Fukunaga-Koontz Transform Research Articles

Spectral representation of EEG data using learned graphs with application to motor imagery decoding

Electroencephalography (EEG) data entail a complex spatiotemporal structure that reflects ongoing organization of brain activity. Characterization of the spatial patterns is an indispensable step in numerous EEG processing pipelines. We present a novel method for transforming EEG data into a spectral representation. First, we learn subject-specific graphs from each subject’s EEG data. Second, by eigendecomposition of the normalized Laplacian matrix of each subject’s graph, an orthonormal basis is obtained using which any given EEG map of the subject can be decomposed, providing a spectral representation of the data. We show that energy of EEG maps is strongly associated with low frequency components of the learned basis, reflecting the smooth topography of EEG maps. As a proof-of-concept for this alternative view of EEG data, we consider the task of decoding two-class motor imagery (MI) data. To this aim, the spectral representations are first mapped into a discriminative subspace for differentiating two-class data using a projection matrix obtained by the Fukunaga–Koontz transform (FKT). An SVM classifier is then trained and tested on the resulting features to differentiate MI classes. The method is benchmarked against features extracted from a subject-specific functional connectivity matrix as well as four alternative MI-decoding methods on Dataset IVa of BCI Competition III. Experimental results show the superiority of the proposed method over alternative approaches in differentiating MI classes, reflecting the added benefit of (i) decomposing EEG data using data-driven, subject-specific harmonic bases, and (ii) accounting for class-specific temporal variations in spectral profiles.

A Funnel Fukunaga–Koontz Transform for Robust Indoor–Outdoor Detection Using Channel-State Information in 5G IoT Context

The massive machine-type communication will be at the core of ambient connectivity, requiring for energy-efficient systems. Earlier studies highlighted the efficiency of positioning approaches based on channel-state information (CSI) in different environments. Many works limited the solution assessment to a single room in a fully indoor testbed. This article extends the application of CSI for indoor–outdoor detection on an unprecedented large area and considers mMTC-oriented long-term evolution and fifth-generation Internet of Things in the sub-GHz frequency band. Hinged on a novel long-term evolution protocol dedicated for machine-type communications, the results focus on a unique packet exchange with a single access point to save battery life and simplify deployment. The study evaluates different input features and investigates the target positioning accuracy for multiple unsupervised and supervised dimensionality reduction methods. We present a new dimension reduction scheme consisting of an unsupervised funnel on top of a supervised dimension reduction approach. Results show that the introduced Funnel Fukunaga–Koontz transform outperforms other dimension reduction approaches, regardless of the input features and the number of locations.

Beamforming Scheme for MIMO Relay Based 5G and beyond Wireless Network

In this paper, in order to attain the maximum ergodic capacity and significantly increase the spectral efficiency of wireless communication systems, novel linear beamforming is proposed for dual-hop amplify-and-forward (AF) multi-relay networks. The linear beamforming is designed based on the maximization of the signal-to-interference-plus-noise ratio (SINR) and signal-to- leakage-and-noise ratio (SLNR). The channel state information (CSI) is used in applying this new design to multi-relay (MR) nodes between the source and relays as well as relays and destination. The beamforming optimization problem is solved by using the Fukunaga-Koontz Transform (FKT). The scheme can achieve intra-node array and distributed gains by using multiple antennas and multi-relays (MRs). The performance of the proposed scheme demonstrates that by considering interference mitigation criteria the ergodic capacity at a significant level is improved as compared to the conventional techniques. Therefore, the proposed techniques based on the maximization of the signal-to-interference-plus-noise ratio (SINR) and signal-to-leakage-and-noise ratio (SLNR) relay processing outperform other conventional techniques in case of a multi-relay dual-hop network in terms of ergodic.

