Χ2 Distance Research Articles

Control Chart T2Qv for Statistical Control of Multivariate Processes with Qualitative Variables

The scientific literature is abundant regarding control charts in multivariate environments for numerical and mixed data; however, there are few publications for qualitative data. Qualitative variables provide valuable information on processes in various industrial, productive, technological, and health contexts. Social processes are no exception. There are multiple nominal and ordinal categorical variables used in economics, psychology, law, sociology, and education, whose analysis adds value to decision-making; therefore, their representation in control charts would be useful. When there are many variables, there is a risk of redundant or excessive information, so the application of multivariate methods for dimension reduction to retain a few latent variables, i.e., a recombination of the original and synthesizing of most of the information, is viable. In this context, the T2Qv control chart is presented as a multivariate statistical process control technique that performs an analysis of qualitative data through Multiple Correspondence Analysis (MCA), and the Hotelling T2 chart. The interpretation of out-of-control points is carried out by comparing MCA charts and analyzing the χ2 distance between the categories of the concatenated table and those that represent out-of-control points. Sensitivity analysis determined that the T2Qv control chart performs well when working with high dimensions. To test the methodology, an analysis was performed with simulated data and with a real case applied to the graduate follow-up process in the context of higher education. To facilitate the dissemination and application of the proposal, a reproducible computational package was developed in R, called T2Qv, and is available on the Comprehensive R Archive Network (CRAN).

Poisson approximation in χ2 distance by the Stein-Chen approach

The main purpose of the paper is to investigate the possibility of applying the Stein-Chen approach to estimate the χ2 distance between Poisson distribution and Poisson binomial distribution. Earlier results concerning χ2 distance between the above mentioned distributions either used analytical approach heavily based on the analysis of the generating functions or on rather lengthy and complicated elementary calculations. Applying the Stein-Chen approach we succeed in providing a very quick proof of upper bounds for χ2 distance that are of comparable strength to the earlier estimates obtained by other approaches.

Influence of Data Distribution on Federated Learning Performance in Tumor Segmentation.

To investigate the correlation between differences in data distributions and federated deep learning (Fed-DL) algorithm performance in tumor segmentation on CT and MR images. Two Fed-DL datasets were retrospectively collected (from November 2020 to December 2021): one dataset of liver tumor CT images (Federated Imaging in Liver Tumor Segmentation [or, FILTS]; three sites, 692 scans) and one publicly available dataset of brain tumor MR images (Federated Tumor Segmentation [or, FeTS]; 23 sites, 1251 scans). Scans from both datasets were grouped according to site, tumor type, tumor size, dataset size, and tumor intensity. To quantify differences in data distributions, the following four distance metrics were calculated: earth mover's distance (EMD), Bhattacharyya distance (BD), χ2 distance (CSD), and Kolmogorov-Smirnov distance (KSD). Both federated and centralized nnU-Net models were trained by using the same grouped datasets. Fed-DL model performance was evaluated by using the ratio of Dice coefficients, θ, between federated and centralized models trained and tested on the same 80:20 split datasets. The Dice coefficient ratio (θ) between federated and centralized models was strongly negatively correlated with the distances between data distributions, with correlation coefficients of -0.920 for EMD, -0.893 for BD, and -0.899 for CSD. However, KSD was weakly correlated with θ, with a correlation coefficient of -0.479. Performance of Fed-DL models in tumor segmentation on CT and MRI datasets was strongly negatively correlated with the distances between data distributions.Keywords: CT, Abdomen/GI, Liver, Comparative Studies, MR Imaging, Brain/Brain Stem, Convolutional Neural Network (CNN), Federated Deep Learning, Tumor Segmentation, Data Distribution Supplemental material is available for this article. © RSNA, 2023See also the commentary by Kwak and Bai in this issue.

Feature extraction of 3D Chinese rose model based on color and shape features.

Flower classification is of great importance to the research fields of plants, food, and medicine. Due to more abundant information on three-dimensional (3D) flower models than two-dimensional 2D images, it makes the 3D models more suitable for flower classification tasks. In this study, a feature extraction and classification method were proposed based on the 3D models of Chinese roses. Firstly, the shape distribution method was used to extract the sharpness and contour features of 3D flower models, and the color features were obtained from the Red-Green-Blue (RGB) color space. Then, the RF-OOB method was employed to rank the extracted flower features. A shape descriptor based on the unique attributes of Chinese roses was constructed, χ2 distance was adopted to measure the similarity between different Chinese roses. Experimental results show that the proposed method was effective for the retrieval and classification tasks of Chinese roses, and the average classification accuracy was approximately 87%, which can meet the basic retrieval requirements of 3D flower models. The proposed method promotes the classification of Chinese roses from 2D space to 3D space, which broadens the research method of flower classification.

