Fourier Features Research Articles

Polarity Identification of Aspect based Sentiment Reviews

Objectives: To show the effectiveness of using random Fourier features in detecting sentiment polarities. Methods/ Statistical Analysis: The paper proposes on identifying the sentiment polarity of laptop and restaurant dataset towards three different polarity categories- positive, negative, and neutral. It provides experimental comparisons on conventional machine learning methods for detecting review polarities. Several articles have shown the effectiveness of random Fourier features are used in classification problems. The present paper prepares random Fourier features corresponding to the polarity data. A regularized least square strategy is adopted to fit a model and to perform the polarity detection task. Findings: Experiments were performed with 10 cross-validations. The proposed method with random Fourier features gives 80% accuracy over conventional classifiers. Initially the features are mapped to a lower dimension (chosen manually) and corresponding random Fourier features are obtained. The experiments are evaluated using Precision, recall, and F-measure. Application/Improvements: The method presented in this paper shows that aspect based polarity detection can be improved by choosing suitable features and mapping to lower dimension.

Fractional Fourier analysis of elastic wave scattering in inhomogeneous materials

To describe the elastic wave scattering, which reflects the performance of propagation control materials, the approximate directional cloaks of an elastic wave are designed using the zero- and first-order approximation coordinate transformation method. Because the convergence features of fractional Fourier transform (FRFT) are more acute and sensitive to the frequency change than those of short time Fourier transform, the spatial signals in the designed materials are transformed in the FRFT domain. The spatial frequency changes of elastic waves through inhomogeneous materials are quantitatively analyzed under several circumstances. The provided time-frequency analysis method with FRFT can support the design evaluation of the material parameters.

Hyperspectral face recognition with log‐polar Fourier features and collaborative representation based voting classifiers

Hyperspectral imagery analysis has become a popular topic for improving face recognition accuracy. Nevertheless, it encounters difficulty in data acquisition, low signal-to-noise ratio, and high dimensionality. As a result, there exists a need to develop better algorithms in order to achieve higher classification rates. In this study, the authors propose a new method for hyperspectral face recognition with very competitive experimental results. Since there is a significant amount of noise in every spectral band, they reduce noise adaptively from each spectral band by using any image denoising method, e.g. block matching and 3D filtering. They then crop each face according to its eye coordinates so that translation invariance can be achieved. They conduct log-polar transform to each cropped face image and extract 2D Fourier spectrum from them. In this way, the extracted features are approximately invariant to translation, rotation, and scaling. They use the collaborative representation-based classifier with voting for hyperspectral face recognition. They perform some experiments to test the authors’ new method for hyperspectral face recognition with very promising results.

Model Selection for Gaussian Kernel Support Vector Machines in Random Fourier Feature Space

Model Selection for Gaussian Kernel Support Vector Machines in Random Fourier Feature Space

A novel forged blurred region detection system for image forensic applications

As new technologies and devices are introduced in the market, the crime rate also increases in developing and developed countries. One such crime is image forgery which can be detected by forensic applications. In this paper, we propose a novel idea for identifying forgery attack done by blur artifact unlike existing forgery attack done by geometrical distortion such as rotation and scaling. The proposed method segment region of interest from the input forgery image based on the combination of statistical analysis with color texture analysis which includes blur artifact region. For each region of interest, we propose a new method for estimating degree of blur to separate forged blur artifact and normal blur artifact. In order to validate the identified forged blur artifact, we explore Fourier and Gabor texture features to study the structure of the forged blur artifact which eliminates false blur forged blur artifact. To evaluate the proposed forged blurred region detection method, we use two standard databases namely, Image data manipulation, and MICC-F220 for experimentation. Experimental results of the proposed method with existing methods show that the proposed method outperforms the existing methods in terms of forged blur artifact region detection.

