Outlier Detection for Water Supply Data Based on Joint Auto-Encoder

With the development of science and technology,the status of the water environment has received more and more attention.In this paper,we propose a deep learning model,named a Joint Auto-Encoder network,to solve the problem of outlier detection in water supply data.The Joint Auto-Encoder network first expands the size of training data and extracts the useful features from the input data,and then reconstructs the input data effectively into an output.The outliers are detected based on the network’s reconstruction errors,with a larger reconstruction error indicating a higher rate to be an outlier.For water supply data,there are mainly two types of outliers:outliers with large values and those with values closed to zero.We set two separate thresholds,and,for the reconstruction errors to detect the two types of outliers respectively.The data samples with reconstruction errors exceeding the thresholds are voted to be outliers.The two thresholds can be calculated by the classification confusion matrix and the receiver operating characteristic(ROC)curve.We have also performed comparisons between the Joint Auto-Encoder and the vanilla Auto-Encoder in this paper on both the synthesis data set and the MNIST data set.As a result,our model has proved to outperform the vanilla Auto-Encoder and some other outlier detection approaches with the recall rate of 98.94 percent in water supply data.

Two-Dimensional Interpolation Criterion Using DFT Coefficients

In this paper,we address the frequency estimator for 2-dimensional(2-D)complex sinusoids in the presence of white Gaussian noise.With the use of the sinc function model of the discrete Fourier transform(DFT)coefficients on the input data,a fast and accurate frequency estimator is devised,where only the DFT coefficient with the highest magnitude and its four neighbors are required.Variance analysis is also included to investigate the accuracy of the proposed algorithm.Simulation results are conducted to demonstrate the superiority of the developed scheme,in terms of the estimation performance and computational complexity.

Accurate and Computational Efficient Joint Multiple Kronecker Pursuit for Tensor Data Recovery

This paper addresses the problem of tensor completion from limited samplings.Generally speaking,in order to achieve good recovery result,many tensor completion methods employ alternative optimization or minimization with SVD operations,leading to a high computational complexity.In this paper,we aim to propose algorithms with high recovery accuracy and moderate computational complexity.It is shown that the data to be recovered contains structure of Kronecker Tensor decomposition under multiple patterns,and therefore the tensor completion problem becomes a Kronecker rank optimization one,which can be further relaxed into tensor Frobenius-norm minimization with a constraint of a maximum number of rank-1 basis or tensors.Then the idea of orthogonal matching pursuit is employed to avoid the burdensome SVD operations.Based on these,two methods,namely iterative rank-1 tensor pursuit and joint rank-1 tensor pursuit are proposed.Their economic variants are also included to further reduce the computational and storage complexity,making them effective for large-scale data tensor recovery.To verify the proposed algorithms,both synthesis data and real world data,including SAR data and video data completion,are used.Comparing to the single pattern case,when multiple patterns are used,more stable performance can be achieved with higher complexity by the proposed methods.Furthermore,both results from synthesis and real world data shows the advantage of the proposed methods in term of recovery accuracy and/or computational complexity over the state-of-the-art methods.To conclude,the proposed tensor completion methods are suitable for large scale data completion with high recovery accuracy and moderate computational complexity.

l_(1)-norm Based GWLP for Robust Frequency Estimation

In this work,we address the frequency estimation problem of a complex single-tone embedded in the heavy-tailed noise.With the use of the linear prediction(LP)property and l_(1)-norm minimization,a robust frequency estimator is developed.Since the proposed method employs the weighted l_(1)-norm on the LP errors,it can be regarded as an extension of the l_(1)-generalized weighted linear predictor.Computer simulations are conducted in the environment of α-stable noise,indicating the superiority of the proposed algorithm,in terms of its robust to outliers and nearly optimal estimation performance.