Minor Component Analysis Algorithm Research Articles

Convergence analysis of a self-stabilizing algorithm for minor component analysis

The Moller algorithm is a self-stabilizing minor component analysis algorithm. This research document involves the study of the convergence and dynamic characteristics of the Moller algorithm using the deterministic discrete time &#x0028 DDT &#x0029 methodology. Unlike other analysis methodologies, the DDT methodology is capable of serving the distinct time characteristic and having no constraint conditions. Through analyzing the dynamic characteristics of the weight vector, several convergence conditions are drawn, which are beneficial for its application. The performing computer simulations and real applications demonstrate the correctness of the analysis&#x02BC s conclusions.

An Improved Minor Component Analysis Algorithm Based on Convergence Analysis of 5G Multi-Dimensional Signals

An Improved Minor Component Analysis Algorithm Based on Convergence Analysis of 5G Multi-Dimensional Signals

Design of Two-Channel Quadrature Mirror Filter Banks Using Minor Component Analysis Algorithm

The design of two-channel quadrature mirror filter banks can be constructed based on real infinite impulse response (IIR) all-pass digital filters without yielding magnitude distortion. The design problem is first formulated as a phase optimization using IIR all-pass filters in the least-squares sense. Then the nonlinear phase optimization is further converted into solving an eigenproblem of an appropriate real, symmetric, and positive-definite matrix. In this paper, the minor component analysis algorithm based on the neural learning rule is exploited to the design of eigenfilter. When the learning algorithm achieves convergence, the weights of the neural system approximate the smallest eigenvector, which are the optimal filter coefficients of the IIR all-pass filters. The simulation results confirm that the proposed neural-based method can achieve accurate performance by incorporating the simple neural model.

Eigenfilter design of linear-phase FIR digital filters using neural minor component analysis

This paper proposes a minor component analysis-based neural learning algorithm for designing linear-phase finite impulse response digital filters. The objective function to be minimized in the least-squares design can be formulated as the eigenvalue problem for solving an appropriate real, symmetric, and positive-definite matrix. To achieve the eigenfilter design, an alternative neural learning rule based on the minor component analysis algorithm is exploited. The optimal filter coefficients corresponding to the eigenvector of the smallest eigenvalue of the positive-definite matrix can be achieved in an iterative manner, avoiding the complex computation of eigenvalue decomposition. Furthermore, the learning step parameter that affects the convergence performance is investigated empirically. The simulation results indicate that the proposed neural-based approach can be applied to eigenfilter design and yields a lower computational complexity compared with traditional matrix algebraic-based approaches.

A Study of MCA Learning Algorithm for Incident Signals Estimation

Many signal subspace-based approaches have already been proposed for determining the fixed Direction of Arrival (DOA) of plane waves impinging on an array of sensors. Two procedures for DOA estimation based neural network are presented. Firstly, Principal Component Analysis (PCA) is employed to extract the maximum eigenvalue and eigenvector from signal subspace to estimate DOA. Secondly, Minor component analysis (MCA) is a statistical method of extracting the eigenvector associated with the smallest eigenvalue of the covariance matrix. In this paper, we will modify a MCA learning algorithm to enhance the Convergence, where a Convergence is essential for MCA algorithm towards practical applications. The learning rate parameter is also presented, which ensures fast convergence of the algorithm, because it has direct effect on the convergence of the weight vector and the error level is affected by this value. MCA is performed to determine the estimated DOA. Simulation results will be furnished to illustrate the theoretical results achieved.

A Globally Convergent MC Algorithm With an Adaptive Learning Rate

This brief deals with the problem of minor component analysis (MCA). Artificial neural networks can be exploited to achieve the task of MCA. Recent research works show that convergence of neural networks based MCA algorithms can be guaranteed if the learning rates are less than certain thresholds. However, the computation of these thresholds needs information about the eigenvalues of the autocorrelation matrix of data set, which is unavailable in online extraction of minor component from input data stream. In this correspondence, we introduce an adaptive learning rate into the OJAn MCA algorithm, such that its convergence condition does not depend on any unobtainable information, and can be easily satisfied in practical applications.

