A. Krzyzak

A. Krzyzak
Concordia University Montreal · Department of Computer Science and Software Engineering

About

240
Publications
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7,494
Citations

Publications

Publications (240)
Article
Recognizing faces under various lighting conditions is a challenging problem in artificial intelligence and applications. In this paper we describe a new face recognition algorithm which is invariant to illumination. We first convert image files to the logarithm domain and then we implement them using the dual-tree complex wavelet transform (DTCWT)...
Article
Image classifiers based on convolutional neural networks are defined, and the rate of convergence of the misclassification risk of the estimates towards the optimal misclassification risk is analyzed. Under suitable assumptions on the smoothness and structure of a posteriori probability, the rate of convergence is shown which is independent of the...
Article
Full-text available
Hyperspectral face recognition plays an important role in remote sensing. However, it faces many challenges such as difficulty in data acquisition, low signal to noise ratio (SNR), and high dimensionality. In this paper, we develop a novel method for hyperspectral face recognition by extracting histogram of oriented features (HOG) and using collabo...
Chapter
Face recognition under varying illumination is a difficult problem in many real-life applications. Various methods have been developed in the literature to deal with this problem. In this paper, we propose a new method for face recognition under varying lighting conditions. Our method calculates the difference of pixel intensity values along a dire...
Article
Recently it was shown in several papers that backpropagation is able to find the global minimum of the empirical risk on the training data using over-parametrized deep neural networks. In this paper, a similar result is shown for deep neural networks with the sigmoidal squasher activation function in a regression setting, and a lower bound is prese...
Article
This paper introduces a new topic and research of geometric classifier ensemble learning using two types of objects: classifier prediction pairwise matrix (CPPM) and decision profiles (DPs). Learning from CPPM requires using Riemannian manifolds (R-manifolds) of symmetric positive definite (SPD) matrices. DPs can be used to build a Grassmann manifo...
Article
In this paper, we revisit the effects of principal component analysis (PCA) on hyperspectral imagery denoising. Our previous work combined PCA with wavelet shrinkage and particularly good denoising results has been achieved. We debate that any denoising methods can be used to replace wavelet shrinkage in our PCA+wavelet shrinkage algorithm. The maj...
Article
Measuring image visual quality is extremely important for many image processing tasks. In the past, several metrics have been proposed for measuring image visual quality such as structural similarity index (SSIM) and visual information fidelity (VIF). Nevertheless, these metrics are not robust to image spatial shifts when the reference and distorte...
Article
In this article we consider asymptotic properties of the normalized radial basis function networks with one hidden layer trained by independent patterns with arbitrary distributions. Convergence and rates of convergence are investigated and the choice of the radial basis functions and the network parameters are discussed.
Preprint
A regression problem with dependent data is considered. Regularity assumptions on the dependency of the data are introduced, and it is shown that under suitable structural assumptions on the regression function a deep recurrent neural network estimate is able to circumvent the curse of dimensionality.
Chapter
In this paper, we briefly present classifier ensembles making use of nonlinear manifolds. Riemannian manifolds have been created using classifier interactions which are presented as symmetric and positive-definite (SPD) matrices. Grassmann manifolds as some particular case of Riemannian manifolds are constructed using decision profiles. Experimenta...
Chapter
Increasingly, politicians and political parties are engaging their electors using social media. In the US Federal Election of 2016, candidates from both parties made heavy use of social media, particularly Twitter. It is then reasonable to attempt to find a correlation between popularity on Twitter, and eventual popular vote in the election. In thi...
Chapter
In this paper we address the problem of medical data scarcity by considering the task of detection of pulmonary diseases from chest X-Ray images using small volume datasets with less than thousand samples. We implemented three deep convolutional neural networks (VGG16, ResNet-50, and InceptionV3) pre-trained on the ImageNet dataset and assesed them...
Chapter
In computer vision, one of the common practices to augment the image dataset is by creating new images using geometric transformation preserving similarity. This data augmentation was one of the most significant factors for winning the Image Net competition in 2012 with vast neural networks. Unlike in computer vision and speech data, there have not...
