Dimensional Data Research Articles

Fast and universal single-molecule localization using multi-dimensional point spread functions

The recent development of single-molecule imaging techniques has enabled not only high accuracy spatial resolution imaging but also information rich functional imaging. Abundant information about single molecules can be encoded in its diffraction pattern and be extracted precisely (e.g. 3D position, wavelength, dipole orientation). However, sophisticated high dimensional point spread function (PSF) modeling and analyzing methods have greatly impeded the broad accessibility of these techniques. Here, we present a graphics processing unit (GPU) -based B-spline PSF modeling method that could flexibly model high dimensional PSFs with arbitrary shape without greatly increasing the model parameters. Our B-spline fitter achieves 100 times speed improvement and minimal uncertainty for each dimension, enabling efficient high dimensional single-molecule analysis. We demonstrated, both in simulations and experiments, the universality and flexibility of our B-spline fitter to accurately extract the abundant information from different types of high dimensional single-molecule data, including multicolor PSF (3D + color), multi-channel four-dimensional 4Pi-PSF (3D + interference phase) and five-dimensional vortex PSF (3D + dipole orientation).

Large-scale gene expression data clustering through incremental ensemble approach

Abstract DNA microarray technology monitors gene activity in real-time in living organisms. It creates a large amount of data that helps scientists learn about how genes work. Clustering this data helps understand gene interactions and uncover important biological processes. However, the traditional clustering techniques have difficulties due to the enormous dimensionality of gene expression data and the intricacy of biological networks. Although ensemble clustering is a viable strategy, such high-dimensional data may not lend itself well to traditional approaches. This study introduces a novel technique for gene expression data clustering called incremental ensemble clustering for gene expression data (IECG). There are two steps in the IECG. A technique for grouping gene expression data into windows is presented in the first step, producing a tree of clusters. This procedure is carried out again for succeeding windows that have distinct feature sets. The base clusterings of two consecutive windows are ensembled using a new goal function to form a new clustering solution. By repeating this step-by-step method for further windows, reliable patterns that are beneficial for medical applications can be extracted. The results from both biological and non-biological data demonstrate that the proposed algorithm outperformed the state-of-the-art algorithms. Additionally, the running time of the proposed algorithm has been examined.

Bayesian clustering of high-dimensional data via latent repulsive mixtures

SUMMARY Model-based clustering of moderate or large dimensional data is notoriously difficult. We propose a model for simultaneous dimensionality reduction and clustering by assuming a mixture model for a set of latent scores, which are then linked to the observations via a Gaussian latent factor model. This approach was recently investigated by Chandra et al. (2023). The authors use a factor-analytic representation and assume a mixture model for the latent factors. However, performance can deteriorate in the presence of model misspecification. Assuming a repulsive point process prior for the component-specific means of the mixture for the latent scores is shown to yield a more robust model that outperforms the standard mixture model for the latent factors in several simulated scenarios. The repulsive point process must be anisotropic to favour well-separated clusters of data, and its density should be tractable for efficient posterior inference. We address these issues by proposing a general construction for anisotropic determinantal point processes. We illustrate our model in simulations as well as a plant species co-occurrence dataset.

Optimum Combination of Spectral Variables for Crop Mapping in Heterogeneous Landscapes based on Sentinel-2 Time Series and Machine Learning

Abstract. This article aimed to determine a workflow for more efficient large-scale crop mapping using a time series of images from the Sentinel-2 Satellite, statistical methods of attribute selection, and machine learning. The proposed methodology explores the best possible combination of spectral variables related to vegetation (16 vegetation indices in the RGB, NIR, SWIR, and Red Edge regions) to characterize different spectro-temporal profiles of Land Use and Land Cover (LULC) in spatially heterogeneous landscapes. First, we applied a data dimensionality reduction analysis using the PCA (Principal Component Analysis) method. Subsequently, the variables that showed the highest statistical correlation between each other were used in the spectro-temporal classification process, using the Random Forest, TempCNN, and LightTAE algorithms, following three different strategies: C1 (ALL), C2 (BE + IV (Red Edge)) and C3 (BE + IV (without Red Edge)), where ALL – All variables; BE – Spectral Bands; IV – Vegetation Indices. Given the results found, the C2 classification scenario (with bands B3, B4, B5, B6, B7, B8, and B8A and the NDRE1, RESI, and MSR indexes) demonstrated the best LULC classification accuracy at the crop pattern level, compared to the other scenarios, with average values of 0.91, 0.88, 0.91, 0.89, and 0.89 (Global Accuracy, Producer Accuracy, User Accuracy, Kappa index, and F1-Score, respectively, for the TempCNN model), the which emphasized the importance of both qualitative and quantitative variability of sampling data and variables based on the Red Edge region for improving LULC classification processes in large-scale heterogeneous landscapes.

