Artificial intelligence-driven radiomics study in cancer:the role of feature engineering and modeling

Modern medicine is reliant on various medical imaging technologies for non-invasively observing patients’anatomy.However,the interpretation of medical images can be highly subjective and dependent on the expertise of clinicians.Moreover,some potentially useful quantitative information in medical images,especially that which is not visible to the naked eye,is often ignored during clinical practice.In contrast,radiomics performs high-throughput feature extraction from medical images,which enables quantitative analysis of medical images and prediction of various clinical endpoints.Studies have reported that radiomics exhibits promising performance in diagnosis and predicting treatment responses and prognosis,demonstrating its potential to be a non-invasive auxiliary tool for personalized medicine.However,radiomics remains in a developmental phase as numerous technical challenges have yet to be solved,especially in feature engineering and statistical modeling.In this review,we introduce the current utility of radiomics by summarizing research on its application in the diagnosis,prognosis,and prediction of treatment responses in patients with cancer.We focus on machine learning approaches,for feature extraction and selection during feature engineering and for imbalanced datasets and multi-modality fusion during statistical modeling.Furthermore,we introduce the stability,reproducibility,and interpretability of features,and the generalizability and interpretability of models.Finally,we offer possible solutions to current challenges in radiomics research.

Point Cloud Classification Using Content-Based Transformer via Clustering in Feature Space

Recently, there have been some attempts of Transformer in 3D point cloud classification. In order to reduce computations, most existing methods focus on local spatial attention,but ignore their content and fail to establish relationships between distant but relevant points. To overcome the limitation of local spatial attention, we propose a point content-based Transformer architecture, called PointConT for short. It exploits the locality of points in the feature space(content-based), which clusters the sampled points with similar features into the same class and computes the self-attention within each class, thus enabling an effective trade-off between capturing long-range dependencies and computational complexity. We further introduce an inception feature aggregator for point cloud classification, which uses parallel structures to aggregate high-frequency and low-frequency information in each branch separately. Extensive experiments show that our PointConT model achieves a remarkable performance on point cloud shape classification. Especially, our method exhibits 90.3% Top-1 accuracy on the hardest setting of ScanObjectN N. Source code of this paper is available at https://github.com/yahuiliu99/PointC onT.

Endoscopic features and treatments of gastric cystica profunda

BACKGROUND Gastric cystica profunda(GCP)represents a rare condition characterized by cystic dilation of gastric glands within the mucosal and/or submucosal layers.GCP is often linked to,or may progress into,early gastric cancer(EGC).AIM To provide a comprehensive evaluation of the endoscopic features of GCP while assessing the efficacy of endoscopic treatment,thereby offering guidance for diagnosis and treatment.METHODS This retrospective study involved 104 patients with GCP who underwent endoscopic resection.Alongside demographic and clinical data,regular patient followups were conducted to assess local recurrence.RESULTS Among the 104 patients diagnosed with GCP who underwent endoscopic resection,12.5%had a history of previous gastric procedures.The primary site predominantly affected was the cardia(38.5%,n=40).GCP commonly exhibited intraluminal growth(99%),regular presentation(74.0%),and ulcerative mucosa(61.5%).The leading endoscopic feature was the mucosal lesion type(59.6%,n=62).The average maximum diameter was 20.9±15.3 mm,with mucosal involvement in 60.6%(n=63).Procedures lasted 73.9±57.5 min,achieving complete resection in 91.3%(n=95).Recurrence(4.8%)was managed via either surgical intervention(n=1)or through endoscopic resection(n=4).Final pathology confirmed that 59.6%of GCP cases were associated with EGC.Univariate analysis indicated that elderly males were more susceptible to GCP associated with EGC.Conversely,multivariate analysis identified lesion morphology and endoscopic features as significant risk factors.Survival analysis demonstrated no statistically significant difference in recurrence between GCP with and without EGC(P=0.72).CONCLUSION The findings suggested that endoscopic resection might serve as an effective and minimally invasive treatment for GCP with or without EGC.

