Face recogniton based on the optimal combination of neural networks, eigenfaces and least squares matching methods

Report of a research project of the Fachhochschule Hannover, University of Applied Sciences and Arts, Department of Information Technologies. Automatic face recognition increases the security standards at public places and border checkpoints. The picture inside the identification documents could widely differ from the face, that is scanned under random lighting conditions and for unknown poses. The paper describes an optimal combination of three key algorithms of object recognition, that are able to perform in real time. The camera scan is processed by a recurrent neural network, by a Eigenfaces (PCA) method and by a least squares matching algorithm. Several examples demonstrate the achieved robustness and high recognition rate.

On-the-Fly Maintenance of Series-Parallel Relationships in Fork-Join Multithreaded Programs

A key capability of data-race detectors is to determine whether one thread executes logically in parallel with another or whether the threads must operate in series. This paper provides two algorithms, one serial and one parallel, to maintain series-parallel (SP) relationships "on the fly" for fork-join multithreaded programs. The serial SP-order algorithm runs in O(1) amortized time per operation. In contrast, the previously best algorithm requires a time per operation that is proportional to Tarjan’s functional inverse of Ackermann’s function. SP-order employs an order-maintenance data structure that allows us to implement a more efficient "English-Hebrew" labeling scheme than was used in earlier race detectors, which immediately yields an improved determinacy-race detector. In particular, any fork-join program running in T₁ time on a single processor can be checked on the fly for determinacy races in O(T₁) time. Corresponding improved bounds can also be obtained for more sophisticated data-race detectors, for example, those that use locks. By combining SP-order with Feng and Leiserson’s serial SP-bags algorithm, we obtain a parallel SP-maintenance algorithm, called SP-hybrid. Suppose that a fork-join program has n threads, T₁ work, and a critical-path length of T[subscript ∞]. When executed on P processors, we prove that SP-hybrid runs in O((T₁/P + PT[subscript ∞]) lg n) expected time. To understand this bound, consider that the original program obtains linear speed-up over a 1-processor execution when P = O(T₁/T[subscript ∞]). In contrast, SP-hybrid obtains linear speed-up when P = O(√T₁/T[subscript ∞]), but the work is increased by a factor of O(lg n).

Exercise sheet 1

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Exercise sheet 1 pdf

Exercises and solutions in PDF

An on-line algorithm of uncertain time delay estimation in a continuous system

In this paper, we present an on-line estimation algorithm for an uncertain time delay in a continuous system based on the observational input-output data, subject to observational noise. The first order Pade approximation is used to approximate the time delay. At each time step, the algorithm combines the well known Kalman filter algorithm and the recursive instrumental variable least squares (RIVLS) algorithm in cascade form. The instrumental variable least squares algorithm is used in order to achieve the consistency of the delay parameter estimate, since an error-in-the-variable model is involved. An illustrative example is utilized to demonstrate the efficacy of the proposed approach.

Fully complex-valued radial basis function networks for orthogonal least squares regression

We consider a fully complex-valued radial basis function (RBF) network for regression application. The locally regularised orthogonal least squares (LROLS) algorithm with the D-optimality experimental design, originally derived for constructing parsimonious real-valued RBF network models, is extended to the fully complex-valued RBF network. Like its real-valued counterpart, the proposed algorithm aims to achieve maximised model robustness and sparsity by combining two effective and complementary approaches. The LROLS algorithm alone is capable of producing a very parsimonious model with excellent generalisation performance while the D-optimality design criterion further enhances the model efficiency and robustness. By specifying an appropriate weighting for the D-optimality cost in the combined model selecting criterion, the entire model construction procedure becomes automatic. An example of identifying a complex-valued nonlinear channel is used to illustrate the regression application of the proposed fully complex-valued RBF network.

Fully complex-valued radial basis function networks: orthogonal least squares regression and classification

We consider a fully complex-valued radial basis function (RBF) network for regression and classification applications. For regression problems, the locally regularised orthogonal least squares (LROLS) algorithm aided with the D-optimality experimental design, originally derived for constructing parsimonious real-valued RBF models, is extended to the fully complex-valued RBF (CVRBF) network. Like its real-valued counterpart, the proposed algorithm aims to achieve maximised model robustness and sparsity by combining two effective and complementary approaches. The LROLS algorithm alone is capable of producing a very parsimonious model with excellent generalisation performance while the D-optimality design criterion further enhances the model efficiency and robustness. By specifying an appropriate weighting for the D-optimality cost in the combined model selecting criterion, the entire model construction procedure becomes automatic. An example of identifying a complex-valued nonlinear channel is used to illustrate the regression application of the proposed fully CVRBF network. The proposed fully CVRBF network is also applied to four-class classification problems that are typically encountered in communication systems. A complex-valued orthogonal forward selection algorithm based on the multi-class Fisher ratio of class separability measure is derived for constructing sparse CVRBF classifiers that generalise well. The effectiveness of the proposed algorithm is demonstrated using the example of nonlinear beamforming for multiple-antenna aided communication systems that employ complex-valued quadrature phase shift keying modulation scheme. (C) 2007 Elsevier B.V. All rights reserved.