A sensitivity analysis of bubble departure behavior in vertical channel nucleate boiling

Boiling is a very efficient heat transfer mechanism and had been exploited in numerous industrial and engineering sectors. However, limited by the experimental techniques and measuring tools, the experimental data related to the bubble dynamics especially in high heat fluxes on the wall surface is still rare and random. To contribute to this knowledge gap, the present paper proposes a statistical analysis method, attempting to identify the effect of input variables to bubble departure diameter on superheated wall by sensitivity analysis. More than 400 experimental data are collected by literature reviewing and a group of simulation data generated by selected correlation are included to supplementary and enlarge the database. Finite Mixture Model (FMM) is employed to conduct the sensitivity analysis study, where the hydraulic diameter of channel, water flow rate, flow subcooling and wall superheat are selected as input variables and the bubble departure diameter is output variable. With adopting two definitions of general distance (Kullback-Leibler divergence and χ2 distance), the sensitivity degree order of the input variables is evaluated. Those two definitions of general distance have almost the same results concerning the order. The innovative sensitivity analysis approach is compared with the standard variance decomposition method (Sobol). The result indicates that FMM is more accurate than Sobol based on present database. The preliminary results of sensitivity analysis approach show that the flow condition has a more significant influence on bubble departure behavior than temperature does.

Change Detection: The Framework of Visual Inspection System for Railway Plug Defects

Railway plug defects impact the safety of a railway system. To detect railway plug defects, we establish the framework of a visual inspection system (VIS), which is the first system that can perform railway plug inspection automatically and intelligently. Using the idea of change detection, the framework includes three algorithm modules, which are named the object location, image alignment and similarity measurement modules. After the image acquisition system captures a rail image as the input, the three algorithm modules process the image in order. First, in the object location module, a deep convolutional neural network is used to perform plug location. Second, in the image alignment module, a simple and fast method is designed to align key images using histogram of oriented gradients features. Third, in the similarity measurement module, the χ2 distance is used to compute the similarity between the two plug regions in an inspection image and in an aligned ground-truth image. The results of the similarity measurement are sorted when all inspection images are processed. Therefore, the inspection images with smaller similarity values are ranked higher and the plugs in the images have larger probabilities of defects. The framework has passed the practice tests, and the visual inspection system using this framework has already been authorized by the China Railway Corporation and will be equipped in many inspection trains belonging to local railway corporations.

CT-based Airway Flow Model to Assess Ventilation in Chronic Obstructive Pulmonary Disease: A Pilot Study.

Background The lack of functional information in thoracic CT remains a limitation of its use in the clinical management of chronic obstructive pulmonary disease (COPD). Purpose To compare the distribution of pulmonary ventilation assessed by a CT-based full-scale airway network (FAN) flow model with hyperpolarized xenon 129 (129Xe) MRI (hereafter, 129Xe MRI) and technetium 99m-diethylenetriaminepentaacetic acid aerosol SPECT ventilation imaging (hereafter, V-SPECT) in participants with COPD. Materials and Methods In this prospective study performed between May and August 2017, pulmonary ventilation in participants with COPD was computed by using the FAN flow model. The modeled pulmonary ventilation was compared with functional imaging data from breath-hold time-series 129Xe MRI and V-SPECT. FAN-derived ventilation images on the coronal plane and volumes of interest were compared with functional lung images. Percentage lobar ventilation estimated by the FAN model was compared with that measured at 129Xe MRI and V-SPECT. The statistical significance of ventilation distribution between FAN and functional images was demonstrated with the Spearman correlation coefficient and χ2 distance. Results For this study, nine participants (seven men [mean age, 65 years ± 5 {standard deviation}] and two women [mean age, 63 years ± 7]) with COPD that was Global Initiative for Chronic Obstructive Lung Disease stage II-IV were enrolled. FAN-modeled ventilation profile showed strong positive correlation with images from 129Xe MRI (ρ = 0.67; P < .001) and V-SPECT (ρ = 0.65; P < .001). The χ2 distances of the ventilation histograms in the volumes of interest between the FAN and 129Xe MRI and FAN and V-SPECT were 0.16 ± 0.08 and 0.28 ± 0.14, respectively. The ratios of lobar ventilations in the models were linearly correlated to images from 129Xe MRI (ρ = 0.67; P < .001) and V-SPECT (ρ = 0.59; P < .001). Conclusion A CT-based full-scale airway network flow model provided regional pulmonary ventilation information for chronic obstructive pulmonary disease and correlates with hyperpolarized xenon 129 MRI and technetium 99m-diethylenetriaminepentaacetic acid aerosol SPECT ventilation imaging. © RSNA, 2019 Online supplemental material is available for this article. See also the editorial by Schiebler and Parraga in this issue.

