arXiv subjects

Faxian Cao

Publications and source records attributed to Faxian Cao.

10 recordsLinked to original sources

arXiv2024

A Novel Numerical Method for Relaxing the Minimal Configurations of TOA-Based Joint Sensors and Sources Localization

This work introduces a novel numerical method that relaxes the minimal configuration requirements for joint sensors and sources localization (JSSL) in 3D space using time of arrival (TOA) measurements. Traditionally, the principle requires that the number of valid equations (TOA measurements) must be equal to or greater than the number of unknown variables (sensor and source locations). State-of-the-art literature suggests that the minimum numbers of sensors and sources needed for localization are four to six and six to four, respectively. However, these stringent configurations limit the application of JSSL in scenarios with an insufficient number of sensors and sources. To overcome this limitation, we propose a numerical method that reduces the required number of sensors and sources, enabling more flexible JSSL configurations. First, we formulate the JSSL task as a series of triangles and apply the law of cosines to determine four unknown distances associated with one pair of sensors and three pairs of sources. Next, by utilizing triangle inequalities, we establish the lower and upper boundaries for these unknowns based on the known TOA measurements. The numerical method then searches within these boundaries to find the global optimal solutions, demonstrating that JSSL in 3D space is achievable with only four sensors and four sources, thus significantly relaxing the minimal configuration requirements. Theoretical proofs and simulation results confirm the feasibility and effectiveness of the proposed method.

eess.SP↗

arXiv2024

Concerns for Self-Localization of Ad-Hoc Arrays Using Time Difference of Arrivals

This document presents some insights and observations regarding the paper that was published in IEEE Transactions on Signal Processing (TSP), titled "Self-Localization of Ad-Hoc Arrays Using Time Difference of Arrivals". In the spirit of constructive feedback, I wish to highlight two key areas of consideration. The first pertains to aspects related to methodology, experimental results, and statements made in the paper. The second part addresses specific equation/typographical errors. This work aims to initiate a constructive dialogue concerning certain aspects of the paper published in IEEE TSP. Our intention is to provide feedback that contributes to the ongoing improvement of the paper's robustness and clarity.

eess.AS↗

arXiv2023

Low Rank Properties for Estimating Microphones Start Time and Sources Emission Time

Uncertainty in timing information pertaining to the start time of microphone recordings and sources' emission time pose significant challenges in various applications, such as joint microphones and sources localization. Traditional optimization methods, which directly estimate this unknown timing information (UTIm), often fall short compared to approaches exploiting the low-rank property (LRP). LRP encompasses an additional low-rank structure, facilitating a linear constraint on UTIm to help formulate related low-rank structure information. This method allows us to attain globally optimal solutions for UTIm, given proper initialization. However, the initialization process often involves randomness, leading to suboptimal, local minimum values. This paper presents a novel, combined low-rank approximation (CLRA) method designed to mitigate the effects of this random initialization. We introduce three new LRP variants, underpinned by mathematical proof, which allow the UTIm to draw on a richer pool of low-rank structural information. Utilizing this augmented low-rank structural information from both LRP and the proposed variants, we formulate four linear constraints on the UTIm. Employing the proposed CLRA algorithm, we derive global optimal solutions for the UTIm via these four linear constraints.Experimental results highlight the superior performance of our method over existing state-of-the-art approaches, measured in terms of both the recovery number and reduced estimation errors of UTIm.

eess.AS↗

arXiv2023

Are Microphone Signals Alone Sufficient for Self-Positioning?

In an era where asynchronous environments pose challenges to traditional self-positioning methods, we propose a new transformation to the existing paradigm. Traditionally, time of arrival (TOA) measurements require both microphone and source signals, limiting their applicability in environments with unknown emission time of human voices or sources and unknown recording start time of independent microphones. To address this issue, our research pioneers a mapping function capable of transforming both TOA and time difference of arrival (TDOA) formulas, demonstrating, for the first time, that they can be identical to one another. This implies that microphone signals alone are sufficient for self-positioning without the need for source signal waveforms, a groundbreaking advancement in the field that carries the potential to revolutionize self-positioning techniques, expanding their applicability in challenging environments. Supported by a robust mathematical proof and compelling experimental results, this research represents a timely and significant contribution to the current discourse in signal, and audio processing.

eess.AS↗

arXiv2023

Justices for Information Bottleneck Theory

This study comes as a timely response to mounting criticism of the information bottleneck (IB) theory, injecting fresh perspectives to rectify misconceptions and reaffirm its validity. Firstly, we introduce an auxiliary function to reinterpret the maximal coding rate reduction method as a special yet local optimal case of IB theory. Through this auxiliary function, we clarify the paradox of decreasing mutual information during the application of ReLU activation in deep learning (DL) networks. Secondly, we challenge the doubts about IB theory's applicability by demonstrating its capacity to explain the absence of a compression phase with linear activation functions in hidden layers, when viewed through the lens of the auxiliary function. Lastly, by taking a novel theoretical stance, we provide a new way to interpret the inner organizations of DL networks by using IB theory, aligning them with recent experimental evidence. Thus, this paper serves as an act of justice for IB theory, potentially reinvigorating its standing and application in DL and other fields such as communications and biomedical research.

cs.LG↗

arXiv2018

Conditioning Optimization of Extreme Learning Machine by Multitask Beetle Antennae Swarm Algorithm