BDPartNet: Feature Decoupling and Reconstruction Fusion Network for Infrared and Visible Image

While single-modal visible light images or infrared images provide limited information,infrared light captures significant thermal radiation data,whereas visible light excels in presenting detailed texture information.Com-bining images obtained from both modalities allows for leveraging their respective strengths and mitigating individual limitations,resulting in high-quality images with enhanced contrast and rich texture details.Such capabilities hold promising applications in advanced visual tasks including target detection,instance segmentation,military surveillance,pedestrian detection,among others.This paper introduces a novel approach,a dual-branch decomposition fusion network based on AutoEncoder(AE),which decomposes multi-modal features into intensity and texture information for enhanced fusion.Local contrast enhancement module(CEM)and texture detail enhancement module(DEM)are devised to process the decomposed images,followed by image fusion through the decoder.The proposed loss function ensures effective retention of key information from the source images of both modalities.Extensive comparisons and generalization experiments demonstrate the superior performance of our network in preserving pixel intensity distribution and retaining texture details.From the qualitative results,we can see the advantages of fusion details and local contrast.In the quantitative experiments,entropy(EN),mutual information(MI),structural similarity(SSIM)and other results have improved and exceeded the SOTA(State of the Art)model as a whole.

Epidemiological and clinical features,treatment status,and economic burden of traumatic spinal cord injury in China:a hospital-based retrospective study

Traumatic spinal cord injury is potentially catastrophic and can lead to permanent disability or even death.China has the largest population of patients with traumatic spinal cord injury.Previous studies of traumatic spinal cord injury in China have mostly been regional in scope;national-level studies have been rare.To the best of our knowledge,no national-level study of treatment status and economic burden has been performed.This retrospective study aimed to examine the epidemiological and clinical features,treatment status,and economic burden of traumatic spinal cord injury in China at the national level.We included 13,465 traumatic spinal cord injury patients who were injured between January 2013 and December 2018 and treated in 30 hospitals in 11 provinces/municipalities representing all geographical divisions of China.Patient epidemiological and clinical features,treatment status,and total and daily costs were recorded.Trends in the percentage of traumatic spinal cord injuries among all hospitalized patients and among patients hospitalized in the orthopedic department and cost of care were assessed by annual percentage change using the Joinpoint Regression Program.The percentage of traumatic spinal cord injuries among all hospitalized patients and among patients hospitalized in the orthopedic department did not significantly change overall(annual percentage change,-0.5%and 2.1%,respectively).A total of 10,053(74.7%)patients underwent surgery.Only 2.8%of patients who underwent surgery did so within 24 hours of injury.A total of 2005(14.9%)patients were treated with high-dose(≥500 mg)methylprednisolone sodium succinate/methylprednisolone(MPSS/MP);615(4.6%)received it within 8 hours.The total cost for acute traumatic spinal cord injury decreased over the study period(-4.7%),while daily cost did not significantly change(1.0%increase).Our findings indicate that public health initiatives should aim at improving hospitals’ability to complete early surgery within 24 hours,which is associated with improved sensorimotor recovery,increasing the awareness rate of clinical guidelines related to high-dose MPSS/MP to reduce the use of the treatment with insufficient evidence.

Automatic Extraction Method of 3D Feature Guidelines for Complex Cultural Relic Surfaces Based on Point Cloud

Cultural relics line graphic serves as a crucial form of traditional artifact information documentation,which is a simple and intuitive product with low cost of displaying compared with 3D models.Dimensionality reduction is undoubtedly necessary for line drawings.However,most existing methods for artifact drawing rely on the principles of orthographic projection that always cannot avoid angle occlusion and data overlapping while the surface of cultural relics is complex.Therefore,conformal mapping was introduced as a dimensionality reduction way to compensate for the limitation of orthographic projection.Based on the given criteria for assessing surface complexity,this paper proposed a three-dimensional feature guideline extraction method for complex cultural relic surfaces.A 2D and 3D combined factor that measured the importance of points on describing surface features,vertex weight,was designed.Then the selection threshold for feature guideline extraction was determined based on the differences between vertex weight and shape index distributions.The feasibility and stability were verified through experiments conducted on real cultural relic surface data.Results demonstrated the ability of the method to address the challenges associated with the automatic generation of line drawings for complex surfaces.The extraction method and the obtained results will be useful for line graphic drawing,displaying and propaganda of cultural relics.