Abstract 2595: Texture variation on a mammogram and risk of breast cancer

Abstract Mammographic density is one of the strongest risk factors for breast cancer. The most widely used measure of mammographic density is based on the percentage of dense tissue on a mammogram (percent mammographic density). However, there is additional information in mammographic images not captured by current mammographic density measurements including heterogeneity in patterns of breast density, often referred to as ‘texture’. More recent research suggests that textural features on a mammogram are associated with breast cancer risk independent of percent mammographic density. Therefore, we evaluated an automated measure called V, which measures the grayscale variation within a mammogram, in relation to subsequent breast cancer risk in 834 breast cancer cases (426 premenopausal and 408 postmenopausal) and 1805 controls (978 premenopausal and 827 postmenopausal) from a nested case-control study of breast cancer in the Nurses’ Health Studies (NHS). Among all women, V was modestly correlated with percent mammographic density (r = 0.48, p<0.01); this correlation did not vary substantially by menopausal status. Among premenopausal women, those in the highest quartile of V had a significantly higher risk of breast cancer (OR = 1.84, 95%CI: 1.30-2.61) compared to those in the lowest quartile. This association was similar, though more modest, among postmenopausal women (OR = 1.54, 95%CI: 1.08-2.19). These associations somewhat attenuated after adjustment for percent mammographic density in both premenopausal women (OR comparing extreme quartiles = 1.41, 95%CI: 0.97-2.03) and in postmenopausal women (OR comparing extreme quartiles = 1.21, 95%CI: 0.81-1.81). Future work will examine the associations between V and risk of breast cancer subtypes (e.g., by ER/PR tumor expression) as well as examine the associations between other measures of texture including markovian, run-length, laws, wavelet, fourier, and power features with breast cancer risk. Citation Format: Megan Rice, Kimberly Bertrand, John Heine, Bernard Rosner, Rulla Tamimi. Texture variation on a mammogram and risk of breast cancer. [abstract]. In: Proceedings of the 107th Annual Meeting of the American Association for Cancer Research; 2016 Apr 16-20; New Orleans, LA. Philadelphia (PA): AACR; Cancer Res 2016;76(14 Suppl):Abstract nr 2595.

Hybrid method for estimating wind loads on ships based on elliptic Fourier analysis and radial basis neural networks

Wind loads on ships and marine objects are complicated phenomena because of the complex configuration of the above-water part of the structure. The estimation of wind loads on ships and other marine objects represents a challenge because of its implications for various analyses related to ship stability, ship speed estimation, maneuvering, station keeping, and berthing. This paper presents a new approach to wind load estimation on ships and other marine objects. The method is based on elliptic Fourier features of a closed contour which are used for ship frontal and lateral closed contour representation. Therefore, this approach takes into account all aspects of the variability of the above-water frontal and lateral ship profile. For the purpose of multivariate nonlinear regression, the radial basis neural network is trained by elliptic Fourier features of closed contours and wind load data derived from wind tunnel tests for three groups of ships: offshore supply vessels, car carriers and container ships. The trained neural network is used for the estimation of non-dimensional wind load coefficients. The results are compared with experimental data.

Online Bimanual Manipulation Using Surface Electromyography and Incremental Learning.

The paradigm of simultaneous and proportional myocontrol of hand prostheses is gaining momentum in the rehabilitation robotics community. As opposed to the traditional surface electromyography classification schema, in simultaneous and proportional control the desired force/torque at each degree of freedom of the hand/wrist is predicted in real-time, giving to the individual a more natural experience, reducing the cognitive effort and improving his dexterity in daily-life activities. In this study we apply such an approach in a realistic manipulation scenario, using 10 non-linear incremental regression machines to predict the desired torques for each motor of two robotic hands. The prediction is enforced using two sets of surface electromyography electrodes and an incremental, non-linear machine learning technique called Incremental Ridge Regression with Random Fourier Features. Nine able-bodied subjects were engaged in a functional test with the aim to evaluate the performance of the system. The robotic hands were mounted on two hand/wrist orthopedic splints worn by healthy subjects and controlled online. An average completion rate of more than 95% was achieved in single-handed tasks and 84% in bimanual tasks. On average, 5 min of retraining were necessary on a total session duration of about 1 h and 40 min. This work sets a beginning in the study of bimanual manipulation with prostheses and will be carried on through experiments in unilateral and bilateral upper limb amputees thus increasing its scientific value.

