A survey on wavelet applications in data mining

Incorporating causality in energy consumption forecasting using deep neural networks

Forecasting energy demand has been a critical process in various decision support systems regarding consumption planning, distribution strategies, and energy policies. Traditionally, forecasting energy consumption or demand methods included trend analyses, regression, and auto-regression. With advancements in machine learning methods, algorithms such as support vector machines, artificial neural networks, and random forests became prevalent. In recent times, with an unprecedented improvement in computing capabilities, deep learning algorithms are increasingly used to forecast energy consumption/demand. In this contribution, a relatively novel approach is employed to use long-term memory. Weather data was used to forecast the energy consumption from three datasets, with an additional piece of information in the deep learning architecture. This additional information carries the causal relationships between the weather indicators and energy consumption. This architecture with the causal information is termed as entangled long short term memory. The results show that the entangled long short term memory outperforms the state-of-the-art deep learning architecture (bidirectional long short term memory). The theoretical and practical implications of these results are discussed in terms of decision-making and energy management systems.

Machine Learning and Image Processing Enabled Evolutionary Framework for Brain MRI Analysis for Alzheimer’s Disease Detection

Alzheimer's disease is characterized by the presence of abnormal protein bundles in the brain tissue, but experts are not yet sure what is causing the condition. To find a cure or aversion, researchers need to know more than just that there are protein differences from the usual; they also need to know how these brain nerves form so that a remedy may be discovered. Machine learning is the study of computational approaches for enhancing performance on a specific task through the process of learning. This article presents an Alzheimer's disease detection framework consisting of image denoising of an MRI input data set using an adaptive mean filter, preprocessing using histogram equalization, and feature extraction by Haar wavelet transform. Classification is performed using LS-SVM-RBF, SVM, KNN, and random forest classifier. An adaptive mean filter removes noise from the existing MRI images. Image quality is enhanced by histogram equalization. Experimental results are compared using parameters such as accuracy, sensitivity, specificity, precision, and recall.

Joint estimation and regularized aggregation of brain network in FMRI data

BACKGROUND

In the Gaussian graphical model framework, precision matrices reveal conditional dependence structure among random variables. In functional magnetic resonance imaging (fMRI) data, estimating such precision matrices of multi-subjects and aggregating them to a group-level is an essential step for constructing a group brain network.

NEW METHOD

In this article, we considered joint estimation of multiple precision matrices with regularized aggregation. Also, in the construction of a group precision matrix, we integrated robust aggregation to the estimation. In the estimation of individual precision matrices, we took a regularization approach to induce sparsity, which made brain network estimation more realistic.

RESULTS

We demonstrated the effectiveness of the proposed method through simulated examples, and analyses on real fMRI data acquired during eye movement tasks assessing cognitive control. For the fMRI data, the joint estimation of multiple precision matrices (JEMP) with regularized aggregation (RA) captured more robust associations between task-relevant neural regions of interest (ROIs), compared to the analyses using JEMP alone. The JEMP with RA also was sensitive to increased neural efficiency after task practice.

COMPARISON WITH EXISTING METHOD(S)

The simple average of individual precision matrices may be affected by outliers and provide inconsistent outcomes between subject-level and group-level networks. In contrast, the proposed method yielded a robust group graph that could identify and ease the effect of outliers.

CONCLUSIONS

The proposed method identified regions of practice-induced attenuation associated with reduced cognitive demand after repeat task exposure. Through simulated and real data, we demonstrated that this method does not require any distribution assumption, can identify outliers, and provides robust, representative group brain networks. This method can be applied to datasets that have extensive variability and/or multiple outliers, including applications to specific, and general, cognitive processes, as well as for studies that may require longitudinal data, such as pharmaceutical trials.

Image Data Mining Based on Wavelet Transform for Visualization of the Unique Characteristics of Image Data

Mining techniques can play an important role in image decomposition, segmentation, classification and retrieval systems. As image data become more complex and growing at a fast pace, searching valuable information and knowledge implicit become more challenging than ever before. In this chapter, authors proposed a WT based DM techniques to optimize and characterize the unique feature of image retrieval, which is fundamental to optimize informative mathematical representation of image objects. Many software, including data exploratory tools such as DM packages contain fast and efficient programs that perform WT. Wavelets have quickly gained popularity among scientists and engineers, both in theoretical research and in applications. The authors discussed in details and introduced a novel method for image database analysis in different scenarios that foster the wide access of image data.

Prediction of Heart Failure Decompensation Events by Trend Analysis of Telemonitoring Data

This paper aims to assess the predictive value of physiological data daily collected in a telemonitoring study in the early detection of heart failure (HF) decompensation events. The main hypothesis is that physiological time series with similar progression (trends) may have prognostic value in future clinical states (decompensation or normal condition). The strategy is composed of two main steps: a trend similarity analysis and a predictive procedure. The similarity scheme combines the Haar wavelet decomposition, in which signals are represented as linear combinations of a set of orthogonal bases, with the Karhunen-Loève transform, that allows the selection of the reduced set of bases that capture the fundamental behavior of the time series. The prediction process assumes that future evolution of current condition can be inferred from the progression of past physiological time series. Therefore, founded on the trend similarity measure, a set of time series presenting a progression similar to the current condition is identified in the historical dataset, which is then employed, through a nearest neighbor approach, in the current prediction. The strategy is evaluated using physiological data resulting from the myHeart telemonitoring study, namely blood pressure, respiration rate, heart rate, and body weight collected from 41 patients (15 decompensation events and 26 normal conditions). The obtained results suggest, in general, that the physiological data have predictive value, and in particular, that the proposed scheme is particularly appropriate to address the early detection of HF decompensation.