Soft sensor model for endpoint carbon content and temperature in BOF steelmaking based on just-in-time learning with multilayer structure preservation and sparse information enhancement

Ensuring precise prediction of the endpoint carbon content and temperature is paramount in controlling the endpoint of the basic oxygen furnace (BOF) steelmaking process. However, due to the frequent fluctuations in real-time blowing conditions, the conventional just-in-time learning soft sensor approach encounters challenges in effectively anticipating the blowing endpoint. To address these aforementioned issues, this research introduces a novel approach known as the pattern-oriented multilayer structure preservation and sparse information enhancement model (POMLSP-SIE). This approach involves dynamically generating a dataset with the same distribution based on the characteristics of the query sample pattern. It is combined with a multi-pathway dimension reduction model to preserve multi-view spatial geometry information while reducing data dimension. The low-dimensional embedding serves as dictionaries containing various hierarchical structural characteristics. Significant information within these dictionaries is sparsely represented to amplify its influence during the regression prediction process while diminishing the impact of less relevant information. This refinement aims to rectify the problem of static regression models being weak to adapt to changing working conditions, ultimately enhancing prediction performance. The effectiveness of the proposed method is substantiated through an experimental study utilising real converter steelmaking process data, thereby confirming its practical applicability.

Model-free feature screening based on Hellinger distance for ultrahigh dimensional data

Model-free feature screening based on Hellinger distance for ultrahigh dimensional data

Nonlinear Dynamic Process Monitoring Based on Discriminative Denoising Autoencoder and Canonical Variate Analysis

Modern industrial processes are characterized by increasing complexity, often exhibiting pronounced dynamic behaviors and significant nonlinearity. Addressing these dynamic and nonlinear characteristics is essential for effective process monitoring. However, many existing methods for process monitoring and fault diagnosis are insufficient in handling these challenges. In this article, we present a novel process monitoring approach, CVA-DisDAE, which integrates an improved Denoising Autoencoder (DAE) with Canonical Variate Analysis (CVA) to address the challenges posed by dynamic behaviors and nonlinear relationships in industrial processes. First, CVA is employed to reduce data dimensionality and minimize information redundancy by maximizing correlations between past and future observations, thereby effectively capturing process dynamics. Following this, we introduce a discriminative DAE model (DisDAE) designed to serve as a semi-supervised denoising autoencoder for precise feature extraction. This is achieved by incorporating both between-class separability and within-class variability into the traditional DAE framework. The key distinction between the proposed DisDAE and the conventional DAE lies in the integration of a linear discriminant analysis (LDA) penalty into the DAE’s loss function, resulting in extracted features that are more conducive to fault classification. Finally, we validate the effectiveness of the proposed semi-supervised dynamic process monitoring approach through its application to the Tennessee Eastman benchmark process, demonstrating its superior performance.

Modeling Functional Brain Networks for ADHD via Spatial Preservation-Based Neural Architecture Search.

Modeling functional brain networks (FBNs) for attention deficit hyperactivity disorder (ADHD) has sparked significant interest since the abnormal functional connectivity is discovered in certain functional magnetic resonance imaging (fMRI)-based brain regions compared to typical developmental control (TC) individuals. However, existing models for modeling FBNs generally use dimensionality reduction techniques to process the high dimensional input data, which results in confusion and an inaccurate representation of voxel interactions between spatially close brain regions, causing misdiagnosis of the disease. To address these issues, we propose a spatial preservation-based neural architecture search (SP-NAS) for FBNs modeling in ADHD. The main work includes three-fold: 1) A spatial preservation module is designed to embed original spatial information into dimensionality reduction data, addressing the challenge of a large number of parameters in the original data and mitigating disease misdiagnosis resulting from voxel confusion between different brain regions caused by dimensionality reduction. 2) A search space using more suitable search operations is constructed to efficiently extract spatial-temporal interaction characteristics of fMRI data in ADHD while narrowing the search space. 3) Cross-regional association differences between ADHD and TC groups are explored for ADHD auxiliary diagnosis since the abnormal activation regions of ADHD relative to TC on the brain regions and the abnormal connectivity between the lesion brain regions are identified. Model validation results on the ADHD-200 dataset show that the FBNs obtained from SP-NAS not only achieve competitive results in ADHD diagnosis but also reveal abnormal connections in the lesion regions of ADHD consistent with clinical diagnosis.