Synergistic Interdecadal Evolution of Precipitation over Eastern China and the Pacific Decadal Oscillation during 1951-2015

By using the multi-taper method(MTM)of singular value decomposition(SVD),this study investigates the interdecadal evolution(10-to 30-year cycle)of precipitation over eastern China from 1951 to 2015 and its relationship with the North Pacific sea surface temperature(SST).Two significant interdecadal signals,one with an 11-year cycle and the other with a 23-year cycle,are identified in both the precipitation and SST fields.Results show that the North Pacific SST forcing modulates the precipitation distribution over China through the effects of the Pacific Decadal Oscillation(PDO)-related anomalous Aleutian low on the western Pacific subtropical high(WPSH)and Mongolia high(MH).During the development stage of the PDO cold phase associated with the 11-year cycle,a weakened WPSH and MH increased the precipitation over the Yangtze River Basin,whereas an intensified WPSH and MH caused the enhanced rain band to move northward to North China during the decay stage.During the development stage of the PDO cold phase associated with the 23-year cycle,a weakened WPSH and MH increased the precipitation over North China,whereas an intensified WPSH and the weakened MH increased the precipitation over South China during the decay stage.The 11-year and 23-year variabilities contribute differently to the precipitation variations in the different regions of China,as seen in the 1998flooding case.The 11-year cycle mainly accounts for precipitation increases over the Yangtze River Basin,while the 23-year cycle is responsible for the precipitation increase over Northeast China.These results have important implications for understanding how the PDO modulates the precipitation distribution over China,helping to improve interdecadal climate prediction.

A Model for Detecting Fake News by Integrating Domain-Specific Emotional and Semantic Features

With the rapid spread of Internet information and the spread of fake news,the detection of fake news becomes more and more important.Traditional detection methods often rely on a single emotional or semantic feature to identify fake news,but these methods have limitations when dealing with news in specific domains.In order to solve the problem of weak feature correlation between data from different domains,a model for detecting fake news by integrating domain-specific emotional and semantic features is proposed.This method makes full use of the attention mechanism,grasps the correlation between different features,and effectively improves the effect of feature fusion.The algorithm first extracts the semantic features of news text through the Bi-LSTM(Bidirectional Long Short-Term Memory)layer to capture the contextual relevance of news text.Senta-BiLSTM is then used to extract emotional features and predict the probability of positive and negative emotions in the text.It then uses domain features as an enhancement feature and attention mechanism to fully capture more fine-grained emotional features associated with that domain.Finally,the fusion features are taken as the input of the fake news detection classifier,combined with the multi-task representation of information,and the MLP and Softmax functions are used for classification.The experimental results show that on the Chinese dataset Weibo21,the F1 value of this model is 0.958,4.9% higher than that of the sub-optimal model;on the English dataset FakeNewsNet,the F1 value of the detection result of this model is 0.845,1.8% higher than that of the sub-optimal model,which is advanced and feasible.

Guided-YNet: Saliency Feature-Guided Interactive Feature Enhancement Lung Tumor Segmentation Network

Multimodal lung tumor medical images can provide anatomical and functional information for the same lesion.Such as Positron Emission Computed Tomography(PET),Computed Tomography(CT),and PET-CT.How to utilize the lesion anatomical and functional information effectively and improve the network segmentation performance are key questions.To solve the problem,the Saliency Feature-Guided Interactive Feature Enhancement Lung Tumor Segmentation Network(Guide-YNet)is proposed in this paper.Firstly,a double-encoder single-decoder U-Net is used as the backbone in this model,a single-coder single-decoder U-Net is used to generate the saliency guided feature using PET image and transmit it into the skip connection of the backbone,and the high sensitivity of PET images to tumors is used to guide the network to accurately locate lesions.Secondly,a Cross Scale Feature Enhancement Module(CSFEM)is designed to extract multi-scale fusion features after downsampling.Thirdly,a Cross-Layer Interactive Feature Enhancement Module(CIFEM)is designed in the encoder to enhance the spatial position information and semantic information.Finally,a Cross-Dimension Cross-Layer Feature Enhancement Module(CCFEM)is proposed in the decoder,which effectively extractsmultimodal image features through global attention and multi-dimension local attention.The proposed method is verified on the lung multimodal medical image datasets,and the results showthat theMean Intersection overUnion(MIoU),Accuracy(Acc),Dice Similarity Coefficient(Dice),Volumetric overlap error(Voe),Relative volume difference(Rvd)of the proposed method on lung lesion segmentation are 87.27%,93.08%,97.77%,95.92%,89.28%,and 88.68%,respectively.It is of great significance for computer-aided diagnosis.