Efficient local statistical analysis via integral histograms with discrete wavelet transform

Histograms computed from local regions are commonly used in many visualization applications, and allowing the user to query histograms interactively in regions of arbitrary locations and sizes plays an important role in feature identification and tracking. Computing histograms in regions with arbitrary location and size, nevertheless, can be time consuming for large data sets since it involves expensive I/O and scan of data elements. To achieve both performance- and storage-efficient query of local histograms, we present a new algorithm called WaveletSAT, which utilizes integral histograms, an extension of the summed area tables (SAT), and discrete wavelet transform (DWT). Similar to SAT, an integral histogram is the histogram computed from the area between each grid point and the grid origin, which can be be pre-computed to support fast query. Nevertheless, because one histogram contains multiple bins, it will be very expensive to store one integral histogram at each grid point. To reduce the storage cost for large integral histograms, WaveletSAT treats the integral histograms of all grid points as multiple SATs, each of which can be converted into a sparse representation via DWT, allowing the reconstruction of axis-aligned region histograms of arbitrary sizes from a limited number of wavelet coefficients. Besides, we present an efficient wavelet transform algorithm for SATs that can operate on each grid point separately in logarithmic time complexity, which can be extended to parallel GPU-based implementation. With theoretical and empirical demonstration, we show that WaveletSAT can achieve fast preprocessing and smaller storage overhead than the conventional integral histogram approach with close query performance.

Compactly Supported Basis Functions as Support Vector Kernels for Classification

Wavelet kernels have been introduced for both support vector regression and classification. Most of these wavelet kernels do not use the inner product of the embedding space, but use wavelets in a similar fashion to radial basis function kernels. Wavelet analysis is typically carried out on data with a temporal or spatial relation between consecutive data points. We argue that it is possible to order the features of a general data set so that consecutive features are statistically related to each other, thus enabling us to interpret the vector representation of an object as a series of equally or randomly spaced observations of a hypothetical continuous signal. By approximating the signal with compactly supported basis functions and employing the inner product of the embedding L2 space, we gain a new family of wavelet kernels. Empirical results show a clear advantage in favor of these kernels.

A method of tumor classification based on wavelet packet transforms and neighborhood rough set

Tumor classification is an important application domain of gene expression data. Because of its characteristics of high dimensionality and small sample size (SSS), and a great number of redundant genes not related to tumor phenotypes, various feature extraction or gene selection methods have been applied to gene expression data analysis. Wavelet packet transforms (WPT) and neighborhood rough sets (NRS) are effective tools to extract and select features. In this paper, a novel approach of tumor classification is proposed based on WPT and NRS. First the classification features are extracted by WPT and the decision tables are formed, then the attributes of the decision tables are reduced by NRS. Thirdly, a feature subset with few attributes and high classification ability is obtained. The experimental results on three gene expression datasets demonstrate that the proposed method is effective and feasible.

Feature selection using Haar wavelet power spectrum

Background

Feature selection is an approach to overcome the 'curse of dimensionality' in complex researches like disease classification using microarrays. Statistical methods are utilized more in this domain. Most of them do not fit for a wide range of datasets. The transform oriented signal processing domains are not probed much when other fields like image and video processing utilize them well. Wavelets, one of such techniques, have the potential to be utilized in feature selection method. The aim of this paper is to assess the capability of Haar wavelet power spectrum in the problem of clustering and gene selection based on expression data in the context of disease classification and to propose a method based on Haar wavelet power spectrum.

Results

Haar wavelet power spectra of genes were analysed and it was observed to be different in different diagnostic categories. This difference in trend and magnitude of the spectrum may be utilized in gene selection. Most of the genes selected by earlier complex methods were selected by the very simple present method. Each earlier works proved only few genes are quite enough to approach the classification problem [1]. Hence the present method may be tried in conjunction with other classification methods. The technique was applied without removing the noise in data to validate the robustness of the method against the noise or outliers in the data. No special softwares or complex implementation is needed. The qualities of the genes selected by the present method were analysed through their gene expression data. Most of them were observed to be related to solve the classification issue since they were dominant in the diagnostic category of the dataset for which they were selected as features.

Conclusion

In the present paper, the problem of feature selection of microarray gene expression data was considered. We analyzed the wavelet power spectrum of genes and proposed a clustering and feature selection method useful for classification based on Haar wavelet power spectrum. Application of this technique in this area is novel, simple, and faster than other methods, fit for a wide range of data types. The results are encouraging and throw light into the possibility of using this technique for problem domains like disease classification, gene network identification and personalized drug design.