A distributionally robust optimization approach to reconstructing missing locations and paths using high-frequency trajectory data

Daily high-frequency trajectory data (e.g., 0.1-s connected vehicle data) provide a promising foundation to improve the observability of travel demand dynamics. However, the raw trajectories are not always accurate and complete due to technical and privacy issues. This paper proposes a data-driven optimization modeling framework to reconstruct the location-duration-path choices for the missing observations from the incomplete trajectories. By processing many-day raw trajectories, we observe a set of historical choices of location-duration-path and identify missing observations in space and time dimensions. To improve computational efficiency, we apply data-driven network-time prisms that reduce the search space for the missing choices. Then, we formulate Distributionally Robust Optimization (DRO) models with likelihood bounds, a special case of data-driven optimization models using phi-divergences (i.e., χ2 distance), to reconstruct the missing choices. To solve the minimax programs of the DRO models while maintaining tractability, we reformulate and solve the equivalent dual problems of the DRO models based on the strong duality theory. To demonstrate and validate the proposed models, we use a real-world connected vehicle dataset containing around 2,800 connected vehicles over two separate months in Southeast Michigan from the Safety Pilot Model Deployment (SPMD) project and a transportation network from OpenStreetMap.

Rapid Annotation of Seizures and Interictal-ictal Continuum EEG Patterns.

Seizures, status epilepticus, and seizure-like rhythmic or periodic activities are common, pathological, harmful states of brain electrical activity seen in the electroencephalogram (EEG) of patients during critical medical illnesses or acute brain injury. Accumulating evidence shows that these states, when prolonged, cause neurological injury. In this study we developed a valid method to automatically discover a small number of homogeneous pattern clusters, to facilitate efficient interactive labelling by EEG experts. 592 time domain and spectral features were extracted from continuous EEG (cEEG) data of 369 ICU (intensive care unit) patients. For each patient, feature dimensionality was reduced using principal component analysis (PCA), retaining 95% of the variance. K-medoids clustering was applied to learn a local dictionary from each patient, consisting of k=100 exemplars/words. Changepoint detection (CPD) was utilized to break each EEG into segments. A bag-of-words (BoW) representation was computed for each segment, specifically, a normalized histogram of the words found within each segment. Segments were further clustered using the BoW histograms by Affinity Propagation (AP) using a χ2 distance to measure similarities between histograms. The resulting 30 50 clusters for each patient were scored by EEG experts through labeling only the cluster medoids. Embedding methods t-SNE (t-distributed stochastic neighbor embedding) and PCA were used to provide a 2D representation for visualization and exploration of the data. Our results illustrate that it takes approximately 3 minutes to annotate 24 hours of cEEG by experts, which is at least 60 times faster than unaided manual review.

Detection of white spot lesions by segmenting laser speckle images using computer vision methods.

This paper aims to develop a method for laser speckle image segmentation of tooth surfaces for diagnosis of early stages caries. The method, applied directly to a raw image obtained by digital photography, is based on the difference between the speckle pattern of a carious lesion tooth surface area and that of a sound area. Each image is divided into blocks which are identified in a working matrix by their χ2 distance between block histograms of the analyzed image and the reference histograms previously obtained by K-means from healthy (h_Sound) and lesioned (h_Decay) areas, separately. If the χ2 distance between a block histogram and h_Sound is greater than thedistance to h_Decay, this block is marked as decayed. The experiments showed that the method can provide effective segmentation for initial lesions. We used 64 images to test the algorithm and we achieved 100% accuracy in segmentation. Differences between the speckle pattern of a sound tooth surface region and a carious region, even in the early stage, can be evidenced by the χ2 distance between histograms. This method proves to be more effective for segmenting the laser speckle image, which enhances the contrast between sound and lesioned tissues. The results were obtained with low computational cost. The method has the potential for early diagnosis in a clinical environment, through the development of low-cost portable equipment.

