Accelerated Matrix Recovery via Random Projection Based on Inexact Augmented Lagrange Multiplier Method

In this paper, a unified matrix recovery model was proposed for diverse corrupted matrices. Resulting from the separable structure of the proposed model, the convex optimization problem can be solved efficiently by adopting an inexact augmented Lagrange multiplier (IALM) method. Additionally, a random projection accelerated technique (IALM+RP) was adopted to improve the success rate. From the preliminary numerical comparisons, it was indicated that for the standard robust principal component analysis (PCA) problem, IALM+RP was at least two to six times faster than IALM with an insignificant reduction in accuracy; and for the outlier pursuit (OP) problem, IALM+RP was at least 6.9 times faster, even up to 8.3 times faster when the size of matrix was 2 000×2 000.

Tensor Train Random Projection

This work proposes a Tensor Train Random Projection(TTRP)method for dimension reduction,where pairwise distances can be approximately preserved.Our TTRP is systematically constructed through a Tensor Train(TT)representation with TT-ranks equal to one.Based on the tensor train format,this random projection method can speed up the dimension reduction procedure for high-dimensional datasets and requires fewer storage costs with little loss in accuracy,comparedwith existingmethods.We provide a theoretical analysis of the bias and the variance of TTRP,which shows that this approach is an expected isometric projectionwith bounded variance,and we show that the scaling Rademacher variable is an optimal choice for generating the corresponding TT-cores.Detailed numerical experiments with synthetic datasets and theMNIST dataset are conducted to demonstrate the efficiency of TTRP.

Face Templates Encryption Technique Based on Random Projection and Deep Learning

Cancellable biometrics is the solution for the trade-off between two concepts:Biometrics for Security and Security for Biometrics.The cancelable template is stored in the authentication system’s database rather than the original biometric data.In case of the database is compromised,it is easy for the template to be canceled and regenerated from the same biometric data.Recoverability of the cancelable template comes from the diversity of the cancelable transformation parameters(cancelable key).Therefore,the cancelable key must be secret to be used in the system authentication process as a second authentication factor in con-junction with the biometric data.The main contribution of this paper is to tackle the risks of stolen/lost/shared cancelable keys by using biometric trait(in different feature domains)as the only authentication factor,in addition to achieving good performance with high security.The standard Generative Adversarial Network(GAN)is proposed as an encryption tool that needs the cancelable key during the training phase,and the testing phase depends only on the biometric trait.Additionally,random projection transformation is employed to increase the proposed system’s security and performance.The proposed transformation system is tested using the standard ORL face database,and the experiments are done by applying different features domains.Moreover,a security analysis for the proposed transformation system is presented.

Rate Adaptation for Decoding-and-Forward Relay Channel by Random Projections Codes

This paper investigates rate adaptation schemes for decoding-and-forward (DF) relay system based on random projections codes (RPC). We consider a classic three node relay system model, where relay node performs on half-duplex mode. Then, we give out receiving diversity relay scheme and coding diversity relay scheme, and present their jointly decoding methods. Furthermore, we discuss the performance of the two schemes with different power allocation coefficients. Simulations show that our relay schemes can achieve different gain with the help of relay node. And, we should allocate power to source node to just guarantee relay node can decode successfully, and allocate remain power to relay node as far as possible. In this way, this DF relay system not only achieves diversity gain, but also achieves higher and smooth spectrum efficiency.

Random projection method for ultra wideband signal acquisition

High-speed high-resolution analog-to-digital （A/D） conversion demanded by ultra wideband （UWB） signal processing is a very challenging problem. This paper proposes a parallel random projection method for UWB signal acquisition. The proposed method can achieve high sampling rate, high resolution and technical feasibility of hardware implementation. In the proposed method, an analog UWB signal is projected over a set of random sign functions. Then the low-rate high-resolution analog-to-digital convertors （ADCs） are used to sample the projection coefficients. The signal can be reconstructed by simple linear calculation with the sampling matrix, without complying with optimization algorithm and prior knowledge. In other aspects, unlike other approaches that need to utilize an accurate time-shift at extremely high frequency, or design a hybrid filter bank, or generate specific basis functions or work for signals with prior knowledge, the proposed method is a universal sampling approach and easy to apply. The simulation results of signal to noise ratio （SNR） and spurious-free dynamic range （SFDR） validate the efficiency of the proposed method for UWB signal acquisition.

