Universal Nonlinear Regression on High Dimensional Data Using Adaptive Hierarchical Trees

Khan, Farhan Hassan; Kari, Dariush; Karatepe, Ilyas Alper; Kozat, Süleyman S.

doi:10.1109/tbdata.2016.2555323

Cited by 12 publications

(11 citation statements)

References 43 publications

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“…In this section, we illustrate the performance of SOTs under different scenarios with respect to stateof-the-art methods. The proposed method has a wide variety of application areas, such as channel equalization [26], underwater communications [27], nonlinear modeling in big data [28], speech and texture analysis [29,Chapter 7] and health monitoring [30]. Yet, in this section, we consider nonlinear modeling for fundamental regression and classification problems.…”

Section: Numerical Resultsmentioning

confidence: 99%

Online Nonlinear Modeling via Self-Organizing Trees

Vanli

Kozat

2018

Adaptive Learning Methods for Nonlinear System Modeling

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Section: Numerical Resultsmentioning

confidence: 99%

Online Nonlinear Modeling via Self-Organizing Trees

Vanli

Kozat

2018

Adaptive Learning Methods for Nonlinear System Modeling

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“…We get an exponentially decaying curve of the health index values that reaches 0 at failure as shown in For non-stationary setting, i.e., when the input data does not follow a static distribution in the healthy state, we assume the data lies on a time varying submanifold and use a multi-model learning of the underlying subspace. We use the notion of multi-scale tracking and MOUSSE algorithm as in [14,12,13].…”

Section: Multi-scale Subspace Tracking For Predictive Analyticsmentioning

confidence: 99%

“…In the proposed approach, instead of regenerating the whole input sequence, we estimate a low dimensional representation of the input and the subspace that it lies in, hence reducing the computational cost and overfitting. Furthermore, since the input and underlying submanifold subspace have different dimension, we incorporate approximate Mahalanobis distance for updating the model parameter during training and later as a measure of degradation [13,14,15,12]. We emphasize that our proposes algorithm suits well to the dynamics of the input data, reduces the computational complexity and achieves significantly higher accuracy than the state-of-the-art.…”

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confidence: 99%

Online Subspace Tracking of Sensors Data for Damage Propagation Modeling and Predictive Analytics

Khan¹

2019

Preprint

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We analyze damage propagation modeling of turbo-engines in a data-driven approach. We investigate subspace tracking assuming a low dimensional manifold structure and a static behavior during the healthy state of the machines. Our damage propagation model is based on the deviation of the data from the static behavior and uses the notion of health index as a measure of the condition.Hence, we incorporate condition-based maintenance and estimate the remaining useful life based on the current and previous health indexes. This paper proposes an algorithm that adapts well to the dynamics of the data and underlying system, and reduces the computational complexity by utilizing the low dimensional manifold structure of the data. A significant performance improvement is demonstrated over existing methods by using the proposed algorithm on CMAPSS Turbo-engine datasets.

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“…For example, one can use tree based online regression methods [54,55] as the constituent filters, and boost them with the proposed approach.…”

Section: Related Workmentioning

confidence: 99%

Boosted adaptive filters

Kari

Mirza

Khan

et al. 2018

Digital Signal Processing

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We investigate boosted online regression and propose a novel family of regression algorithms with strong theoretical bounds. In addition, we implement several variants of the proposed generic algorithm. We specifically provide theoretical bounds for the performance of our proposed algorithms that hold in a strong mathematical sense. We achieve guaranteed performance improvement over the conventional online regression methods without any statistical assumptions on the desired data or feature vectors. We demonstrate an intrinsic relationship, in terms of boosting, between the adaptive mixture-of-experts and data reuse algorithms. Furthermore, we introduce a boosting algorithm based on random updates that is significantly faster than the conventional boosting methods and other variants of our proposed algorithms while achieving an enhanced performance gain. Hence, the random updates method is specifically applicable to the fast and high dimensional streaming data. Specifically, we investigate Recursive Least Squares (RLS)-based and Least Mean Squares (LMS)-based linear regression algorithms in a mixture-of-experts setting, and provide several variants of these well known adaptation methods. Moreover, we extend the proposed algorithms to other filters. Specifically, we investigate the effect of the proposed algorithms on piecewise linear filters. Furthermore, we provide theoretical bounds for the computational complexity of our proposed algorithms. We demonstrate substantial performance gains in terms of mean square error over the constituent filters through an extensive set of benchmark real data sets and simulated examples.

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Universal Nonlinear Regression on High Dimensional Data Using Adaptive Hierarchical Trees

Cited by 12 publications

References 43 publications

Online Nonlinear Modeling via Self-Organizing Trees

Online Nonlinear Modeling via Self-Organizing Trees

Online Subspace Tracking of Sensors Data for Damage Propagation Modeling and Predictive Analytics

Boosted adaptive filters

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