Feature Construction and Calibration for Clustering Daily Load Curves from Smart-Meter Data

This paper proposes and compares feature construction and calibration methods for clustering daily electricity load curves. Such load curves describe electricity demand over a period of time. A rich body of the literature has studied clustering of load curves, usually using temporal features. This limits the potential to discover new knowledge, which may not be best represented as models consisting of all time points on load curves. This paper presents three new methods to construct features: 1) conditional filters on time-resolution-based features; 2) calibration and normalization; and 3) using profile errors. These new features extend the potential of clustering load curves. Moreover, smart metering is now generating high-resolution time series, and so the dimensionality reduction offered by these features is welcome. The clustering results using the proposed new features are compared with clusterings obtained from temporal features, as well as clusterings with Fourier features, using household electricity consumption time series as test data. The experimental results suggest that the proposed feature construction methods offer new means for gaining insight in energy-consumption patterns.

On the influence of interpolation method on rotation invariance in texture recognition

In this paper, rotation invariance and the influence of rotation interpolation methods on texture recognition using several local binary patterns (LBP) variants are investigated. We show that the choice of interpolation method when rotating textures greatly influences the recognition capability. Lanczos 3 and B-spline interpolation are comparable to rotating the textures prior to image acquisition, whereas the recognition capability is significantly and increasingly lower for the frequently used third order cubic, linear and nearest neighbour interpolation. We also show that including generated rotations of the texture samples in the training data improves the classification accuracies. For many of the descriptors, this strategy compensates for the shortcomings of the poorer interpolation methods to such a degree that the choice of interpolation method only has a minor impact. To enable an appropriate and fair comparison, a new texture dataset is introduced which contains hardware and interpolated rotations of 25 texture classes. Two new LBP variants are also presented, combining the advantages of local ternary patterns and Fourier features for rotation invariance.

Periodicity analysis of galactic cosmic rays using Fourier, Hilbert, and higher-order spectral methods

Galactic cosmic rays (GCRs) that traverse the heliosphere, in the energy range from several 100 MeV to a few GeV, are subjected to heliospheric modulation. GCRs interact with varying fields of the heliosphere to produce fluctuations in cosmic-ray intensity with variations in solar activity. The effects of modulation are continuously measured by the well-established world-wide neutron monitor network. Solar activity indices and cosmic-ray neutron monitor rates (at different cut-off rigidities) have been used to compare Fourier, Hilbert, and higher-order spectral (bispectral) features of GCR intensity variations at six stations for a period of nearly 50 years. The present study reveals that GCRs exhibit a number of short- and long-term periodicities that vary between 9 days and 22 years. The bispectral analysis shows the characteristic features of nonlinear coupling and complex phase relationships between various harmonics present in GCRs and solar activity proxies. We also offer possible explanations for the observed periodicities with the help of the previous findings.

Quasi-Monte Carlo feature maps for shift-invariant kernels

We consider the problem of improving the efficiency of randomized Fourier feature maps to accelerate training and testing speed of kernel methods on large data sets. These approximate feature maps ...

Hardwood species classification with DWT based hybrid texture feature extraction techniques