L1-norm unsupervised Fukunaga-Koontz transform

The Fukunaga-Koontz transform (FKT) is a powerful supervised feature extraction method used in two-class recognition problems, particularly when the classes have equal mean vectors but different covariance matrices. The present work proves that it is also possible to perform the FKT in an unsupervised manner, sparing the need for labeled data, by using a variant of L1-norm Principal Component Analysis (L1-PCA) that minimizes the L1-norm in the feature space. Rigorous proof is given in the case of data drawn from a mixture of Gaussians. A working iterative algorithm based on gradient-descent in the Stiefel manifold is put forward to perform L1-norm minimization with orthogonal constraints. A number of numerical experiments on synthetic and real data confirm the theoretical findings and the good convergence characteristics of the proposed algorithm.

Improved Fukunaga–Koontz Transform with Compositional Kernel Combination for Hyperspectral Target Detection

This article presents a novel supervised target detection approach on hyperspectral images based on Fukunaga–Koontz Transform (FKT) with compositional kernel combination. The Fukunaga–Koontz Transform is one of the most effective techniques for solving problems that involve two-pattern characteristics. To capture nonlinear properties of data, researchers have extended FKT to kernel FKT (KFKT) by means of kernel machines. However, the performance of KFKT depends on choosing convenient kernel functions and/or selection of the proper parameter(s). In this work, instead of selecting a single kernel for nonlinear version of FKT, we have applied a compositional kernel combination approach to capture the underlying local distributions of hyperspectral remote sensing data. Optimal parameter selection for each kernel function is achieved applying an evolutionary technique called differential evolution algorithm. The proposed new nonlinear target detection algorithm is tested for hyperspectral images. The experimental results verify that the proposed target detection algorithm has effective and promising performance compared to the conventional version for supervised target detection applications.

Target oriented dimensionality reduction of hyperspectral data by Kernel Fukunaga–Koontz Transform

Principal component analysis (PCA) is a popular technique in remote sensing for dimensionality reduction. While PCA is suitable for data compression, it is not necessarily an optimal technique for feature extraction, particularly when the features are exploited in supervised learning applications (Cheriyadat and Bruce, 2003) [1]. Preserving features belonging to the target is very crucial to the performance of target detection/recognition techniques. Fukunaga–Koontz Transform (FKT) based supervised band reduction technique can be used to provide this requirement. FKT achieves feature selection by transforming into a new space in where feature classes have complimentary eigenvectors. Analysis of these eigenvectors under two classes, target and background clutter, can be utilized for target oriented band reduction since each basis functions best represent target class while carrying least information of the background class. By selecting few eigenvectors which are the most relevant to the target class, dimension of hyperspectral data can be reduced and thus, it presents significant advantages for near real time target detection applications. The nonlinear properties of the data can be extracted by kernel approach which provides better target features. Thus, we propose constructing kernel FKT (KFKT) to present target oriented band reduction. The performance of the proposed KFKT based target oriented dimensionality reduction algorithm has been tested employing two real-world hyperspectral data and results have been reported consequently.

Hyperspectral Imaging and Nonlinear Fukunaga-Koontz Transform Based Food Inspection

Hyperspectral Imaging and Nonlinear Fukunaga-Koontz Transform Based Food Inspection

Efficient Linear Processing for Non-regenerative MIMO Relay Network with Perfect CSI

In this study, two hop non-regenerative Multiple Input Multiple Output (MIMO) relay network is considered. Each node of the network is equipped with multiple antennas. We apply an efficient linear processing at the relay node only. We utilize Minimum Mean Square Error (MMSE) as the relay receive beamforming and Per-Antenna-Signal to Leakage plus Noise Ratio (PA-SLNR) maximization criteria using Fukunaga Koontz Transform (FKT) is considered to generate relay downlink precoding to mitigate the interference due to the leakage signal. The relay acquires perfect channel state information of the channel between source to relay and relay to the destination. Monte Carlo simulation confirms better performance in terms of ergodic capacity offered by the proposed scheme.