Radiomics nomogram combined with clinical factors for predicting pathological complete response in resectable esophageal squamous cell carcinoma

IntroductionPredicting the efficacy of neoadjuvant immunochemotherapy (NICT) for esophageal squamous cell carcinoma (ESSC) prior to surgery can minimize unnecessary surgical interventions and facilitate personalized treatment strategies. Our goal is to develop and validate an image-based radiomic model using preoperative computed tomography (CT) scans and clinical data to predict pathological complete response (pCR) in resectable ESSC following neoadjuvant immunotherapy.MethodsWe retrospectively collected data from patients diagnosed with ESCC at the First Affiliated Hospital of Soochow University between January 2018 and May 2023, who received preoperative neoadjuvant immunochemotherapy. Eligible patients were randomly divided into training and validation sets. Radiomic features extracted from preprocessed CT images were used to develop a radiomic model, incorporating Radiomic score (Rad-score) and clinical factors through multivariate logistic regression analysis. The model’s performance was assessed for calibration, discrimination, and clinical utility in an independent validation cohort.ResultsWe enrolled a total of 105 eligible participants who were randomly divided into two groups: a training set (N=74) and a validation set (N=31). After data dimension reduction and feature selection, we identified 11 radiomic features, which collectively formed the Rad-score. Rad-score had an area under the curve (AUC) of 0.83 (95% CI 0.72-0.93) in the training set and 0.78 (95% CI 0.60-0.95) in the validation set. Multivariate analysis revealed that radiological response and Neutrophil–Lymphocyte Ratio (NLR) were independent predictors of pCR, with p-values of 0.0026 and 0.0414, respectively. We developed and validated a nomogram combining Rad-score and clinical features, achieving AUCs of 0.90 (95% CI 0.82-0.98) in the training set and 0.85 (95% CI 0.70-0.99) in the validation set. The Delong test confirmed the nomogram’s superiority over pure radiomic and clinical models. Decision curve analysis (DCA) and integrated discrimination improvement (IDI) assessment supported the clinical value and superiority of the combined model.ConclusionThe nomogram, which integrates Rad-score and clinical features, offers a precise and reliable method for predicting pCR status in ESCC patients who have undergone neoadjuvant immunochemotherapy. This tool aids in tailoring treatment strategies to individual patients.

Generalization error guaranteed auto-encoder-based nonlinear model reduction for operator learning

Many physical processes in science and engineering are naturally represented by operators between infinite-dimensional function spaces. The problem of operator learning, in this context, seeks to extract these physical processes from empirical data, which is challenging due to the infinite or high dimensionality of data. An integral component in addressing this challenge is model reduction, which reduces both the data dimensionality and problem size. In this paper, we utilize low-dimensional nonlinear structures in model reduction by investigating Auto-Encoder-based Neural Network (AENet). AENet first learns the latent variables of the input data and then learns the transformation from these latent variables to corresponding output data. Our numerical experiments validate the ability of AENet to accurately learn the solution operator of nonlinear partial differential equations. Furthermore, we establish a mathematical and statistical estimation theory that analyzes the generalization error of AENet. Our theoretical framework shows that the sample complexity of training AENet is intricately tied to the intrinsic dimension of the modeled process, while also demonstrating the robustness of AENet to noise.

Data-driven optimization of coastal sea level monitoring: Leveraging known patterns for enhanced reconstruction

Efficiently configuring sea level monitoring stations is crucial for obtaining accurate spatiotemporal data while managing operational and maintenance costs and addressing the challenges posed by missing data. This study focuses on optimizing the selection of stations within Turkey's coastal sea level monitoring network by leveraging the inherent lower dimensionality in data. The network consists of 18 stations distributed along Turkey's coastline. To identify dominant patterns in historical sea level data, Empirical Orthogonal Function (EOF) analysis was employed, followed by the application of the QR decomposition with column pivoting algorithm. Model performance is assessed using the Nash-Sutcliffe coefficient of efficiency (CE) and root mean square error (RMSE). Remarkably, the results demonstrated that reconstructing the entire dataset, encompassing all 18 stations was possible with a CE of 0.94 and an RMSE of 0.06. Even utilizing data from two or three stations alone achieves acceptable reconstruction accuracy. The effectiveness of EOF analysis combined with QR with column pivoting algorithm suggests promising applications in various scientific fields.