In this work, discrete wavelet transform (DWT) based hybrid texture feature extraction techniques have been used to categorize the microscopic images of hardwood species into 75 different classes. Initially, the DWT has been employed to decompose the image up to 7 levels using Daubechies (db3) wavelet as decomposition filter. Further, first-order statistics (FOS) and four variants of local binary pattern (LBP) descriptors are used to acquire distinct features of these images at various levels. The linear support vector machine (SVM), radial basis function (RBF) kernel SVM and random forest classifiers have been employed for classification. The classification accuracy obtained with state-of-the-art and DWT based hybrid texture features using various classifiers are compared. The DWT based FOS-uniform local binary pattern (DWTFOSLBPu2) texture features at the 4th level of image decomposition have produced best classification accuracy of 97.67 ± 0.79% and 98.40 ± 064% for grayscale and RGB images, respectively, using linear SVM classifier. Reduction in feature dataset by minimal redundancy maximal relevance (mRMR) feature selection method is achieved and the best classification accuracy of 99.00 ± 0.79% and 99.20 ± 0.42% have been obtained for DWT based FOS-LBP histogram Fourier features (DWTFOSLBP-HF) technique at the 5th and 6th levels of image decomposition for grayscale and RGB images, respectively, using linear SVM classifier. The DWTFOSLBP-HF features selected with mRMR method has also established superiority amongst the DWT based hybrid texture feature extraction techniques for randomly divided database into different proportions of training and test datasets.

Computerized measurement of melanocytic tumor depth in skin histopathological images

Measuring the tumor depth of invasion in skin tissue is of great importance for decision making in treatment of melanoma. Traditionally, measuring the tumor depth is based on the examination of histopathological slides by pathologist under the microscope which is time consuming and prone to intra and inter observer variability. In this paper, we propose a method for computer assisted measurement of tumor depth. At first, cornified layer is segmented based on entropy of the ridges detected in the image. Then, segmentation of cells nuclei is done using color features and active contour model. Melanocytes are distinguished from lymphocytes by applying convergence index filter and Fourier feature extraction. Experimental results indicate that the method performs well in automated measurement of tumor invasion depth.

On the second order spatiochromatic structure of natural images

We provide a theoretical analysis of some empirical facts about the second order spatiochromatic structure of natural images in color. In particular, we show that two simple assumptions on the covariance matrices of color images yield eigenvectors made by the Kronecker product of Fourier features times the triad given by luminance plus color opponent channels. The first of these assumptions is second order stationarity while the second one is commutativity between color correlation matrices. The validity of these assumptions and the predicted shape of the PCA components of color images are experimentally observed on two large image databases. As a by-product of this experimental study, we also provide novel data to support an exponential decay law of the spatiochromatic covariance between pairs of pixels as a function of their spatial distance.

Dependent online kernel learning with constant number of random Fourier features.

Traditional online kernel learning analysis assumes independently identically distributed (i.i.d.) about the training sequence. Recent studies reveal that when the loss function is smooth and strongly convex, given T i.i.d. training instances, a constant sampling complexity of random Fourier features is sufficient to ensure O(logT/T) convergence rate of excess risk, which is optimal in online kernel learning up to a logT factor. However, the i.i.d. hypothesis is too strong in practice, which greatly impairs their value. In this paper, we study the sampling complexity of random Fourier features in online kernel learning under non-i.i.d. assumptions. We prove that the sampling complexity under non-i.i.d. settings is also constant, but the convergence rate of excess risk is O(logT/T+ ϕ) , where ϕ is the mixing coefficient measuring the extent of non-i.i.d. of training sequence. We conduct experiments both on artificial and real large-scale data sets to verify our theories.

Wavelet Based Modern Finger Knuckle Authentication

Biometrics is a prominent technology for accurate and safe detection of claim identity. This paper explores new biometrics trait named finger knuckle (FK) for authentication. Finger Knuckle has unique bending and makes a distinctive biometric identifier. We use middle part of back surface of finger for recognition. The system consists of proposed prototype finger knuckle capturing device, own FK images acquired from this device and Kekre Wavelet Transform based feature for matching. Finger knuckle image capturing device is modified structurally using SolidWorks13. Feature extraction is based on Kekre Wavelet Transform which gives energy coefficient as unique features for matching. Experimental tests are performed on right index and middle finger knuckle of 50 users of own FK image data base acquired from proposed device and standard Hong Kong Polytechnic University (Poly U) database. Proposed Kekre Wavelet Transform (KWT) algorithm is tested on both FK database shows improved recognition accuracy of 90% as compared to conventional wavelet based method. The experimental results shows that wavelet based fusion of local and global features shows improved recognition accuracy of 92.5%, which is more than integration of local features only. The local features namely local orientation, local phase, and phase congruency are integrated with one global feature of Fourier transform coefficient