A Globally Convergent MCA Algorithm by Generalized Eigen-Decomposition

Minor component analysis (MCA) are used in many applications such as curve and surface fitting, robust beamforming, and blind signal separation. Based on the generalized eigen-decomposition, we present a completely different approach that leads to derive a novel MCA algorithm. First, in the sense of generalized eigen-decomposition, by using gradient ascent approach, we derive an algorithm for extracting the first minor eigenvector. Then, the algorithm used to extract multiple minor eigenvectors is proposed by using the orthogonality property. The proofs and rigorous theoretical analysis show that our proposed algorithm is convergent to their corresponding minor eigenvectors. We identify three important characteristics of these algorithms. The first is that the algorithm for extracting minor eigenvectors can be extended to generalized minor eigenvectors easily. The second is that the corresponding eigenvalues can be computed simultaneously as a byproduct of this algorithm. The third is that the algorithm i...

On the Discrete-Time Dynamics of a Class of Self-Stabilizing MCA Extraction Algorithms

The minor component analysis (MCA) deals with the recovery of the eigenvector associated to the smallest eigenvalue of the autocorrelation matrix of the input dada, and it is a very important tool for signal processing and data analysis. This brief analyzes the convergence and stability of a class of self-stabilizing MCA algorithms via a deterministic discrete-time (DDT) method. Some sufficient conditions are obtained to guarantee the convergence of these learning algorithms. Simulations are carried out to further illustrate the theoretical results achieved. It can be concluded that these self-stabilizing algorithms can efficiently extract the minor component (MC), and they outperform some existing MCA methods.

A unified learning algorithm to extract principal and minor components

Recently, many unified learning algorithms have been developed to solve the task of principal component analysis (PCA) and minor component analysis (MCA). These unified algorithms can be used to extract principal component and if altered simply by the sign, it can also serve as a minor component extractor. This is of practical significance in the implementations of algorithms. Convergence of the existing unified algorithms is guaranteed only under the condition that the learning rates of algorithms approach zero, which is impractical in many practical applications. In this paper, we propose a unified PCA & MCA algorithm with a constant learning rate, and derive the sufficient conditions to guarantee convergence via analyzing the discrete-time dynamics of the proposed algorithm. The achieved theoretical results lay a solid foundation for the applications of our proposed algorithm.

A stable MCA learning algorithm

Minor component analysis (MCA) is an important statistical tool for signal processing and data analysis. Neural networks can be used to extract online minor component from input data. Compared with traditional algebraic approaches, a neural network method has a lower computational complexity. Stability of neural networks learning algorithms is crucial to practical applications. In this paper, we propose a stable MCA neural networks learning algorithm, which has a more satisfactory numerical stability than some existing MCA algorithms. Dynamical behaviors of the proposed algorithm are analyzed via deterministic discrete time (DDT) method and the conditions are obtained to guarantee convergence. Simulations are carried out to illustrate the theoretical results achieved.

Convergence analysis of a simple minor component analysis algorithm

Minor component analysis (MCA) is a powerful statistical tool for signal processing and data analysis. Convergence of MCA learning algorithms is an important issue in practical applications. In this paper, we will propose a simple MCA learning algorithm to extract minor component from input signals. Dynamics of the proposed MCA learning algorithm are analysed using a corresponding deterministic discrete time (DDT) system. It is proved that almost all trajectories of the DDT system will converge to minor component if the learning rate satisfies some mild conditions and the trajectories start from points in an invariant set. Simulation results will be furnished to illustrate the theoretical results achieved.

Convergence analysis of the OJAn MCA learning algorithm by the deterministic discrete time method

Minor component analysis (MCA) is a statistical method of extracting the eigenvector associated with the smallest eigenvalue of the covariance matrix of input signals. Convergence is essential for MCA algorithms towards practical applications. Traditionally, the convergence of MCA algorithms is indirectly analyzed via their corresponding deterministic continuous time (DCT) systems. However, the DCT method requires the learning rate to approach zero, which is not reasonable in many applications due to the round-off limitation and tracking requirements. This paper studies the convergence of the deterministic discrete time (DDT) system associated with the OJAn MCA learning algorithm. Unlike the DCT method, the DDT method does not require the learning rate to approach zero. In this paper, some important convergence results are obtained for the OJAn MCA learning algorithm via the DDT method. Simulations are carried out to illustrate the theoretical results achieved.

Some chaotic behaviors in a MCA learning algorithm with a constant learning rate

Abstract Douglas’s minor component analysis algorithm with a constant learning rate has both stability and chaotic dynamical behavior under some conditions. The paper explores such dynamical behavior of this algorithm. Certain stability and chaos of this algorithm are derived. Waveform plots, Lyapunov exponents and bifurcation diagrams are presented to illustrate the existence of chaotic behavior.

