Maximum relevance, minimum redundancy feature extraction for hyperspectral images

Optimizing highway alignments through complex environments is a difficult problem. Optimal alignment is influenced by many factors and should be based on trade-offs among various supplier and user cost components. Previous works on alignment optimization usually have neglected some important components of the total cost function that should influence the optimal solution. The formulations of different cost components for two-lane rural highways are presented. The proposed cost functions are based on the geometric features of both horizontal and vertical alignments. The cost formulations can be employed in models for simultaneously optimizing three-dimensional alignments. Possible methods for solving such optimization problems are provided. A numerical example also is presented to illustrate the optimization of three-dimensional alignments with the proposed cost functions.

We propose a new scheme of subband adaptive digital filter(ADF) which allows massive parallel processing. We discuss the power spectral density of the down-sampled processes and propose a new cost function which is suitable for subband ADF. The subband scheme of adaptive system identification using the proposed cost function is considered. It is shown that we can carry out precise system identification based on the frequency domain sampling theorem, in which the proposed cost function is applied to the subband ADF using polyphase filter banks. The cost function is defined in each bin; as a result, it enables the perfect parallel processing of ADFs. >

Hundreds of contiguous bands of remotely sensed hyperspectral image (HSI) capture the spectral signatures of observed objects or materials on the earth's surface. Although the HSI data is able to provide huge information with great details, it poses challenges to image analysis because of the high computational cost due to the large dimensionality of the feature space, redundancy in information, and curse of dimensionality. To overcome these difficulties, this paper proposes an information-theoretic feature selection approach for selecting an informative feature subset considering the maximum of the minimum approach. The minimum of conditional mutual information based estimation is used to select a feature among the selected feature subset. This selected feature with the corresponding candidate feature is then exploited using the mutual information and joint mutual information based valuation to find the maximum relevance of the candidate features with the target classes. The effectiveness of the proposed approach, called joint-conditional mutual information for selecting informative feature (JCIF), is assessed by implementing it in some synthetic data and three remotely sensed HSI data. Several known feature selection algorithms are also used for comparison purposes. The results of the experiments with K-Nearest Neighbors and Support Vector Machine classifiers reveal that JCIF performs better in selecting informative features.

This paper discusses the problem of local path planning in a static-obstacle environment by designing a PSO-based receding horizon control approach. In order to avoid obstacles, a virtual robot is first designed and moves along the boundary of obstacles. Then, in the framework of receding horizon control, a cost function is proposed where the virtual robot and the target position are integrated, which implies that mobile robots are controlled to keep a security distance and velocity consensus with virtual robots, and to move toward the target position. Next, the proposed cost function with constraints is processed by a particle swarm optimization (PSO) algorithm such that the PSO-based receding horizon control approach is developed. By solving the proposed cost function, a control sequence is obtained and then the first control input is used to enable the robot toward the target and avoid obstacles. Finally, the performance capabilities of the PSO-based receding horizon control approach are illustrated by simulation results.

In this paper, a robust face recognition algorithm is proposed, which is based on the elastic graph matching (EGM) and discriminative feature analysis algorithm. We introduce a cost function for the EGM taking account of variations in face pose and facial expressions, and propose its optimization procedure. Our proposed cost function uses a set of Gabor-wavelet-based features, called robust jet, which are robust against the variations. The robust jet is defined in terms of discrete Fourier transform coefficients of Gabor coefficients. To cope with the difference between face poses of test face and reference faces, 2 x 2 warping matrix is incorporated in the proposed cost function. For the discriminative feature analysis, linear projection discriminant analysis and kernel-based projection discriminant analysis are introduced. These methods are motivated to solve the small-size problem of training samples. The basic idea of PDA is that a class is represented by a subspace spanned by some training samples of the class instead of using sample mean vector, that the distance from a pattern to a class is defined by using the error vector between the pattern and its projection to the subspace representing the class, and that an optimum feature selection rule is developed using the distance concept in a similar way as in the conventional linear discriminant analysis. In order to evaluate the performance of our face recognition algorithm, we carried out some experiments using the well-known FERET face database, and compared the performance with recently developed approaches. We observed that our algorithm outperformed the compared approaches.

