. There is a notable absence of such tools designed with both temporal-adaptivity to accommodate drift and the autonomy to not rely on control parameter tuning. Streaming analytics with these properties can be developed using an Adaptive Forgetting (AF) framework, with roots in adaptive filtering. The fundamental contributions of this thesis are to extend the streaming toolkit by using the AF framework to develop autonomous and temporally-adaptive streaming analytics. The first contribution uses the AF framework to demonstrate the development of a model, and validation procedure, for estimating time-varying parameters of bivariate data streams from cyber-physical systems. This is accompanied by a novel continuous monitoring change detection system that compares adaptive and non-adaptive estimates. The second contribution is the development of a streaming analytic for the correlation coefficient and an associated change detector to monitor changes to correlation structures across streams. This is demonstrated on cybersecurity network data. The third contribution is a procedure for estimating time-varying binomial data with thorough exploration of the nuanced behaviour of this estimator. The final contribution is a framework to enhance extant streaming quantile estimators with autonomous, temporally-adaptive properties. In addition, a novel streaming quantile procedure is developed and demonstrated, in an extensive simulation study, to show appealing performance.Open Acces

Sparse least squares support vector regression for nonstationary systems

A new adaptive sparse least squares support vector regression algorithm, referred to as SLSSVR has been introduced for the adaptive modeling of nonstationary systems. Using a sliding window of recent data set of size N to track t he non-stationary characteristics of the incoming data, our adaptive model is initially formulated based on least squares support vector regression with forgetting factor (without bias term). In order to obtain a sparse model in which some parameters are exactly zeros, a l 1 penalty was applied in parameter estimation in the dual problem. Furthermore we exploit the fact that since the associated system/kernel matrix in positive definite, the dual solution of least squares support vector machine without bias term, can be solved iteratively with guaranteed convergence. Furthermore since the models between two consecutive time steps there are (N-1) shared kernels/parameters, the online solution can be obtained efficiently using coordinate descent algorithm in the form of Gauss-Seidel algorithm with minimal number of iterations. This allows a very sparse model per time step to be obtained very efficiently, avoiding expensive matrix inversion. The real stock market dataset and simulated examples have shown that the proposed approaches can lead to superior performances in comparison with the linear recursive least algorithm and a number of online non-linear approaches in terms of modelling performance and model size