A new minor component analysis method based on Douglas-Kung-Amari minor subspace analysis method

This letter presents a new minor component analysis algorithm that is based on the transformation of the known minor subspace analysis algorithm. The minor subspace analysis method that is adopted is the one proposed by Douglas, Kung, and Amari. The proposed minor component analysis algorithm extracts N minor components of the K-dimensional vector stationary random process N<K. Since the chosen minor subspace analysis method is fully homogeneous from the point of view of the individual neuron, the proposed minor component analysis method is also fully homogeneous from the point of view of the individual neuron.

Global convergence analysis of a self-stabilizing MCA learning algorithm

On minor component analysis (MCA) neural networks, a new algorithm is proposed. It is a self-stabilizing MCA algorithm, which means that the sign of the temporal change of the weight vector length is independent of the presented input vector. Algorithms without this property may suffer fluctuations and divergence. With suitable conditions on the initial weight vector and learning rate, a rigorous global convergence proof is given. The techniques used in the proof will be useful in many research issues such as independent component analysis, principle component analysis, etc.

The MCA EXIN neuron for the minor component analysis

The minor component analysis (MCA) deals with the recovery of the eigenvector associated to the smallest eigenvalue of the autocorrelation matrix of the input data and is a very important tool for signal processing and data analysis. It is almost exclusively solved by linear neurons. This paper presents a linear neuron endowed with a novel learning law, called MCA EXINn and analyzes its features. The neural literature about MCA is very poor, in the sense that both a little theoretical basis is given (almost always focusing on the ODE asymptotic approximation) and only experiments on toy problems (at most four-dimensional problems) are presented, without any numerical analysis. This work addresses these problems and lays sound theoretical foundations for the neural MCA theory. In particular, it classifies the MCA neurons according to the Riemannian metric and justifies, from the analysis of the degeneracy of the error cost; the different behavior in approaching convergence. The cost landscape is studied and used as a basis for the analysis of the asymptotic behavior. All the phases of the dynamics of the MCA algorithms are investigated in detail and, together with the numerical analysis, lead to the identification of three possible kinds of divergence, here called sudden, dynamic, and numerical. The importance of the choice of low initial conditions is also explained. A lot of importance is given to the experimental part, where simulations on high-dimensional problems are,presented and analyzed. The orthogonal regression or total least squares (TLS) technique is also presented, together with a real-world application on the identification of the parameters of an electrical machine. It can be concluded that MCA EXIN is the best MCA neuron in terms of stability (no finite time divergence), speed, and accuracy.

Sequential Extraction of Minor Components

Principal component analysis (PCA) and Minor component analysis (MCA) are similar but have different dynamical performances. Unexpectedly, a sequential extraction algorithm for MCA proposed by Luo and Unbehauen l11r does not work for MCA, while it works for PCA. We propose a different sequential-addition algorithm which works for MCA. We also show a conversion mechanism by which any PCA algorithms are converted to dynamically equivalent MCA algorithms and vice versa.

A general theory of a class of linear neural nets for principal and minor component analysis

This paper presents a unified theory of a class of learning neural nets for principal component analysis (PCA) and minor component analysis (MCA). First, some fundamental properties are addressed which all neural nets in the class have in common. Second, a subclass called the generalized asymmetric learning algorithm is investigated, and the kind of asymmetric structure which is required in general to obtain the individual eigenvectors of the correlation matrix of a data sequence is clarified. Third, focusing on a single-neuron model, a systematic way of deriving both PCA and MCA learning algorithms is shown, through which a relation between the normalization in PCA algorithms and that in MCA algorithms is revealed.

Neural fitting: Robustness by anti-Hebbian learning

A nonlinear neuron, learning by anti-Hebbian learning rules, can perform robust fitting of parametric models to data. Robustness means that the solution is tolerant to non-Gaussian noise and resistant to outliers. The convergence of nonlinear anti-Hebbian learning rules, called here nonlinear Minor Component Analysis algorithms, is analyzed using a simple outlier data model. Both rigorous mathematical results and computer simulations are given. The results show that the linear algorithm, minimizing a Total Least Squares criterion, always has a unique solution which is the direction of the smallest variance of the input data, and thus it is sensitive to outliers. Contrary to this, the nonlinear algorithms exhibit a richer behavior. They do not have a unique solution in general, but will converge to one of several stable fixed points. They are able to maintain their robustness when the effect of the outliers is increasing.