Reliable Multi-View Clustering

With the advent of multi-view data, multi-view learning (MVL) has become an important research direction in machine learning. It is usually expected that multi-view algorithms can obtain better performance than that of merely using a single view. However, previous researches have pointed out that sometimes the utilization of multiple views may even deteriorate the performance. This will be a stumbling block for the practical use of MVL in real applications, especially for tasks requiring high dependability. Thus, it is eager to design reliable multi-view approaches, such that their performance is never degenerated by exploiting multiple views.This issue is vital but rarely studied. In this paper, we focus on clustering and propose the Reliable Multi-View Clustering (RMVC) method. Based on several candidate multi-view clusterings, RMVC maximizes the worst-case performance gain against the best single view clustering, which is equivalently expressed as no label information available. Specifically, employing the squared χ2 distance for clustering comparison makes the formulation of RMVC easy to solve, and an efficient strategy is proposed for optimization. Theoretically, it can be proved that the performance of RMVC will never be significantly decreased under some assumption. Experimental results on a number of data sets demonstrate that the proposed method can effectively improve the reliability of multi-view clustering.

Human Face Identification from Profile Projection

This paper presents face recognition from front face. The idea is to extract the facial profile from a frontal view to provide a measurement for automatic face recognition. The profile is derived from the intensity of horizontal projection of the face image and using profile measure such χ2 distance for face identification. Three profile projections from 4 images or more are taken for each person, average values are calculated and stored in a database file. Profile measurements are compared with other profile in the database file. Results of experiments to the faces with or without spectacles rotate head (lift, right) and different face expression show that the proposed approach is robust and efficient way of face matching.

Musical Learning and Teaching Conceptions as Sociocultural Productions in Classical, Flamenco, and Jazz Cultures

This study analyzes the discourse of musicians from three different cultures of musical learning, ranging from the more formal classical European culture, through the jazz culture, to the less formal flamenco culture in Roma communities. It is based on cultural studies of learning and education and the implicit conceptions theory. Thirty-one semi-professional guitarists were interviewed about learning and teaching music. We applied the lexicometrical method using correspondence analysis. We found significant lexical differences among the three cultures for all the three educational dimensions analyzed (teaching, learning, and evaluation). We describe literal answers from the most representative participants from each culture (using the automatic selection of modal response procedure according to χ2 distance) and a qualitative analysis of their full answers. Finally, we project a distribution of the three cultures of learning onto a factorial plane, which summarizes distribution of the three cultures of learning according to two axes that we have interpreted in terms of (a) locus of control (self-others) and (b) phenomenology (analytical–emotional distance–conceptual–explicit knowledge/sensory–involvement–embodied–implicit knowledge), respectively. The discourse of classical and flamenco participants expressed other-regulated learning, although classical participants were closer to an explicit, conceptual pole, whereas flamenco participants were closer to an implicit, embodied pole. The discourse of jazz participants lay in between the other two, closer to the explicit pole, but including characteristic language about self-regulation.

Improved Text Clustering Using k-Mean Bayesian Vectoriser

In literature studies, high-dimensional data reduces the efficiency of clustering algorithms and maximises execution time. Therefore, in this paper, we propose an approach called a BV-kmeans (Bayesian Vectorisation along with k-means) that aims to improve document representation models for text clustering. This approach consists of integrating the k-means document clustering with the Bayesian Vectoriser that is used to compute the probability distribution of the documents in the vector space in order to overcome the problems of high-dimensional data and lower the consumption time. We have used various similarity measures which are namely: K divergence, Squared Euclidean distance and Squared χ2 distance in order to determine the effective metrics for modelling the similarity between documents with the proposed approach. We have evaluated the proposed approach on a set of common newspaper websites that have highly dimensional data. Experimental results show that the proposed approach can increase the degree to which a cluster encases documents from a specific category by 85%. This is in comparison with the standard k-means algorithm and it has succeeded in lowering the runtime using the proposed approach by 95% compared to the standard k-means algorithm.

Gujrati character recognition using weighted k-NN and Mean χ 2 distance measure

With advances in the field of digitization, document analysis and handwriting recognition have emerged as key research areas. Authors present a handwritten character recognition system for Gujrati, an Indian language spoken by 40 million people. The proposed system extracts four features. A unique pattern descriptor and Gabor phase XNOR pattern are the two features that are newly proposed for isolated handwritten character set of Gujrati. In addition to these two features, we use contour direction probability distribution function and autocorrelation features. Next contribution is the weighted k-NN classifier. This research finally contributes is a novel mean χ 2 distance measure. Proposed classifier exploits a combination of feature weights, new distance measure along with a triangular distance and Euclidian distance for performance that improves conventional k-NN classifier. The implementation on a comprehensive data set show 86.33 % recognition efficiency. Facts and figures show that proposed approach outperforms conventional k-NN. It is concluded that despite the shape ambiguities in Indian scripts, proposed classification algorithm could be a dominant technique in the field of handwritten character recognition.