Preprint
Image classifiers based on convolutional neural networks are defined, and the rate of convergence of the misclassification risk of the estimates towards the optimal misclassification risk is analyzed. Under suitable assumptions on the smoothness and structure of the aposteriori probability a rate of convergence is shown which is independent of the...
Chapter
In this paper we introduce the supervised classification algorithm called Box algorithm based on feature space partitioning. The construction of Box algorithm is closely linked to the solution of computational geometry problem involving heuristic maximal clique cover problem satisfying the k-nearest neighbor rule. We first apply a heuristic algorit...
Chapter
In this study, we focus on the problem of computer-aided diagnosis of breast cancer using cytological images of fine needle biopsies. We explore the potential of modern deep neural network architectures by comparing five different convolutional neural networks trained to classify the specimen as either benign or malignant. For experimentation, we u...
Preprint
Recently it was shown in several papers that backpropagation is able to find the global minimum of the empirical risk on the training data using over-parametrized deep neural networks. In this paper a similar result is shown for deep neural networks with the sigmoidal squasher activation function in a regression setting, and a lower bound is presen...
Preprint
Recent results in nonparametric regression show that for deep learning, i.e., for neural network estimates with many hidden layers, we are able to achieve good rates of convergence even in case of high-dimensional predictor variables, provided suitable assumptions on the structure of the regression function are imposed. The estimates are defined by...
Preprint
Full-text available
Deep neural networks (DNNs) achieve impressive results for complicated tasks like object detection on images and speech recognition. Motivated by this practical success, there is now a strong interest in showing good theoretical properties of DNNs. To describe for which tasks DNNs perform well and when they fail, it is a key challenge to understand...
Article
In the paper we consider the supervised classification problem using space partitioning into multidimensional rectangular boxes. We show that the problem at hand can be reduced to computational geometry problem involving heuristic minimum clique cover problem satisfying the k-nearest neighbor rule. We first apply heuristic algorithm for partitionin...
Chapter
In the paper we study convergence of the RBF networks with so-called regular radial kernels. The parameters of the network are learned by the empirical risk minimization. Mean square convergence of \(L_2\) error is investigated using the machine learning tools such as VC dimension and covering numbers. RBF network estimates are applied in nonlinear...
Article
Full-text available
In this article, we develop a new algorithm for illumination invariant face recognition. We first transform the face images to the logarithm domain, which makes the dark regions brighter. We then use dual-tree complex wavelet transform to generate face images that are approximately invariant to illumination changes and use collaborative representat...
Article
A simulation model with an outcome (Y = m(X) is considered, where X is an Rd-valued random variable and Rd→R is a smooth function. Estimates of the αn-quantile qm(X),αn of m(X) based on surrogate model of m and on importance sampling are constructed which use at most n evaluations of the function m. Results concerning the rate of convergence of the...
Article
Uncertainty quantification of a technical system can be done using density estimation. The starting point there is usually a stochastic model, which is fitted to the technical system, and the density estimation is done using data from this stochastic model. However, in any application such a stochastic model will not be perfect, and estimation of t...
Conference Paper
Full-text available
Tablicedecyzyjneposiadajączteryczęści,któremożnaopisaćfunkcjamilogicznymi boolowskimi lub wielowartościowymi: zbiór warunków (nazwy atrybutów), zbiór wskaźników warunków(realizowalne kombinacje wartości atrybutów napisane kolumnowo jako reguły decyzji), zbiory czynności (nazwy czynności), zbiór wskaźników czynności (dowolne kombinacje czynności jed...
Article
In this article, we consider the problem of estimating quantiles related to the outcome of experiments with a technical system given the distribution of the input together with an (imperfect) simulation model of the technical system and (few) data points from the technical system. The distribution of the outcome of the technical system is estimated...
Article
In this study, the authors develop a new algorithm for face recognition with varying lighting conditions. Their method first performs low-pass and high-pass filtering to the face image, and then takes the ratio between the two filtered images. The authors take the arctangent to the ratio and use these features to classify an unknown face image. In...
Article
The starting point in uncertainty quantification is a stochastic model, which is fitted to a technical system in a suitable way, and prediction of uncertainty is carried out within this stochastic model. In any application, such a model will not be perfect, so any uncertainty quantification from such a model has to take into account the inadequacy...
