Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userGeneralized Two-Dimensional Quaternion Principal Component Analysis with Weighting for Color Image Recognition
222
0
0.0
(
0
)
Added by
Zhigang Jia
Publication date
2020
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
A generalized two-dimensional quaternion principal component analysis (G2DQPCA) approach with weighting is presented for color image analysis. As a general framework of 2DQPCA, G2DQPCA is flexible to adapt different constraints or requirements by imposing $L_{p}$ norms both on the constraint function and the objective function. The gradient operator of quaternion vector functions is redefined by the structure-preserving gradient operator of real vector function. Under the framework of minorization-maximization (MM), an iterative algorithm is developed to obtain the optimal closed-form solution of G2DQPCA. The projection vectors generated by the deflating scheme are required to be orthogonal to each other. A weighting matrix is defined to magnify the effect of main features. The weighted projection bases remain the accuracy of face recognition unchanged or moving in a tight range as the number of features increases. The numerical results based on the real face databases validate that the newly proposed method performs better than the state-of-the-art algorithms.
rate research
Read More
A sample-relaxed two-dimensional color principal component analysis (SR-2DCPCA) approach is presented for face recognition and image reconstruction based on quaternion models. A relaxation vector is automatically generated according to the variances of training color face images with the same label. A sample-relaxed, low-dimensional covariance matrix is constructed based on all the training samples relaxed by a relaxation vector, and its eigenvectors corresponding to the $r$ largest eigenvalues are defined as the optimal projection. The SR-2DCPCA aims to enlarge the global variance rather than to maximize the variance of the projected training samples. The numerical results based on real face data sets validate that SR-2DCPCA has a higher recognition rate than state-of-the-art methods and is efficient in image reconstruction.
The two-dimensional principal component analysis (2DPCA) has become one of the most powerful tools of artificial intelligent algorithms. In this paper, we review 2DPCA and its variations, and propose a general ridge regression model to extract features from both row and column directions. To enhance the generalization ability of extracted features, a novel relaxed 2DPCA (R2DPCA) is proposed with a new ridge regression model. R2DPCA generates a weighting vector with utilizing the label information, and maximizes a relaxed criterion with applying an optimal algorithm to get the essential features. The R2DPCA-based approaches for face recognition and image reconstruction are also proposed and the selected principle components are weighted to enhance the role of main components. Numerical experiments on well-known standard databases indicate that R2DPCA has high generalization ability and can achieve a higher recognition rate than the state-of-the-art methods, including in the deep learning methods such as CNNs, DBNs, and DNNs.
A relaxed two dimensional principal component analysis (R2DPCA) approach is proposed for face recognition. Different to the 2DPCA, 2DPCA-$L_1$ and G2DPCA, the R2DPCA utilizes the label information (if known) of training samples to calculate a relaxation vector and presents a weight to each subset of training data. A new relaxed scatter matrix is defined and the computed projection axes are able to increase the accuracy of face recognition. The optimal $L_p$-norms are selected in a reasonable range. Numerical experiments on practical face databased indicate that the R2DPCA has high generalization ability and can achieve a higher recognition rate than state-of-the-art methods.
In this paper we develop a new approach to sparse principal component analysis (sparse PCA). We propose two single-unit and two block optimization formulations of the sparse PCA problem, aimed at extracting a single sparse dominant principal component of a data matrix, or more components at once, respectively. While the initial formulations involve nonconvex functions, and are therefore computationally intractable, we rewrite them into the form of an optimization program involving maximization of a convex function on a compact set. The dimension of the search space is decreased enormously if the data matrix has many more columns (variables) than rows. We then propose and analyze a simple gradient method suited for the task. It appears that our algorithm has best convergence properties in the case when either the objective function or the feasible set are strongly convex, which is the case with our single-unit formulations and can be enforced in the block case. Finally, we demonstrate numerically on a set of random and gene expression test problems that our approach outperforms existing algorithms both in quality of the obtained solution and in computational speed.
We consider the problem of inferring the interactions between a set of N binary variables from the knowledge of their frequencies and pairwise correlations. The inference framework is based on the Hopfield model, a special case of the Ising model where the interaction matrix is defined through a set of patterns in the variable space, and is of rank much smaller than N. We show that Maximum Lik elihood inference is deeply related to Principal Component Analysis when the amp litude of the pattern components, xi, is negligible compared to N^1/2. Using techniques from statistical mechanics, we calculate the corrections to the patterns to the first order in xi/N^1/2. We stress that it is important to generalize the Hopfield model and include both attractive and repulsive patterns, to correctly infer networks with sparse and strong interactions. We present a simple geometrical criterion to decide how many attractive and repulsive patterns should be considered as a function of the sampling noise. We moreover discuss how many sampled configurations are required for a good inference, as a function of the system size, N and of the amplitude, xi. The inference approach is illustrated on synthetic and biological data.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