System identification using partitioned least squares

A novel partitioned least squares (PLS) algorithm is presented, in which estimates from several simple system models are combined by means of a Bayesian methodology of pooling partial knowledge. The method has the added advantage that, when the simple models are of a similar structure, it lends itself directly to parallel processing procedures, thereby speeding up the entire parameter estimation process by several factors.

Nonlinear model structure design and construction using orthogonal least squares and D-optimality design

A very efficient learning algorithm for model subset selection is introduced based on a new composite cost function that simultaneously optimizes the model approximation ability and model robustness and adequacy. The derived model parameters are estimated via forward orthogonal least squares, but the model subset selection cost function includes a D-optimality design criterion that maximizes the determinant of the design matrix of the subset to ensure the model robustness, adequacy, and parsimony of the final model. The proposed approach is based on the forward orthogonal least square (OLS) algorithm, such that new D-optimality-based cost function is constructed based on the orthogonalization process to gain computational advantages and hence to maintain the inherent advantage of computational efficiency associated with the conventional forward OLS approach. Illustrative examples are included to demonstrate the effectiveness of the new approach.

Structural matching of 2D electrophoresis gels using deformed graphs

2D electrophoresis is a well-known method for protein separation which is extremely useful in the field of proteomics. Each spot in the image represents a protein accumulation and the goal is to perform a differential analysis between pairs of images to study changes in protein content. It is thus necessary to register two images by finding spot correspondences. Although it may seem a simple task, generally, the manual processing of this kind of images is very cumbersome, especially when strong variations between corresponding sets of spots are expected (e.g. strong non-linear deformations and outliers). In order to solve this problem, this paper proposes a new quadratic assignment formulation together with a correspondence estimation algorithm based on graph matching which takes into account the structural information between the detected spots. Each image is represented by a graph and the task is to find a maximum common subgraph. Successful experimental results using real data are presented, including an extensive comparative performance evaluation with ground-truth data. (C) 2010 Elsevier B.V. All rights reserved.

Least squares learning and the US Treasury bill rate

Understanding how agents formulate their expectations about Fed behavior is important for market participants because they can potentially use this information to make more accurate estimates of stock and bond prices. Although it is commonly assumed that agents learn over time, there is scant empirical evidence in support of this assumption. Thus, in this paper we test if the forecast of the three month T-bill rate in the Survey of Professional Forecasters (SPF) is consistent with least squares learning when there are discrete shifts in monetary policy. We first derive the mean, variance and autocovariances of the forecast errors from a recursive least squares learning algorithm when there are breaks in the structure of the model. We then apply the Bai and Perron (1998) test for structural change to a forecasting model for the three month T-bill rate in order to identify changes in monetary policy. Having identified the policy regimes, we then estimate the implied biases in the interest rate forecasts within each regime. We find that when the forecast errors from the SPF are corrected for the biases due to shifts in policy, the forecasts are consistent with least squares learning. © 2014 Elsevier B.V.

Corrigendum to “Least squares learning and the US treasury bill rate” [Econ. Syst. 38 (2014) 194–204]

Understanding how agents formulate their expectations about Fed behavior is important for market participants because they can potentially use this information to make more accurate estimates of stock and bond prices. Although it is commonly assumed that agents learn over time, there is scant empirical evidence in support of this assumption. Thus, in this paper we test if the forecast of the three month T-bill rate in the Survey of Professional Forecasters (SPF) is consistent with least squares learning when there are discrete shifts in monetary policy. We first derive the mean, variance and autocovariances of the forecast errors from a recursive least squares learning algorithm when there are breaks in the structure of the model. We then apply the Bai and Perron (1998) test for structural change to a forecasting model for the three month T-bill rate in order to identify changes in monetary policy. Having identified the policy regimes, we then estimate the implied biases in the interest rate forecasts within each regime. We find that when the forecast errors from the SPF are corrected for the biases due to shifts in policy, the forecasts are consistent with least squares learning.

Using the EM Algorithm to Train Neural Networks: Misconceptions and a New Algorithm for Multiclass Classification

The expectation-maximization (EM) algorithm has been of considerable interest in recent years as the basis for various algorithms in application areas of neural networks such as pattern recognition. However, there exists some misconceptions concerning its application to neural networks. In this paper, we clarify these misconceptions and consider how the EM algorithm can be adopted to train multilayer perceptron (MLP) and mixture of experts (ME) networks in applications to multiclass classification. We identify some situations where the application of the EM algorithm to train MLP networks may be of limited value and discuss some ways of handling the difficulties. For ME networks, it is reported in the literature that networks trained by the EM algorithm using iteratively reweighted least squares (IRLS) algorithm in the inner loop of the M-step, often performed poorly in multiclass classification. However, we found that the convergence of the IRLS algorithm is stable and that the log likelihood is monotonic increasing when a learning rate smaller than one is adopted. Also, we propose the use of an expectation-conditional maximization (ECM) algorithm to train ME networks. Its performance is demonstrated to be superior to the IRLS algorithm on some simulated and real data sets.