Mutual Information estimation is an important task for many data mining and machine learning applications. In particular, many feature selection algorithms make use of the mutual information criterion and could thus benefit greatly from a reliable way to estimate this criterion. More precisely, the multivariate mutual informa- tion (computed between multivariate random variables) can naturally be combined with very popular search procedure such as the greedy forward to build a subset of the most relevant features. Estimating the mutual information (especially through density functions estimations) between high-dimensional variables is however a hard task in practice, due to the limited number of available data points for real-world problems. This paper compares different popular mutual information estimators and shows how a nearest neighbors-based estimator largely outperforms its competitors when used with high-dimensional data.

In this paper we present a new method for the determination of geometrical misalignments in cone-beam CT scanners, from the analysis of the projection data of a generic object. No a priori knowledge of the object shape and positioning is required. We show that a cost function, which depends on the misalignment parameters, can be defined using the projection data and that such a cost function has a local minimum in correspondence to the actual parameters of the system. Hence, the calibration of the scanner can be carried out by minimizing the cost function using standard optimization techniques. The method is developed for a particular class of 3D object functions, for which the redundancy of the fan beam sinogram in the transaxial midplane can be extended to cone-beam projection data, even at wide cone angles. The method has an approximated validity for objects which do not belong to that class; in that case, a suitable subset of the projection data can be selected in order to compute the cost function. We show by numerical simulations that our method is capable to determine with high accuracy the most critical misalignment parameters of the scanner, i.e., the transversal shift and the skew of the detector. Additionally, the detector slant can be determined. Other parameters such as the detector tilt, the longitudinal shift and the error in the source–detector distance cannot be determined with our method, as the proposed cost function has a very weak dependence on them. However, due to the negligible influence of these latter parameters in the reconstructed image quality, they can be kept fixed at estimated values in both calibration and reconstruction processes without compromising the final result. A trade-off between computational cost and calibration accuracy must be considered when choosing the data subset used for the computation of the cost function. Results on real data of a mouse femur as obtained with a small animal micro-CT are shown as well, proving the capability of the proposed calibration method. In principle, the method can be adapted to other cone-beam imaging modalities (e.g., single photon emission computed tomography).

Traditional Discrete Wavelet Transform (DWT) image compression fails to reserve texture information. JPEG2000 part 2 extends to allow arbitrary subband decomposition and different decomposition direction. In this paper, we aim to provide a suitable wavelet packet basis selection for JPEG2000 by the improved cost function. Various cost functions used to search for the optimal wavelet basis are discussed and compared, and the estimated coding cost (ECC) is chosen as our criterion to achieve both accuracy and simplified computation. Then the entropy coding scheme of JPEG2000 is analyzed in detail and modeled to get our cost function. Experimental results show that compared with other cost function, the proposed cost function with ECC is more efficient in terms of PSNR (Peak Signal to Noise Rate). The proposed adaptive wavelet packet coding can provides higher visual quality than original JPEG2000.

The significantly increased density of pins of stan-dard cells and the reduced number of routing tracks at sub-10nm nodes have made the pin access problem in detailed routing very difficult. To alleviate this pin accessibility problem in detailed routing, recent works have proposed to make a small perturbation of cell shifting, cell flipping, and adjacent cells swapping in the detailed placement stage. Here, an essential element for the success of pin accessibility aware detailed placement is the installed cost function, which should be sufficiently accurate in predicting the degree of routing difficulty in accessing pins. In this work, we propose a new model of cost function that is comprehensively devised to overcome the limitations of the prior ones. Precisely, unlike the conventional cost functions, our proposed cost function model is based on the empirical routing data in order to fully reflect the potential outcomes of detailed routing. Through experiments with benchmark circuits, it is shown that using our proposed cost function in detailed placement is able to reduce the routing errors by 44 % on average while using the existing cost functions reduce the routing errors on average by at most 15 %.

Feature selection has been shown to be beneficial for many data mining and machine learning tasks, especially for big data analytics. Mutual Information (MI) is a well-known information-theoretic approach used to evaluate the relevance of feature subsets and class labels. However, estimating high-dimensional MI poses significant challenges. Consequently, a great deal of research has focused on using low-order MI approximations or computing a lower bound on MI called Variational Information (VI). These methods often require certain assumptions made on the probability distributions of features such that these distributions are realistic yet tractable to compute. In this paper, we reveal two sets of distribution assumptions underlying many MI and VI based methods: Feature Independence Distribution and Geometric Mean Distribution. We systematically analyze their strengths and weaknesses and propose a logical extension called Arithmetic Mean Distribution, which leads to an unbiased and normalised estimation of probability densities. We conduct detailed empirical studies across a suite of 29 real-world classification problems and illustrate improved prediction accuracy of our methods based on the identification of more informative features, thus providing support for our theoretical findings.