Conference Paper
Full-text available
A prime factor deciding the survival rate of a breast cancer patient is the accuracy with which the malignancy grade of a breast tumor is determined. A Fine Needle Aspiration (FNA) biopsy is a key mechanism for breast cancer diagnosis as well as for assigning grades to malignant cases. In this paper, based on published cytological malignancy gradin...
Conference Paper
Full-text available
Wybrane zagadnienia analizy dokładności logicznych wielowartościowych drzew decyzyjnych z uwzględnieniem zmiennych warunkowych Tradycyjne boolowskie drzewa logiczne mają zastosowanie do strukturalnych procesów decyzyjnych ze względu na występowanie ciągłych ścieżek. Jednak po minimalizacji ana-litycznej powstają niekorzystne gałązki izolowane. Sytu...
Article
Nonparametric estimation of a quantile of a random variable m(X) is considered, where \(m: \mathbb {R}^d\rightarrow \mathbb {R}\) is a function which is costly to compute and X is a \(\mathbb {R}^d\)-valued random variable with a given density. An importance sampling quantile estimate of m(X), which is based on a suitable estimate \(m_n\) of m, is...
Article
Epilepsy is a common neurological disorder that is difficult to treat. Monitoring brain activity using electroencephalography (EEG) has become an important tool for the diagnosis of epilepsy. In this paper, we propose a method for EEG seizure detection by decomposing EEG signals for up to six wavelet scales without downsampling. Then, we perform th...
Article
A scheme to form a basis and a frame for a Hilbert space of quaternion valued square integrable function from a basis and a frame, respectively, of a Hilbert space of complex valued square integrable functions is introduced. Using the discretization techniques for 2D-continuous wavelet transform of the SIM (2) group, the quaternionic continuous wav...
Article
In this paper, we introduce the so-called hierarchical interaction models, where we assume that the computation of the value of a function m : ℝ <sup xmlns:xlink="http://www.w3.org/1999/xlink">d</sup> → ℝ is done in several layers, where in each layer a function of at most d* inputs computed by the previous layer is evaluated. We investigate two di...
Article
Full-text available
In this paper a nonparametric latent variable model is estimated without specifying the underlying distributions. The main idea is to estimate in a first step a common factor analysis model under the assumption that each manifest variable is influenced by at most one of the latent variables. In a second step nonparametric regression is used to anal...
Article
Nonparametric estimation of a quantile q <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m(X),α</sub> of a random variable m(X) is considered, where m : ℝ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sup> → ℝ is a function, which is costly to compute...
Conference Paper
Support vector machine (SVM) is one of the most popular classification techniques in pattern recognition community. However, because of outliers in the training samples, SVM tends to perform poorly under such circumstances. In this paper, we borrow the idea from compressive sensing by introducing an extra term to the objective function of the stand...
Article
In this paper, we study the problem of density estimation from data that contains small measurement errors. The only assumption on these errors is that the maximal measurement error is bounded by some real number converging to zero for sample size tending to infinity. In particular, we do not assume that the measurement errors are independent with...
Conference Paper
Features that are widely used in digital image analysis and pattern recognition tasks are from three main categories: shape, intensity, and texture invariant features. For computer-aided diagnosis in medical imaging for many specific types of medical problem, the most effective choice of a subset of these features through feature selection is still...
Conference Paper
In this paper we address a problem arising from the classification of breast cancer malignancy data. Due to the fact that there is much smaller number of patients which are diagnosed with high malignancy, data sets are prone to have a high imbalance between malignancy classes. To overcome this problem we have applied state-of-the-art methods for im...
Article
The effectiveness of the treatment of breast cancer depends on its timely detection. An early step in the diagnosis is the cytological examination of breast material obtained directly from the tumor. This work reports on advances in computeraided breast cancer diagnosis based on the analysis of cytological images of fine needle biopsies to characte...
Conference Paper
In the past two decades, Support Vector Machine (SVM) has become one of the most famous classification techniques. The optimal parameters in an SVM kernel are normally obtained by cross validation, which is a time-consuming process. In this paper, we propose to learn the parameters in an SVM kernel while solving the dual optimization problem. The n...