Kernel Fukunaga–Koontz Transform Subspaces for Classification of Hyperspectral Images With Small Sample Sizes

In this letter, a novel supervised classification approach is presented for the classification of hyperspectral images using kernel Fukunaga–Koontz transform (KFKT). The Fukunaga–Koontz transform (FKT) is originally a powerful target detection method used in remote sensing tasks, and it is an especially good classification tool for two-class problems. The traditional FKT method has been kernelized for increasing the nonlinear discrimination ability and capturing higher order of statistics of data. The proposed approach in this letter aims to solve the multiclass problem by regarding one class as target that is tried to be separated from the remaining classes (as clutter) like one-against-all methodology. The KFKT provides superior performance in the classification of hyperspectral data even using small number of samples because of nonlinear separability of data in higher dimensional space. The experiments confirm that KFKT has better and promising results than FKT and support vector machine in classification of hyperspectral images.

Hyperspectral Image Classification Using Kernel Fukunaga-Koontz Transform

This paper presents a novel approach for the hyperspectral imagery (HSI) classification problem, using Kernel Fukunaga-Koontz Transform (K-FKT). The Kernel based Fukunaga-Koontz Transform offers higher performance for classification problems due to its ability to solve nonlinear data distributions. K-FKT is realized in two stages: training and testing. In the training stage, unlike classical FKT, samples are relocated to the higher dimensional kernel space to obtain a transformation from non-linear distributed data to linear form. This provides a more efficient solution to hyperspectral data classification. The second stage, testing, is accomplished by employing the Fukunaga- Koontz Transformation operator to find out the classes of the real world hyperspectral images. In experiment section, the improved performance of HSI classification technique, K-FKT, has been tested comparing other methods such as the classical FKT and three types of support vector machines (SVMs).

A new discriminant subspace analysis approach for multi-class problems

Fukunaga-Koontz Transform (FKT) is a famous feature extraction method in statistical pattern recognition, which aims to find a set of vectors that have the best representative power for one class while the poorest representative power for the other class. Li and Savvides [1] propose a one-against-all strategy to deal with multi-class problems, in which the two-class FKT method can be directly applied to find the presentative vectors of each class. Motivated by the FKT method, in this paper we propose a new discriminant subspace analysis (DSA) method for the multi-class feature extraction problems. To solve DSA, we propose an iterative algorithm for the joint diagonalization (JD) problem. Finally, we generalize the linear DSA method to handle nonlinear feature extraction problems via the kernel trick. To demonstrate the effectiveness of the proposed method for pattern recognition problems, we conduct extensive experiments on real data sets and show that the proposed method outperforms most commonly used feature extraction methods.

A Statistical Approach for Multiclass Target Detection

Fukunaga-Koontz Transform (FKT) is a statistical technique which has many application areas for two-class classification or detection problems. In this paper, we have proposed improved target detection algorithm for hyperspectral imagery (HSI) based on enhanced FKT which gives better results for multi-class target detection problems.Hyperspectral imagery is popular for target detection applications due to its additional properties compare to multispectral images. It presents one dimensional (spectral) and two dimensional (spatial) features of targets for detection problems. For multi-class target detection in hyperspectral images, we have selected each target's 1D features, called signature of targets, to introduce to enhanced FKT during learning stage. After learning stage of FKT, we have applied our operators, obtained by enhanced FKT, to HSI images to detect more than one target simultaneously.The experimental results show that multi-class FKT has satisfactory performance over 95 percent of true detection rate especially on the pixel sized targets. In addition, multi-class processing ability of the proposed enhanced FKT is very important for many applications such as classification, recognition, clustering, tracking problems in the literature.

DETECT INFRARED POINT TARGETS BASED ON KERNEL FUKUNAGA-KOONTZ TRANSFORM

Fukunaga-Koontz transform(FKT) is a pattern recognition tool for two-class problems.It can only capture the second-order statistical features of images without considering high-order statistical properties because it stems from the principal component analysis(PCA).So the satisfying detection performance can hardly be achieved.For improving the detection performance,Fukunaga-Koontz transform was firstly extended to the higher-dimensional space in order to capture the higher-order statistics of images in this study.And it is named as kernel Fukunaga-Koontz transform.The kernel Fukunaga-Koontz transform can be used to detect infrared point targets.