Predicting Hass Avocado Maturity with NIR Spectroscopy for Non-invasive Dry Matter Estimation in Hass Avocados

Aims: To develop a rapid, non-invasive method for predicting Hass avocado maturity using near- infrared diffuse reflectance spectroscopy (NIR-DRS) combined with machine learning algorithms, and to identify the optimal NIR wavelength range for accurate dry matter content prediction. Study Design: An experimental design involving spectral data collection from Hass avocados and the development of machine learning models for dry matter prediction. Methodology: Spectral data from 200 Hass avocados were collected using near-infrared diffuse reflectance spectroscopy (900-2500 nm). To improve the quality of the spectral data and reduce noise, standard normal variate was used to correct for scattering and remove unwanted variability in the spectral data. PCA was then performed to reduce the dimension of the spectral data while retaining the most significant variance. Following preprocessing, machine learning models, including Convolutional Neural Networks (CNN), were trained to predict dry matter content, and the optimal wavelength range was determined for accurate prediction. Results: The CNN model demonstrated superior performance for dry matter prediction with R² of 0.91 in the testing set. The wavelength range of 1000-1500 nm was identified as optimal, offering accurate predictions while reducing computational complexity. This range shows potential for developing cost-effective NIR devices for real-time maturity assessment. Conclusion: NIR spectroscopy combined with machine learning offers a non-invasive, accurate method for predicting avocado dry matter, with potential applications for quality control in the avocado industry. The findings demonstrate that focusing on specific wavelength ranges can lead to more affordable and efficient NIR solutions.

Feature screening filter for high dimensional survival data in the reproducing kernel Hilbert space

We consider the issue of screening uninformative variables associate with survival outcome in ultra high-dimensional situation. specifically, we focus on Hilbert-Schmits Independent criteria (HSIC) statistic defined in the Reproducing kernel Hilbert Space(RKHS) and use the HSIC as a feature screening approach to avoid from difficulty occurred from the ultra high dimensionality. Generally, it is known that the HSIC can account for the flexible relationship between the outcome and predictor variables. Compared with the typical approaches such as regularization and model free screening approaches, our approach does not require the complex non parametric computation or the complicated numerical optimization, Thereby, our proposed approach effectively and flexibly filters out the uninformative predictor. We will show the advantages of our method in numerical simulation studies and illustrate the usefulness of it by applying to diffuse large-B-cell lymphoma data.

Research on wireless channel model based on improved ray tracing algorithm that considers multiple diffuse scattering and employs pyramid-shaped ray tubes as the carrier

This paper extensively utilizes fine three dimensional environmental data obtained from laser point clouds. Based on theories such as geometrical optics and effective roughness theory, a deterministic wireless channel model is established, which integrates higher-order diffuse scattering. This model is referred to as the ray tracing fusion with higher-order diffuse scattering model. To expedite the collision calculation between rays and the scene, this paper introduces a combined approach of voxelization and signed distance field, resulting in a remarkable 16-fold improvement in computational speed. Moreover, aiming to balance accuracy and efficiency, the paper systematically analyzes the optimization computation parameters of the model. Finally, the proposed model is validated using measurement data in the frequency range of 1 GHz to 6 GHz in mountainous terrain. The results indicate that the predicted outcomes of the proposed model have an accuracy within 6 dB compared to the measurement results, and are superior to ITU-R P.1546, which is an international standard recommended by the International Telecommunication Union for modeling electromagnetic wave propagation in undulating terrain. This provides necessary technical support for network planning and optimization.