Fuzzy rough set theory can model uncertainty in data and has been applied to feature selection for machine learning tasks. The existence of noise in data is one of the reasons for data uncertainty. However, most classical fuzzy rough set models are often sensitive to the noise in data, which somewhat degrades their applicability to process uncertainty of data. Furthermore, a robust feature evaluation function is nontrivial in a fuzzy rough set model as a nonoptimal feature subsets may be selected due to the perturbations from redundant features. In this article, we delve into local density and indispensable features for fuzzy rough feature selection to address these challenges. We first propose a local density-based fuzzy rough set (LDFRS) model to tackle noisy data. Mutual information is then plugged into the proposed LDFRS model to evaluate uncertainty in data. A joint feature evaluation function on the indispensability and relevance of features is constructed to evaluate the significance of features. On this basis, a fuzzy rough feature selection algorithm is built upon the LDFRS model. Experimental results using four typical classifiers demonstrate the robustness and effectiveness of the proposed model including our feature selection algorithm and its superiority against baseline methods.

In this paper, we present a general analytical framework for the exact mutual information (MI) cumulants of multiple-input multiple-output (MIMO) systems with perfect receiver channel state information (CSI) and no transmitter CSI. Our derivation is based on a recent parameterization of the joint ordered eigenvalue probability density function (PDF), that encompasses both uncorrelated/semi-correlated Rayleigh channels as well as uncorrelated Rician channels. In addition, we extend our framework to account for the cumulants of doubly-correlated Rayleigh channels and also to deduce tractable expressions in the high Signal-to-Noise ratio (SNR) regime. The cumulants are particularly useful to study all high-order statistics (HOS) of the MI; in fact, they can be used to express the MI mean and variance as a finite sum of determinants. Our analytical expressions are then validated via Monte-Carlo simulations with the attained accuracy being excellent in all cases.

Mutual information (MI) is quite popular as a cost function for intensity based registration of images due to its ability to handle highly non-linear relationships between intensities of the two images. More recently, quadratic mutual information (QMI) has been proposed as an alternative measure that computes Euclidean distance instead of KL divergence between the joint and the product of the marginal densities of pixel intensities. In this paper, we examine the conditions under which QMI is advantageous over the classical MI measure, for the image registration problem. We show that QMI is a better cost function to use for optimization methods such as stochastic gradient descent. We show that the QMI cost function remains much smoother than the classical MI measure on stochastic subsampling of the image data. As a consequence, QMI has a higher probability of convergence, even for larger degrees of initial misalignment of the images.

In this study, due to the redundant and irrelevant features contained in the multi-dimensional feature parameter set, the information fusion performance of the subspace learning algorithm was reduced. To solve the above problem, a mutual information (MI) and fractal dimension-based unsupervised feature parameters selection method was proposed. The key to this method was the importance ordering algorithm based on the comprehensive consideration of the relevance and redundancy of features, and then the method of fractal dimension-based feature parameter subset evaluation criterion was adopted to obtain the optimal feature parameter subset. To verify the validity of the proposed method, a brushless direct current (DC) motor performance degradation test was designed. Vibrational sample data during motor performance degradation was used as the data source, and motor health-fault diagnosis capacity and motor state prediction effect ware evaluation indexes to compare the information fusion performance of the subspace learning algorithm before and after the use of the proposed method. According to the comparison result, the proposed method is able to eliminate highly-redundant parameters that are less correlated to feature parameters, thereby enhancing the information fusion performance of the subspace learning algorithm.

Virtual network embedding has been gaining interest due to the diverse applications of virtual networks. Especially building a cooperative testbed for future network design requires highly efficient virtual network embedding There have been many virtual network embedding algorithms proposed so far. However, these algorithms assume simple cost functions such as minimizing the maximum utilization or maximizing the number of virtual networks embedded in the physical network under given constraints. In this paper, we propose to use a more realistic cost function so that it can take into account diverse aspects of costs in the virtual network embedding Furthermore, we propose a Greedy embedding algorithm that is suitable for the proposed cost function. Through extensive simulation analysis, we show that our proposed Greedy approach performs much better compared to a Random approach. We also show that the performance is similar to a theoretical lower bound for small to medium resource demands.