Performance analysis of adaptive lattice filters for FM signals and alpha-stable processes

The performance of an adaptive filter may be studied through the behaviour of the optimal and adaptive coefficients in a given environment. This thesis investigates the performance of finite impulse response adaptive lattice filters for two classes of input signals: (a) frequency modulated signals with polynomial phases of order p in complex Gaussian white noise (as nonstationary signals), and (b) the impulsive autoregressive processes with alpha-stable distributions (as non-Gaussian signals). Initially, an overview is given for linear prediction and adaptive filtering. The convergence and tracking properties of the stochastic gradient algorithms are discussed for stationary and nonstationary input signals. It is explained that the stochastic gradient lattice algorithm has many advantages over the least-mean square algorithm. Some of these advantages are having a modular structure, easy-guaranteed stability, less sensitivity to the eigenvalue spread of the input autocorrelation matrix, and easy quantization of filter coefficients (normally called reflection coefficients). We then characterize the performance of the stochastic gradient lattice algorithm for the frequency modulated signals through the optimal and adaptive lattice reflection coefficients. This is a difficult task due to the nonlinear dependence of the adaptive reflection coefficients on the preceding stages and the input signal. To ease the derivations, we assume that reflection coefficients of each stage are independent of the inputs to that stage. Then the optimal lattice filter is derived for the frequency modulated signals. This is performed by computing the optimal values of residual errors, reflection coefficients, and recovery errors. Next, we show the tracking behaviour of adaptive reflection coefficients for frequency modulated signals. This is carried out by computing the tracking model of these coefficients for the stochastic gradient lattice algorithm in average. The second-order convergence of the adaptive coefficients is investigated by modeling the theoretical asymptotic variance of the gradient noise at each stage. The accuracy of the analytical results is verified by computer simulations. Using the previous analytical results, we show a new property, the polynomial order reducing property of adaptive lattice filters. This property may be used to reduce the order of the polynomial phase of input frequency modulated signals. Considering two examples, we show how this property may be used in processing frequency modulated signals. In the first example, a detection procedure in carried out on a frequency modulated signal with a second-order polynomial phase in complex Gaussian white noise. We showed that using this technique a better probability of detection is obtained for the reduced-order phase signals compared to that of the traditional energy detector. Also, it is empirically shown that the distribution of the gradient noise in the first adaptive reflection coefficients approximates the Gaussian law. In the second example, the instantaneous frequency of the same observed signal is estimated. We show that by using this technique a lower mean square error is achieved for the estimated frequencies at high signal-to-noise ratios in comparison to that of the adaptive line enhancer. The performance of adaptive lattice filters is then investigated for the second type of input signals, i.e., impulsive autoregressive processes with alpha-stable distributions . The concept of alpha-stable distributions is first introduced. We discuss that the stochastic gradient algorithm which performs desirable results for finite variance input signals (like frequency modulated signals in noise) does not perform a fast convergence for infinite variance stable processes (due to using the minimum mean-square error criterion). To deal with such problems, the concept of minimum dispersion criterion, fractional lower order moments, and recently-developed algorithms for stable processes are introduced. We then study the possibility of using the lattice structure for impulsive stable processes. Accordingly, two new algorithms including the least-mean P-norm lattice algorithm and its normalized version are proposed for lattice filters based on the fractional lower order moments. Simulation results show that using the proposed algorithms, faster convergence speeds are achieved for parameters estimation of autoregressive stable processes with low to moderate degrees of impulsiveness in comparison to many other algorithms. Also, we discuss the effect of impulsiveness of stable processes on generating some misalignment between the estimated parameters and the true values. Due to the infinite variance of stable processes, the performance of the proposed algorithms is only investigated using extensive computer simulations.

The rademacher complexity of coregularized kernel classes

In the multi-view approach to semisupervised learning, we choose one predictor from each of multiple hypothesis classes, and we co-regularize our choices by penalizing disagreement among the predictors on the unlabeled data. We examine the co-regularization method used in the co-regularized least squares (CoRLS) algorithm, in which the views are reproducing kernel Hilbert spaces (RKHS's), and the disagreement penalty is the average squared difference in predictions. The final predictor is the pointwise average of the predictors from each view. We call the set of predictors that can result from this procedure the co-regularized hypothesis class. Our main result is a tight bound on the Rademacher complexity of the co-regularized hypothesis class in terms of the kernel matrices of each RKHS. We find that the co-regularization reduces the Rademacher complexity by an amount that depends on the distance between the two views, as measured by a data dependent metric. We then use standard techniques to bound the gap between training error and test error for the CoRLS algorithm. Experimentally, we find that the amount of reduction in complexity introduced by co regularization correlates with the amount of improvement that co-regularization gives in the CoRLS algorithm.