Evaluating 3D spatial pyramids for classifying 3D shapes

This paper focuses on the problem of 3D shape categorization. For a given set of training 3D shapes, a 3D shape recognition system must be able to predict the class label for a test 3D shape. We introduce a novel discriminative approach for recognizing 3D shape categories which is based on a 3D Spatial Pyramid (3DSP) decomposition. 3D local descriptors computed on the 3D shapes have to be extracted, to be then quantized in order to build a 3D visual vocabulary for characterizing the shapes. Our approach repeatedly subdivides a cube inscribed in the 3D shape, and computes a weighted sum of histogram of visual word occurrences at increasingly fine sub-volumes. Additionally, we integrate this pyramidal representation with different types of kernels, such as the Histogram Intersection Kernel and the extended Gaussian Kernel with χ2 distance. Finally, we perform a thorough evaluation on different publicly available datasets, defining an elaborate experimental setup to be used for establishing further comparisons among different 3D shape categorization methods.

Two-Way Classification of a Data Table with Non Negative Entries: The Role of the χ2 Distance and Correspondence Analysis

We developed an approach to two-way classification based on the χ2 distance and Correspondence Analysis. We present, in particular, two classification algorithms: the first one operates a dimension reduction before applying clustering techniques to rows and columns. The second one, successively partitions the data matrix to extract several classification schemes rather than one. Applications to gene expression and web data are presented. The results are compared with an optimal partition algorithm.

Authorship attribution based on a probabilistic topic model

This paper describes, evaluates and compares the use of Latent Dirichlet allocation (LDA) as an approach to authorship attribution. Based on this generative probabilistic topic model, we can model each document as a mixture of topic distributions with each topic specifying a distribution over words. Based on author profiles (aggregation of all texts written by the same writer) we suggest computing the distance with a disputed text to determine its possible writer. This distance is based on the difference between the two topic distributions. To evaluate different attribution schemes, we carried out an experiment based on 5408 newspaper articles (Glasgow Herald) written by 20 distinct authors. To complement this experiment, we used 4326 articles extracted from the Italian newspaper La Stampa and written by 20 journalists. This research demonstrates that the LDA-based classification scheme tends to outperform the Delta rule, and the χ2 distance, two classical approaches in authorship attribution based on a restricted number of terms. Compared to the Kullback–Leibler divergence, the LDA-based scheme can provide better effectiveness when considering a larger number of terms.

Gaussian-curvature-derived invariants for isometry

Surface deformations without tearing or stretching, preserving the intrinsic properties, are called isometries. This paper presents a new definition of Gaussian curvature moments (GCMs) by the integral of n power of Gaussian curvature. Then a series of moment invariants, called Gaussian curvature moment invariants (GCMIs), are derived via GCMs. These moment invariants share many good properties under rigid transformations and isometric non-rigid transformations, and Gaussian-Bonnet theorem is a special case of GCMI. GCMIs are invariant under isometry and scaling transformations. We construct an invariant vector as a descriptor for a surface via GCMIs, and a modified χ2 distance is defined as a measure of similarity. Finally, experiments show that it is a reliable descriptor for isometric non-rigid shape.

Near Duplicate Identification With Spatially Aligned Pyramid Matching

A new framework, termed spatially aligned pyramid matching, is proposed for near duplicate image identification. The proposed method robustly handles spatial shifts as well as scale changes, and is extensible for video data. Images are divided into both overlapped and non-overlapped blocks over multiple levels. In the first matching stage, pairwise distances between blocks from the examined image pair are computed using earth mover's distance (EMD) or the visual word with χ2 distance based method with scale-invariant feature transform (SIFT) features. In the second stage, multiple alignment hypotheses that consider piecewise spatial shifts and scale variation are postulated and resolved using integer-flow EMD. Moreover, to compute the distances between two videos, we conduct the third step matching (i.e., temporal matching) after spatial matching. Two application scenarios are addressed-near duplicate retrieval (NDR) and near duplicate detection (NDD). For retrieval ranking, a pyramid-based scheme is constructed to fuse matching results from different partition levels. For NDD, we also propose a dual-sample approach by using the multilevel distances as features and support vector machine for binary classification. The proposed methods are shown to clearly outperform existing methods through extensive testing on the Columbia Near Duplicate Image Database and two new datasets. In addition, we also discuss in depth our framework in terms of the extension for video NDR and NDD, the sensitivity to parameters, the utilization of multiscale dense SIFT descriptors, and the test of scalability in image NDD.