Binary Random Projections with Controllable Sparsity Patterns

Random projection is often used to project higher-dimensional vectors onto a lower-dimensional space,while approximately preserving their pairwise distances.It has emerged as a powerful tool in various data processing tasks and has attracted considerable research interest.Partly motivated by the recent discoveries in neuroscience,in this paper we study the problem of random projection using binary matrices with controllable sparsity patterns.Specifically,we proposed two sparse binary projection models that work on general data vectors.Compared with the conventional random projection models with dense projection matrices,our proposed models enjoy significant computational advantages due to their sparsity structure,as well as improved accuracies in empirical evaluations.

Research on Data Compression of WSN Based on Compressed Sensing

For Wireless Sensor Networks （WSN） is responsible for sensing, collecting, processing and monitoring of environmental data, but it might be limited in resources. This paper describes in detail the compressed sensing theory, study the wireless sensor network data conventional compression and network coding method. The linear network coding scheme based on sparse random projection theory of compressed sensing. Simulation results show that this system satisfies the requirements of the reconstruction error of packets needed to reduce the number of nodes to the total number of 30%, improves the efficiency of data communications in wireless sensor network, reduce the energy consumption of the system. With other wireless sensor network data compression algorithm, the proposed algorithm has the advantages of simple realization, the compression effect is good, especially suitable for resource limited, and the accuracy requirements are not particularly stringent in wireless sensor networks.

Randomized Algorithms for Orthogonal Nonnegative Matrix Factorization

Orthogonal nonnegative matrix factorization(ONMF)is widely used in blind image separation problem,document classification,and human face recognition.The model of ONMF can be efficiently solved by the alternating direction method of multipliers and hierarchical alternating least squares method.When the given matrix is huge,the cost of computation and communication is too high.Therefore,ONMF becomes challenging in the large-scale setting.The random projection is an efficient method of dimensionality reduction.In this paper,we apply the random projection to ONMF and propose two randomized algorithms.Numerical experiments show that our proposed algorithms perform well on both simulated and real data.

Large-Scale Estimation of Distribution Algorithms with Adaptive Heavy Tailed Random Pro jection Ensembles

We present new variants of Estimation of Distribution Algorithms (EDA) for large-scale continuous optimisation that extend and enhance a recently proposed random projection (RP) ensemble based approach. The main novelty here is to depart from the theory of RPs that require (sub-)Gaussian random matrices for norm-preservation, and instead for the purposes of high-dimensional search we propose to employ random matrices with independent and identically distributed entries drawn from a t-distribution. We analytically show that the implicitly resulting high-dimensional covariance of the search distribution is enlarged as a result. Moreover, the extent of this enlargement is controlled by a single parameter, the degree of freedom. For this reason, in the context of optimisation, such heavy tailed random matrices turn out to be preferable over the previously employed (sub-)Gaussians. Based on this observation, we then propose novel covariance adaptation schemes that are able to adapt the degree of freedom parameter during the search, and give rise to a flexible approach to balance exploration versus exploitation. We perform a thorough experimental study on high-dimensional benchmark functions, and provide statistical analyses that demonstrate the state-of-the-art performance of our approach when compared with existing alternatives in problems with 1000 search variables.

A Novel Algorithm for Finding Interspersed Repeat Regions

The analysis of repeats in the DNA sequences is an important subject in bioin- formatics. In this paper, we propose a novel projection-assemble algorithm to ?nd unknown interspersed repeats in DNA sequences. The algorithm employs random projection algorithm to obtain a candidate fragment set, and exhaustive search algorithm to search each pair of fragments from the candidate fragment set to ?nd potential linkage, and then assemble them together. The complexity of our projection-assemble algorithm is nearly linear to the length of the genome sequence, and its memory usage is limited by the hardware. We tested our algo- rithm with both simulated data and real biology data, and the results show that our projection-assemble algorithm is e?cient. By means of this algorithm, we found an un-labeled repeat region that occurs ?ve times in Escherichia coli genome, with its length more than 5,000 bp, and a mismatch probability less than 4%.