Conference Paper
In this paper, an invariant algorithm for object recognition is proposed by using the Radon and Fourier transforms. It has been shown that this algorithm is invariant to the translation and rotation of pattern images. The scaling invariance can be achieved by the standard normalization techniques. Our algorithm works even when the center of the pat...
Conference Paper
Support Vector Machine (SVM) is one of the most famous classification techniques in the pattern recognition community. However, due to outliers in the training samples, the SVM tend to be over-trained. This means that the generalization ability of the SVM will decrease for further training. In this paper, we borrow the idea of compressive sensing/s...
Conference Paper
This paper presents a novel short-time frequency analysis algorithm, namely Instantaneous Harmonic Analysis (IHA), which can be used in Multiple Fundamental Frequency Estimation. Given a set of reference pitches, the objective of the algorithm is to transform the real-valued time-domain audio signal into a set of complex time-domain signals in such...
Article
In this paper, we propose a novel method for the classification of small bowel images into normal or abnormal class for automatic detection of cancers. We extract the Fourier features from the input small bowel image, and then the Zernike moment features are computed from the Fourier features. We then use the canonical discriminant analysis (CDA) t...
Conference Paper
We consider a flexible joint two-link flexible joint space manipulator. Manipulator dynamics is derived from Euler-Lagrange formulation. The joint dynamics includes non-linear stiffness and friction components. A simplified model of the manipulator is represented by a Hammerstein model consisting of a memoryless nonlinearity followed by a dynamic,...
Conference Paper
Full-text available
Reducing noise in a video sequence is of vital importance in many applications. Despite the fact that many good video denoising methods were proposed in recent years, there is still a need to further improve the existing video denoising methods. Video block matching 3-D filtering (VBM3D), which was developed by Dabov et al. in 2007, is one of the r...
Article
Full-text available
We design a data-dependent metric in $\mathbb R^d$ and use it to define the $k$-nearest neighbors of a given point. Our metric is invariant under all affine transformations. We show that, with this metric, the standard $k$-nearest neighbor regression estimate is asymptotically consistent under the usual conditions on $k$, and minimal requirements o...
Conference Paper
Full-text available
The research presented in this paper ultimately aims at accurate Unmanned Aerial Vehicle (UAV) navigation using camera(s) to augment inertial navigation unit data while flying through an urban environment. Accurate position and depth determination requires precise image feature location and matching. This paper investigates accurate feature matchin...
Article
We consider nonlinear function estimation using Radial Basis Function Networks. We analytically determine the optimal radial kernel minimizing the Mean Integrated Square Error (MISE) and the optimal MISE rate of convergence. The rates of convergence for various classes of nonlinear functions and input densities are also considered.
Article
Given an independent and identically distributed sample of the distribution of an -valued random vector (X,Y), the problem of estimation of the essential supremum of the corresponding regression function is considered. Estimates are constructed, which converge almost surely to this value whenever the dependent variable Y satisfies some weak integra...
Article
The denoising of a natural signal/image corrupted by Gaussian white noise is a classical problem in signal/image processing. However, it is still in its infancy to denoise high dimensional data. In this paper, we extended Sendur and Selesnick's bivariate wavelet thresholding from two-dimensional (2D) image denoising to three-dimensional (3D) data c...
Conference Paper
Full-text available
This work focuses on the segmentation and counting of peripheral blood smear particles which plays a vital role in medical diagnosis. Our approach profits from some powerful processing techniques. Firstly, the method used for denoising a blood smear image is based on the Bivariate wavelet. Secondly, image edge preservation uses the Kuwahara filter....
Conference Paper
This research was motivated by a need for accurate UAV navigation using camera(s) to augment inertial navigation unit data while flying over, or through an urban environment. The process of position determination using cameras follows a sequence of well defined steps. First features must be found in consecutive-in-time images and then matched acros...
Conference Paper
The denoising of a natural signal/image corrupted by Gaussian white noise is a classical problem in signal/image processing. However, it is still in its infancy to denoise high dimensional data. In this paper, we extended Sendur and Selesnick’s bivariate wavelet thresholding from two-dimensional image denoising to three dimensional data denoising....
