Fisher discriminant model based on LASSO logistic regression for computed tomography imaging diagnosis of pelvic rhabdomyosarcoma in children

Computed tomography (CT) has been widely used for the diagnosis of pelvic rhabdomyosarcoma (RMS) in children. However, it is difficult to differentiate pelvic RMS from other pelvic malignancies. This study aimed to analyze and select CT features by using least absolute shrinkage and selection operator (LASSO) logistic regression and established a Fisher discriminant analysis (FDA) model for the quantitative diagnosis of pediatric pelvic RMS. A total of 121 pediatric patients who were diagnosed with pelvic neoplasms were included in this study. The patients were assigned to an RMS group (n = 36) and a non-RMS group (n = 85) according to the pathological results. LASSO logistic regression was used to select characteristic features, and an FDA model was constructed for quantitative diagnosis. Leave-one-out cross-validation and receiver operating characteristic (ROC) curve analysis were used to evaluate the diagnostic ability of the FDA model. Six characteristic variables were selected by LASSO logistic regression, all of which were CT morphological features. Using these CT features, the following diagnostic models were established: (RMS group)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${G}_{1}=-14.283+6.613{x}_{1}+5.333{x}_{2}+5.753{x}_{3}+12.361{x}_{4}+8.095{x}_{5}-0.715{x}_{6}$$\end{document}G1=-14.283+6.613x1+5.333x2+5.753x3+12.361x4+8.095x5-0.715x6; (Non-RMS group)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${G}_{2}=-2.008+3.539{x}_{1}+1.080{x}_{2}+1.154{x}_{3}+2.307{x}_{4}+1.656{x}_{5}+1.380{x}_{6}$$\end{document}G2=-2.008+3.539x1+1.080x2+1.154x3+2.307x4+1.656x5+1.380x6, where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${x}_{1}$$\end{document}x1, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${x}_{2}$$\end{document}x2, … and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${x}_{6}$$\end{document}x6 are lower than normal muscle density (1 = yes; 0 = no), multinodular fusion (1 = yes; 0 = no), enhancement at surrounding blood vessels (1 = yes; 0 = no), heterogeneous progressive centripetal enhancement (1 = yes; 0 = no), ring enhancement (1 = yes; 0 = no), and hemorrhage (1 = yes; 0 = no), respectively. The calculated area under the ROC curve (AUC) of the model was 0.992 (0.982–1.000), with a sensitivity of 94.4%, a specificity of 96.5%, and an accuracy of 95.9%. The calculated sensitivity, specificity and accuracy values were consistent with those from cross-validation. An FDA model based on the CT morphological features of pelvic RMS was established and could provide an easy and efficient method for the diagnosis and differential diagnosis of pelvic RMS in children.

Implementing Kernel Methods Incrementally by Incremental Nonlinear Projection Trick

Recently, the nonlinear projection trick (NPT) was introduced enabling direct computation of coordinates of samples in a reproducing kernel Hilbert space. With NPT, any machine learning algorithm can be extended to a kernel version without relying on the so called kernel trick. However, NPT is inherently difficult to be implemented incrementally because an ever increasing kernel matrix should be treated as additional training samples are introduced. In this paper, an incremental version of the NPT (INPT) is proposed based on the observation that the centerization step in NPT is unnecessary. Because the proposed INPT does not change the coordinates of the old data, the coordinates obtained by INPT can directly be used in any incremental methods to implement a kernel version of the incremental methods. The effectiveness of the INPT is shown by applying it to implement incremental versions of kernel methods such as, kernel singular value decomposition, kernel principal component analysis, and kernel discriminant analysis which are utilized for problems of kernel matrix reconstruction, letter classification, and face image retrieval, respectively.

Correlation dimension-based classifier

Correlation dimension (CD), singularity exponents, also called scaling exponents, are widely used in multifractal chaotic series analysis. CD and other measures of effective dimensionality are used for characterization of data in applications. A direct use of CD to multidimensional data classification has not been hitherto presented. There are observations that the correlation integral is a distribution function of distances between all pairs of data points, and that by using polynomial expansion of distance with exponent equal to the CD this distribution is transformed into locally uniform. The classifier is based on consideration that the influence of neighbor points of some class on the probability that the query point belongs to this class is inversely proportional to its distance to the CD, power. New classification approach is based on summing up all these influences for each class. We prove that a resulting formula gives an estimate of probability of the class, not a measure of membership to a class only, to which the query point belongs. For this assertion to be valid, it is necessary that exponent of the polynomial transformation must be the CD. We also propose an averaging approach that speeds up computation of the CD especially for large data sets. It is demonstrated that the CD-based classifier can outperform more sophisticated classifiers.

Kernel Density Estimation, Kernel Methods, and Fast Learning in Large Data Sets

Kernel methods such as the standard support vector machine and support vector regression trainings take O(N(3)) time and O(N(2)) space complexities in their naïve implementations, where N is the training set size. It is thus computationally infeasible in applying them to large data sets, and a replacement of the naive method for finding the quadratic programming (QP) solutions is highly desirable. By observing that many kernel methods can be linked up with kernel density estimate (KDE) which can be efficiently implemented by some approximation techniques, a new learning method called fast KDE (FastKDE) is proposed to scale up kernel methods. It is based on establishing a connection between KDE and the QP problems formulated for kernel methods using an entropy-based integrated-squared-error criterion. As a result, FastKDE approximation methods can be applied to solve these QP problems. In this paper, the latest advance in fast data reduction via KDE is exploited. With just a simple sampling strategy, the resulted FastKDE method can be used to scale up various kernel methods with a theoretical guarantee that their performance does not degrade a lot. It has a time complexity of O(m(3)) where m is the number of the data points sampled from the training set. Experiments on different benchmarking data sets demonstrate that the proposed method has comparable performance with the state-of-art method and it is effective for a wide range of kernel methods to achieve fast learning in large data sets.

Voting among virtually generated versions of a classification problem

A classifier combining strategy, virtual voting by random projection (VVRP), is presented. VVRP takes advantage from the bounded distortion incurred by random projection in order to improve accuracies of stable classifiers like discriminant analysis (DA) where existing classifier combining strategies are known to be failed. It uses the distortion to virtually generate different training sets from the total available training samples in a way that does not have the potential for overfitting. Then, a majority voting combines the base learners trained on these versions of the original problem. VVRP is very simple and just needs determining a proper dimensionality for the versions, an often very easy task. It is shown to be stable in a very large region of the hyperplane constructed by the dimensionality and the number of the versions. VVRP improves the best state-of-the-art DA algorithms in both small and large sample size problems in various classification fields.

AN ENHANCED LIPSCHITZ EMBEDDING CLASSIFIER FOR MULTI-EMOTION SPEECH ANALYSIS

This paper proposes an Enhanced Lipschitz Embedding based Classifier (ELEC) for the classification of multi-emotions from speech signals. ELEC adopts geodesic distance to preserve the intrinsic geometry at all scales of speech corpus, instead of Euclidean distance. Based on the minimal geodesic distance to vectors of different emotions, ELEC maps the high dimensional feature vectors into a lower space. Through analyzing the class labels of the neighbor training vectors in the compressed low space, ELEC classifies the test data into six archetypal emotional states, i.e. neutral, anger, fear, happiness, sadness and surprise. Experimental results on clear and noisy data set demonstrate that compared with the traditional methods of dimensionality reduction and classification, ELEC achieves 15% improvement on average for speaker-independent emotion recognition and 11% for speaker-dependent.