GOG-MBSHO: multi-strategy fusion binary sea-horse optimizer with Gaussian transfer function for feature selection of cancer gene expression data

Cancer gene expression data has the characteristics of high-dimensional, multi-text and multi-classification. The problem of cancer subtype diagnosis can be solved by selecting the most representative and predictive genes from a large number of gene expression data. Feature selection technology can effectively reduce the dimension of data, which helps analyze the information on cancer gene expression data. A multi-strategy fusion binary sea-horse optimizer based on Gaussian transfer function (GOG-MBSHO) is proposed to solve the feature selection problem of cancer gene expression data. Firstly, the multi-strategy includes golden sine strategy, hippo escape strategy and multiple inertia weight strategies. The sea-horse optimizer with the golden sine strategy does not disrupt the structure of the original algorithm. Embedding the golden sine strategy within the spiral motion of the sea-horse optimizer enhances the movement of the algorithm and improves its global exploration and local exploitation capabilities. The hippo escape strategy is introduced for random selection, which avoids the algorithm from falling into local optima, increases the search diversity, and improves the optimization accuracy of the algorithm. The advantage of multiple inertial weight strategies is that dynamic exploitation and exploration can be carried out to accelerate the convergence speed and improve the performance of the algorithm. Then, the effectiveness of multi-strategy fusion was demonstrated by 15 UCI datasets. The simulation results show that the proposed Gaussian transfer function is better than the commonly used S-type and V-type transfer functions, which can improve the classification accuracy, effectively reduce the number of features, and obtain better fitness value. Finally, comparing with other binary swarm intelligent optimization algorithms on 15 cancer gene expression datasets, it is proved that the proposed GOG1-MBSHO has great advantages in the feature selection of cancer gene expression data.

Automated detection of stale beef from electronic nose data

AbstractAccurate detection of stale beef on the market is important for protecting the legitimate rights and interests of consumers. To this end, we combined electronic nose measurements with machine learning technology to classify beef samples. We used an electronic nose to collect information about the odor characteristics of different beef samples and used linear discriminant analysis to reduce data dimensionality. We then classified samples using the following algorithms: extreme gradient boosting, logistic regression, K‐nearest neighbor, random forest, support vector machine, and neural networks for pattern recognition. We assessed model performance using a 10‐fold cross‐validation technique. All these methods reached an accuracy of 95% or above, with F1 scores and AUC values above 0.96. The support vector machine algorithm outperformed all other models, achieving perfect recognition with 100% accuracy and F1/AUC scores of 1.0. Our study demonstrates that electronic nose data combined with support vector machine can be used to successfully discriminate between stale and fresh beef, paving the way for novel research directions in the detection of stale beef.

Mcadet: A feature selection method for fine-resolution single-cell RNA-seq data based on multiple correspondence analysis and community detection.

Single-cell RNA sequencing (scRNA-seq) data analysis faces numerous challenges, including high sparsity, a high-dimensional feature space, and biological noise. These challenges hinder downstream analysis, necessitating the use of feature selection methods to identify informative genes, and reduce data dimensionality. However, existing methods for selecting highly variable genes (HVGs) exhibit limited overlap and inconsistent clustering performance across benchmark datasets. Moreover, these methods often struggle to accurately select HVGs from fine-resolution scRNA-seq datasets and minority cell types, which are more difficult to distinguish, raising concerns about the reliability of their results. To overcome these limitations, we propose a novel feature selection framework for scRNA-seq data called Mcadet. Mcadet integrates Multiple Correspondence Analysis (MCA), graph-based community detection, and a novel statistical testing approach. To assess the effectiveness of Mcadet, we conducted extensive evaluations using both simulated and real-world data, employing unbiased metrics for comparison. Our results demonstrate the superior performance of Mcadet in the selection of HVGs in scenarios involving fine-resolution scRNA-seq datasets and datasets containing minority cell populations. Overall, we demonstrate that Mcadet enhances the reliability of selected HVGs, although the impact of HVG selection on various downstream analyses varies and needs to be further investigated.

Application of mass cytometry in multiparametric characterization of precancerous cervical lesions.