Extreme learning machine (ELM) as a simple and rapid neural network has been shown its good performance in various areas. Different from the general single hidden layer feedforward neural network (SLFN), the input weights and biases in hidden layer of ELM are generated randomly, so that it only takes a little computation overhead to train the model. However, the strategy of selecting input weights and biases at random may result in ill-posed problem. Aiming to optimize the conditioning of ELM, we propose an effective particle swarm heuristic algorithm called Multitask Beetle Antennae Swarm Algorithm (MBAS), which is inspired by the structures of artificial bee colony (ABS) algorithm and Beetle Antennae Search (BAS) algorithm. Then, the proposed MBAS is applied to optimize the input weights and biases of ELM. Experiment results show that the proposed method is capable of simultaneously reducing the condition number and regression error, and achieving good generalization performances.

cs.NE↗

arXiv2017

Sparse Representation Based Augmented Multinomial Logistic Extreme Learning Machine with Weighted Composite Features for Spectral Spatial Hyperspectral Image Classification

Although extreme learning machine (ELM) has been successfully applied to a number of pattern recognition problems, it fails to pro-vide sufficient good results in hyperspectral image (HSI) classification due to two main drawbacks. The first is due to the random weights and bias of ELM, which may lead to ill-posed problems. The second is the lack of spatial information for classification. To tackle these two problems, in this paper, we propose a new framework for ELM based spectral-spatial classification of HSI, where probabilistic modelling with sparse representation and weighted composite features (WCF) are employed respectively to derive the op-timized output weights and extract spatial features. First, the ELM is represented as a concave logarithmic likelihood function under statistical modelling using the maximum a posteriori (MAP). Second, the sparse representation is applied to the Laplacian prior to effi-ciently determine a logarithmic posterior with a unique maximum in order to solve the ill-posed problem of ELM. The variable splitting and the augmented Lagrangian are subsequently used to further reduce the computation complexity of the proposed algorithm and it has been proven a more efficient method for speed improvement. Third, the spatial information is extracted using the weighted compo-site features (WCFs) to construct the spectral-spatial classification framework. In addition, the lower bound of the proposed method is derived by a rigorous mathematical proof. Experimental results on two publicly available HSI data sets demonstrate that the proposed methodology outperforms ELM and a number of state-of-the-art approaches.

cs.CV↗

arXiv2017

Linear vs Nonlinear Extreme Learning Machine for Spectral-Spatial Classification of Hyperspectral Image

As a new machine learning approach, extreme learning machine (ELM) has received wide attentions due to its good performances. However, when directly applied to the hyperspectral image (HSI) classification, the recognition rate is too low. This is because ELM does not use the spatial information which is very important for HSI classification. In view of this, this paper proposes a new framework for spectral-spatial classification of HSI by combining ELM with loopy belief propagation (LBP). The original ELM is linear, and the nonlinear ELMs (or Kernel ELMs) are the improvement of linear ELM (LELM). However, based on lots of experiments and analysis, we found out that the LELM is a better choice than nonlinear ELM for spectral-spatial classification of HSI. Furthermore, we exploit the marginal probability distribution that uses the whole information in the HSI and learn such distribution using the LBP. The proposed method not only maintain the fast speed of ELM, but also greatly improves the accuracy of classification. The experimental results in the well-known HSI data sets, Indian Pines and Pavia University, demonstrate the good performances of the proposed method.

cs.CV↗

arXiv2017

Does Normalization Methods Play a Role for Hyperspectral Image Classification?

For Hyperspectral image (HSI) datasets, each class have their salient feature and classifiers classify HSI datasets according to the class's saliency features, however, there will be different salient features when use different normalization method. In this letter, we report the effect on classifiers by different normalization methods and recommend the best normalization methods for classifier after analyzing the impact of different normalization methods on classifiers. Pavia University datasets, Indian Pines datasets and Kennedy Space Center datasets will apply to several typical classifiers in order to evaluate and analysis the impact of different normalization methods on typical classifiers.

cs.CV↗

arXiv2017

Extreme Sparse Multinomial Logistic Regression: A Fast and Robust Framework for Hyperspectral Image Classification

Although the sparse multinomial logistic regression (SMLR) has provided a useful tool for sparse classification, it suffers from inefficacy in dealing with high dimensional features and manually set initial regressor values. This has significantly constrained its applications for hyperspectral image (HSI) classification. In order to tackle these two drawbacks, an extreme sparse multinomial logistic regression (ESMLR) is proposed for effective classification of HSI. First, the HSI dataset is projected to a new feature space with randomly generated weight and bias. Second, an optimization model is established by the Lagrange multiplier method and the dual principle to automatically determine a good initial regressor for SMLR via minimizing the training error and the regressor value. Furthermore, the extended multi-attribute profiles (EMAPs) are utilized for extracting both the spectral and spatial features. A combinational linear multiple features learning (MFL) method is proposed to further enhance the features extracted by ESMLR and EMAPs. Finally, the logistic regression via the variable splitting and the augmented Lagrangian (LORSAL) is adopted in the proposed framework for reducing the computational time. Experiments are conducted on two well-known HSI datasets, namely the Indian Pines dataset and the Pavia University dataset, which have shown the fast and robust performance of the proposed ESMLR framework.

cs.CV↗