On the Sample Complexity of Random Fourier Features for Online Learning

We study the sample complexity of random Fourier features for online kernel learning—that is, the number of random Fourier features required to achieve good generalization performance. We show that when the loss function is strongly convex and smooth, online kernel learning with random Fourier features can achieve an O (log T / T ) bound for the excess risk with only O (1/λ 2 ) random Fourier features, where T is the number of training examples and λ is the modulus of strong convexity. This is a significant improvement compared to the existing result for batch kernel learning that requires O ( T ) random Fourier features to achieve a generalization bound O (1/√T). Our empirical study verifies that online kernel learning with a limited number of random Fourier features can achieve similar generalization performance as online learning using full kernel matrix. We also present an enhanced online learning algorithm with random Fourier features that improves the classification performance by multiple passes of training examples and a partial average.

Fourier–Dedekind sums and an extension of Rademacher reciprocity

Fourier–Dedekind sums are a generalization of Dedekind sums—important number-theoretical objects that arise in many areas of mathematics, including lattice point enumeration, signature defects of manifolds, and pseudorandom number generators. A remarkable feature of Fourier–Dedekind sums is that they satisfy a reciprocity law called Rademacher reciprocity. In this paper, we study several aspects of Fourier–Dedekind sums: properties of general Fourier–Dedekind sums, extensions of the reciprocity law, average behavior of Fourier–Dedekind sums, and finally, extrema of 2-dimensional Fourier–Dedekind sums. On properties of general Fourier–Dedekind sums, we show that a general Fourier–Dedekind sum is simultaneously a convolution of simpler Fourier–Dedekind sums, and, in a precise sense, almost a linear combination of these with integer coefficients. We show that Fourier–Dedekind sums can be extended naturally to a group under convolution. We introduce “Reduced Fourier–Dedekind sums,” which encapsulate the complexity of a Fourier–Dedekind sum, describe these in terms of generating functions, and give a geometric interpretation. Next, by finding interrelations among Fourier–Dedekind sums, we extend the range on which Rademacher Reciprocity Theorem holds. We study the average behavior of Fourier–Dedekind sums, showing that the average behavior of a Fourier–Dedekind sum is described concisely by a lower-dimensional, simpler Fourier–Dedekind sum. Finally, we focus our study on 2-dimensional Fourier–Dedekind sums. We find tight upper and lower bounds on these for a fixed $$t$$ , estimates on the argmax and argmin, and bounds on the sum of their “reciprocals.”

Reformulation of the Nosé–Hoover thermostat for heat conduction simulation at nanoscale

This paper investigates the heat conduction phenomena at nanoscale by reformulating the Nose–Hoover thermostat for nonequilibrium molecular dynamics simulation. Inspired by the Nose–Hoover mechanics, the feedback temperature force caused by the temperature control is reformulated to a more general level, aiming at (1) controlling the temperature locally at several distinct spots and (2) eliminating the rigid-body translation and rotation which are unexpectedly introduced into the system due to the feedback temperature force, so that accurate trajectories of atoms can be generated and the heat conduction simulation at nanoscale can be performed successfully. Correspondingly, the definition of temperature is modified; the expression of the Hamiltonian is generalized. To demonstrate the capability and feasibility of this newly formulated algorithm, we studied heat conduction phenomenon in a beam-like finite size specimen via our in-house developed computer code. The results, temperature distributions across the specimen, are shown to reach steady state after a period of time which cannot be achieved by the original Nose–Hoover thermostat. Also, it is concluded that the heat conduction at nanoscale exhibits the same feature of Fourier’s law at macroscopic scale, namely that the heat flux is linearly proportional to the temperature gradient, if the temperature is averaged over a sufficiently large time interval and large spatial region. The thermal conductivity can thereafter be calculated based on the linear relation between the heat flux and the temperature gradient. It is found that the obtained numerical value of thermal conductivity matches the experimental result very well.