Cervical cancer (CC) is the fourth most common malignant tumor in women worldwide. Detecting different biomarkers together on single cells by novel method mass cytometry could contribute to more precise screening. Liquid-based cytology (LBC) cervical samples were collected (N = 53) from women categorized as normal and precancerous lesions. Human papillomavirus was genotyped by polymerase chain reaction, while simultaneous examination of the expression of 29 proteins was done by mass cytometry (CyTOF). Differences in cluster abundances were assessed with Spearman's rank correlation as well as high dimensional data analysis (t-SNE, FlowSOM). Cytokeratin (ITGA6, Ck5, Ck10/13, Ck14, Ck7) expression patterns allowed determining the presence of different cells in the cervical epithelium. FlowSOM analysis enabled to phenotype cervical cells in five different metaclusters and find new markers that could be important in CC screening. The markers Ck18, Ck18, and CD63 (Metacluster 3) showed significantly increasing associated with severity of the precancerous lesions (Spearman rank correlation rho 0.304, p = 0.0271), while CD71, KLF4, LRIG1, E-cadherin, Nanog and p53 (Metacluster 1) decreased with severity of the precancerous lesions (Spearman rank correlation rho -0.401, p = 0.0029). Other metaclusters did not show significant correlation, but metacluster 2 (Ck17, MCM, MMP7, CD29, E-cadherin, Nanog, p53) showed higher abundance in low- and high-grade intraepithelial lesion cases. CyTOF appears feasible and should be considered when examining novel biomarkers on cervical LBC samples. This study enabled us to characterize different cells in the cervical epithelium and find markers and populations that could distinguish precancerous lesions.

When does adjusting covariate under randomization help? A comparative study on current practices

PurposeWe aim to thoroughly compare past and current methods that leverage baseline covariate information to estimate the average treatment effect (ATE) using data from of randomized clinical trials (RCTs). We especially focus on their performance, efficiency gain, and power.MethodsWe compared 6 different methods using extensive Monte-Carlo simulation studies: the unadjusted estimator, i.e., analysis of variance (ANOVA), the analysis of covariance (ANCOVA), the analysis of heterogeneous covariance (ANHECOVA), the inverse probability weighting (IPW), the augmented inverse probability weighting (AIPW), and the overlap weighting (OW) as well as the augmented overlap weighting (AOW) estimators. The performance of these methods is assessed using the relative bias (RB), the root mean square error (RMSE), the model-based standard error (SE) estimation, the coverage probability (CP), and the statistical power.ResultsEven with a well-executed randomization, adjusting for baseline covariates by an appropriate method can be a good practice. When the outcome model(s) used in a covariate-adjusted method is closer to the correctly specified model(s), the efficiency and power gained can be substantial. We also found that most covariate-adjusted methods can suffer from the high-dimensional curse, i.e., when the number of covariates is relatively high compared to the sample size, they can have poor performance (along with lower efficiency) in estimating ATE. Among the different methods we compared, the OW performs the best overall with smaller RMSEs and smaller model-based SEs, which also result in higher power when the true effect is non-zero. Furthermore, the OW is more robust when dealing with the high-dimensional issue.ConclusionTo effectively use covariate adjustment methods, understanding their nature is important for practical investigators. Our study shows that outcome model misspecification and high-dimension are two main burdens in a covariate adjustment method to gain higher efficiency and power. When these factors are appropriately considered, e.g., performing some variable selections if the data dimension is high before adjusting covariate, these methods are expected to be useful.

Association between Radiological and First-Order Statistical Features of the Mammogram, and the Tumor Phenotype in Breast Cancer Patients

Background: Breast cancer is among the most prevalent cancers which can effectively be screened by mammography. The spatial distribution of grey levels of the mammogram known as first-order statistical features (FOSFs) contain higher dimensional data which describe the breast composition. We aim to test these basic measures to differentiate density categories in breast cancer patients, and use them as covariates to investigate the relationship between radiologic and pathologic features of the tumor. Methods: Data from Eighty-five breast cancer subjects, their BI-RADS breast density category (a to d), percentage density (PD), and FOSFs of the mammogram including median, mean, interquartile range, kurtosis, maximum, minimum, standard deviation, skewness, and energy, were extracted. The tumor grade and the percentage of Ki67, ER, PR, and Her2 status were recorded. A linear discriminant analysis, and a support vector machine (SVM) were used to discriminate each density category from others. Then, the relation between variables were investigated using ANCOVA and regression analysis. Results: Density categories a and d were classified by SVM with high accuracy. The key feature of a and d were interquartile range and maximum intensities respectively. Reported tumor margins were related to Her2 overexpression and PR positivity. Spiculated tumor margin predicted percentage of PR expression, with a cumulative odds ratio of 7.85 (CI 2.5- 24.78), when adjusted for age, area of breast, density, and FOSFs, (p=0.0004). Conclusion: The findings of this study suggest that FOSFs can be incorporated in computer-aided systems to adjust for differences in breast composition and to refine risk profiles.