On the approximate discrete KLT of fractional Brownian motion and applications

Gupta, Anubha; Joshi, Sachindra; Singh, Pushpendra

doi:10.1016/j.jfranklin.2018.09.023

Cited by 24 publications

(12 citation statements)

References 42 publications

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“…The smoothness of the signal is captured by the parameter called Hurst exponent (H). If H > 0.5, the signals are smoother and their KL basis can be approximated by DCT [7]. In order to validate this, we computed the Hurst exponent, H of the considered data [10] and it was observed to be nearly 0.7 in the time domain.…”

Section: Proposed Pci-mdr Methodsmentioning

confidence: 99%

PCI-MDR: Missing Data Recovery in Wireless Sensor Networks Using Partial Canonical Identity Matrix

Jain

Gupta

2019

IEEE Wireless Commun. Lett.

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Data loss in wireless sensor networks (WSNs) is quite prevalent. Since sensor nodes are employed for various critical applications, accurate recovery of missing data is important. Researchers have exploited different characteristics of WSN data, such as low rank, spatial and temporal correlation for missing data recovery. However, the performance of existing methods is dependent on various factors. For instance, correct rank estimation is required for exploiting the low-rank behaviour of WSNs, whereas correlation information among the nodes should be known for exploiting spatial correlation. Further, the amount of missing data should not be massive for exploiting temporal correlation. To overcome the above-mentioned drawbacks, a novel method 'PCI-MDR' has been proposed in this paper. It utilizes compressive sensing with partial canonical identity matrix for the recovery of missing data in WSNs. To validate the proposed method, the results have been obtained on the real dataset of temperature sensors from the Intel Lab. The proposed method is observed to perform superior to the existing methods, yielding significant improvement.

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Section: Proposed Pci-mdr Methodsmentioning

confidence: 99%

PCI-MDR: Missing Data Recovery in Wireless Sensor Networks Using Partial Canonical Identity Matrix

Jain

Gupta

2019

IEEE Wireless Commun. Lett.

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“…Columns and rows of the gene expression matrix were studied in the DCT domain and were observed to be highly sparse as shown in Figure 2. Based on this observation, Discrete Cosine Transform was chosen as the sparsifying transform in DSNN method because DCT acts as a KL-type basis for slow-varying signals (25) and data is sparse in the DCT domain. Thus, the missing data recovery problem was formulated in a compressive sensing framework, where the sensing matrix was of size r × s and had "0" entries for missing values in data matrix Y, while rest of the entries were "1."…”

Section: Stage-1: Compressive Sensing Based Matrix Completionmentioning

confidence: 99%

Imputation of Gene Expression Data in Blood Cancer and Its Significance in Inferring Biological Pathways

Farswan

Gupta

et al. 2020

Front. Oncol.

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Purpose: Gene expression data generated from microarray technology is often analyzed for disease diagnostics and treatment. However, this data suffers with missing values that may lead to inaccurate findings. Since data capture is expensive, time consuming, and is required to be collected from subjects, it is worthwhile to recover missing values instead of recollecting the data. In this paper, a novel but simple method, namely, DSNN (Doubly Sparse DCT domain with Nuclear Norm minimization) has been proposed for imputing missing values in microarray data. Extensive experiments including pathway enrichment have been carried out on four blood cancer dataset to validate the method as well as to establish the significance of imputation. Methods: A new method, namely, DSNN, was proposed for missing value imputation on gene expression data. Method was validated on four dataset, CLL, AML, MM (Spanish data), and MM (Indian data). All the dataset were downloaded from GEO repository. Missing values were introduced in the original data from 10 to 90% in steps of 10% because method validation requires ground truth. Quantitative results on normalized mean square error (NMSE) between the ground truth and imputed data were computed. To further validate and establish the significance of the proposed imputation method, two experiments were carried out on the data imputed with the proposed method, data imputed with the state-of-art methods, and data with missing values. In the first experiment, classification of normal vs. cancer subjects was carried out. In the second experiment, biological significance of imputation was ascertained by identifying top candidate tumor drivers using the existing state-of-the-art SPARROW algorithm, followed by gene list enrichment analysis on top candidate drivers. Results: Quantitative NMSE results of the DSNN method were compared with three state-of-the-art imputation methods. DSNN method was observed to perform better compared to these other methods both at high as well as low observable data. Experiment-1 demonstrated superior results on classification with imputation compared to that performed on missing data matrix as well as compared to classification on imputed data with existing methods. In experiment-2, cancer affected pathways were discovered with higher significance in the data imputed with the proposed method compared to those discovered with the missing data matrix. Farswan et al. Significance of Missing Value Recovery in Pathways Conclusion: Missing value problem in microarray data is a serious problem and can adversely influence downstream analysis. A novel method, namely, DSNN is proposed for missing value imputation. The method is validated quantitatively on the application of classification and biologically by performing pathway enrichment analysis.

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“…Song et al [24] use fBm for short-term power load forecasting. Gupta et al [25] establish the relationship between DCT and discrete fBm to provide a theoretical basis for applying DCT to fBm signal reconstruction. FBm can be considered as a generalized form of the Brownian Motion (BM).…”

Section: Introductionmentioning

confidence: 99%

Multifractional Brownian Motion and Quantum-Behaved Partial Swarm Optimization for Bearing Degradation Forecasting

et al. 2020

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Gradual degradation of the bearing vibration signal is usually studied as a nonstationary stochastic time series. Roller bearings are working at high speed in a heavy load environment so that the combination of bearing faults gradually degraded during the rotation might lead to unpredicted catastrophic accidents. The degradation process has the property of long-range dependence (LRD), so that the fractional Brownian motion (fBm) is taken into account for a prediction model. Because of the dramatic changes in the bearing degradation process, the Hurst exponent that describes the fBm will change during the degradation process. A priori Hurst value of the conventional fBm in the prediction is fixed, thus inducing a minor accuracy of the prediction. To avoid this problem, we propose an improved prediction method. Based on the following steps, at the initial data processing, a skip-over factor is selected as the characteristics parameter of the bearing degradation process. A multifractional Brownian motion (mfBm) replaces the fBm for the degradation modeling. We will show that also our mfBm has the same property of long-range dependence as the fBm. Moreover, a time-varying Hurst exponent H(t) is taken to replace the constant H in fBm. Finally, we apply the quantum-behaved partial swarm optimization (QPSO) to optimize H(t) for a finite interval. Some tests and corresponding experimental results will show that our model QPSO + mfBm have a much better performance on the prediction effect than fBm.

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On the approximate discrete KLT of fractional Brownian motion and applications

Cited by 24 publications

References 42 publications

PCI-MDR: Missing Data Recovery in Wireless Sensor Networks Using Partial Canonical Identity Matrix

PCI-MDR: Missing Data Recovery in Wireless Sensor Networks Using Partial Canonical Identity Matrix

Imputation of Gene Expression Data in Blood Cancer and Its Significance in Inferring Biological Pathways

Multifractional Brownian Motion and Quantum-Behaved Partial Swarm Optimization for Bearing Degradation Forecasting

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