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A new fractal interpolation method called PPA (Pointed Point Algorithm) based on IFS is proposed to interpolate the self-affine signals with the expected interpolation error, solving the problem that the ordinary fractal interpolation can't get the value of any arbitrary point directly, which has not been found in the existing literatures. At the same time, a new method to calculate the vertical scaling factors is proposed based on the genetic algorithm, which works together with the PPA algorithm to get the better interpolation performance. Experiments on the theoretical data and real field seismic data show that the proposed interpolation schemes can not only get the expected point's value, but also get a great accuracy in reconstruction of the seismic profile, leading to a significant improvement over other trace interpolation methods.

In this paper, we present a supervised ensemble learning algorithm, called SCAV1, and its application to face recognition. This algorithm exploits the uncertainty space of the ensemble classifiers. Its design includes six different nearest-neighbor (NN) classifiers that are based on different and diverse image attributes: histogram, variogram, texture analysis, edges, bidimensional discrete wavelet transform and Zernike moments. In this approach each attribute, together with its corresponding type of the analysis (local or global), and the distance criterion (p-norm) induces a different individual NN classifier. The ensemble classifier SCAV1 depends on a set of parameters: the number of candidate images used by each individual method to perform the final classification and the individual weights given to each individual classifier. SCAV1 parameters are optimized/sampled using a supervised approach via the regressive particle swarm optimization algorithm (RR-PSO). The final classifier exploits the uncertainty space of SCAV1 and uses majority voting (Borda Count) as a final decision rule. We show the application of this algorithm to the ORL and PUT image databases, obtaining very high and stable accuracies (100% median accuracy and almost null interquartile range). In conclusion, exploring the uncertainty space of ensemble classifiers provides optimum results and seems to be the appropriate strategy to adopt for face recognition and other classification problems.

In this paper, we propose different ensemble learning algorithms and their application to the face recognition problem. Three types of attributes are used for image representation: statistical, spectral, and segmentation features and regional descriptors. Classification is performed by nearest neighbor using different p-norms defined in the corresponding spaces of attributes. In this approach, each attribute together with its corresponding type of the analysis (local or global) and the distance criterion (norm or cosine), define a different classifier. The classification is unsupervised since no class information is used to improve the design of the different classifiers. Three different versions of ensemble classifiers are proposed in this paper: CAV1, CAV2, and CBAG, being the main differences among them the way the image candidates that perform the consensus are selected. The main results shown in this paper are the following: 1. The statistical attributes (local histogram and percentiles) are the individual classifiers that provided the higher accuracies, followed by the spectral methods (DWT), and the regional features (texture analysis). 2. No single attribute is able to provide systematically 100% accuracy over the ORL database. 3. The accuracy and stability of the classification is increased by consensus classification (ensemble learning techniques). 4. Optimum results are obtained by reducing the number of classifiers taking into account their diversity, and by optimizing the parameters of these classifiers using a member of the Particle Swarm Optimization (PSO) family. These results are in accord with the conclusions that are presented in the literature using ensemble learning methodologies, that is, it is possible to build strong classifiers by assembling different weak (or simple) classifiers based on different and diverse image attributes. Due to these encouraging results, future research will be devoted to the use of supervised ensemble techniques in face recognition and in other important biometric problems.

Face recognition is a challenging problem in computer vision and artificial intelligence. One of the main challenges consists in establishing a low-dimensional feature representation of the images having enough discriminatory power to perform high accuracy classification. Different methods of supervised and unsupervised classification can be found in the literature, but few numerical comparisons among them have been performed on the same computing platform. In this paper, we perform this kind of comparison, revisiting the main spectral decomposition methods for face recognition. We also introduce for the first time, the use of the noncentered PCA and the 2D discrete Chebyshev transform for biometric applications. Faces are represented by their spectral features, that is, their projections onto the different spectral basis. Classification is performed using different norms and/or the cosine defined by the Euclidean scalar product in the space of spectral attributes. Although this constitutes a simple algorithm of unsupervised classification, several important conclusions arise from this analysis: (1) All the spectral methods provide approximately the same accuracy when they are used with the same energy cutoff. This is an important conclusion since many publications try to promote one specific spectral method with respect to other methods. Nevertheless, there exist small variations on the highest median accuracy rates: PCA, 2DPCA and DWT perform better in this case. Also all the covariance-free spectral decomposition techniques based on single images (DCT, DST, DCHT, DWT, DWHT, DHT) are very interesting since they provide high accuracies and are not computationally expensive compared to covariance-based techniques. (2) The use of local spectral features generally provide higher accuracies than global features for the spectral methods which use the whole training database (PCA, NPCA, 2DPCA, Fisher's LDA, ICA). For the methods based on orthogonal transformations of single images, global features calculated using the whole size of the images appear to perform better. (3) The distance criterion generally provides a higher accuracy than the cosine criterion. The use of other p-norms (p > 2) provides similar results to the Euclidean norm, nevertheless some methods perform better. (4) No spectral method can provide 100% accuracy by itself. Therefore, other kind of attributes and supervised learning algorithms are needed. These results are coherent for the ORL and FERET databases. Finally, although this comparison has been performed for the face recognition problem, it could be generalized to other biometric authentication problems.

The PSO algorithm can be physically interpreted as a stochastic damped mass-spring system: the so-called PSO continuous model. Furthermore, PSO corresponds to a particular discretization of the PSO continuous model. Based on this mechanical analogy we derived in the past a family of PSO-like versions, where the acceleration is discretized using a centered scheme and the velocity of the particles can be regressive (GPSO), progressive (CP-GPSO) or centered (CC-GPSO). Although the first and second order trajectories of these algorithms are isomorphic, CC-GPSO and CP-GPSO are very different from GPSO. In this paper we present two other PSO-like methods: PP-GPSO and RR-GPSO. These algorithms correspond respectively to progressive and regressive discretizations in acceleration and velocity. PP-PSO has the same velocity update than GPSO, but the velocities used to update the trajectories are delayed one iteration, thus, PP-PSO acts as a Jacobi system updating positions and velocities at the same time. RR-GPSO is similar to a GPSO with stochastic constriction factor. Both versions have a very different behavior from GPSO and the other family members introduced in the past: CC-PSO and CP-PSO. RR-PSO seems to have the greatest convergence rate and its good parameter sets can be calculated analytically since they are along a straight line located in the first order stability region. Conversely PP-PSO seems to be a more explorative version, although the behavior of these algorithms can be partly problem dependent. Both exhibit a very peculiar behavior, very different from other family members, and thus they can be called distant PSO relatives. RR-PSO have the greatest convergence rate of all family members for a wide range of benchmark functions with different numerical complexity in 10, 30 and 50 dimensions. These algorithms have been succesfully applied for protein secondary structure prediction and in oil and gas reservoir optimization.