Automatically detect and track infrared small targets with kernel Fukunaga-Koontz transform and Kalman prediction

Fukunaga-Koontz transform (FKT), stemming from principal component analysis (PCA), is used in many pattern recognition and image-processing fields. It cannot capture the higher-order statistical property of natural images, so its detection performance is not satisfying. PCA has been extended into kernel PCA in order to capture the higher-order statistics. However, thus far there have been no researchers who have definitely proposed kernel FKT (KFKT) and researched its detection performance. For accurately detecting potential small targets from infrared images, we first extend FKT into KFKT to capture the higher-order statistical properties of images. Then a framework based on Kalman prediction and KFKT, which can automatically detect and track small targets, is developed. Results of experiments show that KFKT outperforms FKT and the proposed framework is competent to automatically detect and track infrared point targets.

Discriminant Subspace Analysis: A Fukunaga-Koontz Approach

The Fisher Linear Discriminant (FLD) is commonly used in pattern recognition. It finds a linear subspace that maximally separates class patterns according to the Fisher Criterion. Several methods of computing the FLD have been proposed in the literature, most of which require the calculation of the so-called scatter matrices. In this paper, we bring a fresh perspective to FLD via the Fukunaga-Koontz Transform (FKT). We do this by decomposing the whole data space into four subspaces with different discriminability, as measured by eigenvalue ratios. By connecting the eigenvalue ratio with the generalized eigenvalue, we show where the Fisher Criterion is maximally satisfied. We prove the relationship between FLD and FKT analytically, and propose a unified framework to understanding some existing work. Furthermore, we extend our our theory to Multiple Discriminant Analysis (MDA). This is done by transforming the data into intra- and extra-class spaces, followed by maximizing the Bhattacharyya distance. Based on our FKT analysis, we identify the discriminant subspaces of MDA/FKT, and propose an efficient algorithm, which works even when the scatter matrices are singular, or too large to be formed. Our method is general and may be applied to different pattern recognition problems. We validate our method by experimenting on synthetic and real data.

Infrared small target detection with kernel Fukunaga–Koontz transform

The Fukunaga–Koontz transform (FKT) has been proposed for many years. It can be used to solve two-pattern classification problems successfully. However, there are few researchers who have definitely extended FKT to kernel FKT (KFKT). In this paper, we first complete this task. Then a method based on KFKT is developed to detect infrared small targets. KFKT is a supervised learning algorithm. How to construct training sets is very important. For automatically detecting targets, the synthetic target images and real background images are used to train KFKT. Because KFKT can represent the higher order statistical properties of images, we expect better detection performance of KFKT than that of FKT. The well-devised experiments verify that KFKT outperforms FKT in detecting infrared small targets.

A Statistical Analysis of Fukunaga–Koontz Transform

The Fukunaga-Koontz transform (FKT) has been proposed as a feature selection methodology for nearly 32 years. There are a huge number of citations. We have not seen a direct analysis between FKT, and a well established statistical method: Fisher quadratic discriminant analysis (QDA). In this letter, under certain assumptions, we establish such a connection. We speculate that a link in a more general situation is hard to find.

1255 Supervised walking program for cancer patients

Fukunaga-Koontz Transform (FKT) is a statistical technique which has many application areas for two-class classification or detection problems. In this paper, we have proposed improved target detection algorithm for hyperspectral imagery (HSI) based on enhanced FKT which gives better results for multi-class target detection problems.Hyperspectral imagery is popular for target detection applications due to its additional properties compare to multispectral images. It presents one dimensional (spectral) and two dimensional (spatial) features of targets for detection problems. For multi-class target detection in hyperspectral images, we have selected each target's 1D features, called signature of targets, to introduce to enhanced FKT during learning stage. After learning stage of FKT, we have applied our operators, obtained by enhanced FKT, to HSI images to detect more than one target simultaneously.The experimental results show that multi-class FKT has satisfactory performance over 95 percent of true detection rate especially on the pixel sized targets. In addition, multi-class processing ability of the proposed enhanced FKT is very important for many applications such as classification, recognition, clustering, tracking problems in the literature.