Conference Paper
Full-text available
We consider pattern recognition problem when classes and their labels are linearly structured (or ordered). We propose the loss function based on the squared differences between the true and the predicted class labels. The optimal Bayes classifier is derived and then estimated by the recursive kernel estimator. Its consistency is established theor...
Conference Paper
We consider American options also called Bermudan options in discrete time.We use the dual approach to derive upper bounds on the price of such options using only a reduced number of nested Monte Carlo steps. The key idea is to use nonparametric regression to estimate continuation values and all other required conditional expectations and to combin...
Article
Full-text available
Breast Cancer is one of the most deadly cancers affecting middle-aged women. Accurate diagnosis and prognosis are crucial to reduce the high death rate. Nowadays there are numerous diagnostic tools for breast cancer diagnosis. In this paper we discuss a role of nuclear segmentation from fine needle aspiration biopsy (FNA) slides and its influence o...
Conference Paper
A new courtesy amount recognition module of CENPARMIpsilas check reading system (CRS) is proposed in this paper. The module consists of 3 main segments: pre-processing, segmentation and recognition, and post-processing. A new feedback-based segmentation algorithm is adopted for the segmentation task. Besides one individual numeral recognizer for nu...
Conference Paper
When linear support vector machines (SVMs) are applied to multi-class text categorization in industry, the size of the linear SVM model is very large, usually greater than several gigabytes. As a result, the model cannot directly fit into the computer memory and the classification process is slow. In this paper, a novel method based on vector norm...
Article
An invariant pattern recognition descriptor is proposed in this paper by using the radon transform, the dual-tree complex wavelet transform and the Fourier transform. The radon transform can capture the directional features of the pattern image by projecting the pattern onto different orientation slices. The dual-tree complex wavelet transform can...
Article
This paper presents a multimodal approach for a biometrics verification system. It is based on face and hand images captured by a cell phone. The algorithm includes all parts that are required for face and hand verification, such as feature extraction, classification and authentication. To find local facial features, such as eyes, mouth and nose, w...
Article
Full-text available
Classification of Breast Cancer Malignancy Using Cytological Images of Fine Needle Aspiration Biopsies According to the World Health Organization (WHO), breast cancer (BC) is one of the most deadly cancers diagnosed among middle-aged women. Precise diagnosis and prognosis are crucial to reduce the high death rate. In this paper we present a framewo...
Article
The paper presents a local learning framework for pattern classification by partitioning a pattern space into different overlapped subsets and combining deci-sions in a local space. In contrast to designing a clas-sifier on the global space, the advantage of the local learning framework is to reduce the complexity of com-ponent classifier which hel...
Article
We discuss rates of convergence of plug-in kernel, partitioning and nearest neighbors classification rules under margin condition. Margin condition characterizes the rate with which a posteriori probabilities cross the decision boundary. We show the rates of convergence of the plug-in classifiers under smoothness conditions on a posteriori probabil...
Conference Paper
Face recognition has rapidly evolved and has become very popular in recent years. It is being intensively researched and found many applications, primarily in biometric security systems. One of the main challenges in face recognition is to identify different features playing fundamental role in face description. The role of color, which appears to...
Conference Paper
Unlike the frontal face detection, multi-pose face detection and recognition techniques, still face the following challenges: large variability of environments such as pose, illumination and backgrounds and unconstrained capturing of facial images. We introduced a new system to deal with this problem. First, the two-step color-based approach is use...
Article
A computer aided root lesion detection method for digital dental X-rays is proposed using level set and complex wavelets. The detection method consists of two stages: preprocessing and root lesion detection. During preprocessing, a level set segmentation is applied to separate the teeth from the background. Tailored for the dental clinical environm...
Article
Let (X,Y) be a -valued random vector where the conditional distribution of Y given X=x is a Poisson distribution with mean m(x). We estimate m by a local polynomial kernel estimate defined by maximizing a localized log-likelihood function. We use this estimate of m(x) to estimate the conditional distribution of Y given X=x by a corresponding Poisso...