MSD-Net: Pneumonia Classification Model Based on Multi-Scale Directional Feature Enhancement

Computer-aided diagnosis of pneumonia based on deep learning is a research hotspot.However,there are some problems that the features of different sizes and different directions are not sufficient when extracting the features in lung X-ray images.A pneumonia classification model based on multi-scale directional feature enhancement MSD-Net is proposed in this paper.The main innovations are as follows:Firstly,the Multi-scale Residual Feature Extraction Module(MRFEM)is designed to effectively extract multi-scale features.The MRFEM uses dilated convolutions with different expansion rates to increase the receptive field and extract multi-scale features effectively.Secondly,the Multi-scale Directional Feature Perception Module(MDFPM)is designed,which uses a three-branch structure of different sizes convolution to transmit direction feature layer by layer,and focuses on the target region to enhance the feature information.Thirdly,the Axial Compression Former Module(ACFM)is designed to perform global calculations to enhance the perception ability of global features in different directions.To verify the effectiveness of the MSD-Net,comparative experiments and ablation experiments are carried out.In the COVID-19 RADIOGRAPHY DATABASE,the Accuracy,Recall,Precision,F1 Score,and Specificity of MSD-Net are 97.76%,95.57%,95.52%,95.52%,and 98.51%,respectively.In the chest X-ray dataset,the Accuracy,Recall,Precision,F1 Score and Specificity of MSD-Net are 97.78%,95.22%,96.49%,95.58%,and 98.11%,respectively.This model improves the accuracy of lung image recognition effectively and provides an important clinical reference to pneumonia Computer-Aided Diagnosis.

Japanese Sign Language Recognition by Combining Joint Skeleton-Based Handcrafted and Pixel-Based Deep Learning Features with Machine Learning Classification

Sign language recognition is vital for enhancing communication accessibility among the Deaf and hard-of-hearing communities.In Japan,approximately 360,000 individualswith hearing and speech disabilities rely on Japanese Sign Language(JSL)for communication.However,existing JSL recognition systems have faced significant performance limitations due to inherent complexities.In response to these challenges,we present a novel JSL recognition system that employs a strategic fusion approach,combining joint skeleton-based handcrafted features and pixel-based deep learning features.Our system incorporates two distinct streams:the first stream extracts crucial handcrafted features,emphasizing the capture of hand and body movements within JSL gestures.Simultaneously,a deep learning-based transfer learning stream captures hierarchical representations of JSL gestures in the second stream.Then,we concatenated the critical information of the first stream and the hierarchy of the second stream features to produce the multiple levels of the fusion features,aiming to create a comprehensive representation of the JSL gestures.After reducing the dimensionality of the feature,a feature selection approach and a kernel-based support vector machine(SVM)were used for the classification.To assess the effectiveness of our approach,we conducted extensive experiments on our Lab JSL dataset and a publicly available Arabic sign language(ArSL)dataset.Our results unequivocally demonstrate that our fusion approach significantly enhances JSL recognition accuracy and robustness compared to individual feature sets or traditional recognition methods.

IMTNet:Improved Multi-Task Copy-Move Forgery Detection Network with Feature Decoupling and Multi-Feature Pyramid

Copy-Move Forgery Detection(CMFD)is a technique that is designed to identify image tampering and locate suspicious areas.However,the practicality of the CMFD is impeded by the scarcity of datasets,inadequate quality and quantity,and a narrow range of applicable tasks.These limitations significantly restrict the capacity and applicability of CMFD.To overcome the limitations of existing methods,a novel solution called IMTNet is proposed for CMFD by employing a feature decoupling approach.Firstly,this study formulates the objective task and network relationship as an optimization problem using transfer learning.Furthermore,it thoroughly discusses and analyzes the relationship between CMFD and deep network architecture by employing ResNet-50 during the optimization solving phase.Secondly,a quantitative comparison between fine-tuning and feature decoupling is conducted to evaluate the degree of similarity between the image classification and CMFD domains by the enhanced ResNet-50.Finally,suspicious regions are localized using a feature pyramid network with bottom-up path augmentation.Experimental results demonstrate that IMTNet achieves faster convergence,shorter training times,and favorable generalization performance compared to existingmethods.Moreover,it is shown that IMTNet significantly outperforms fine-tuning based approaches in terms of accuracy and F_(1).

FIBTNet:Building Change Detection for Remote Sensing Images Using Feature Interactive Bi-Temporal Network

In this paper,a feature interactive bi-temporal change detection network(FIBTNet)is designed to solve the problem of pseudo change in remote sensing image building change detection.The network improves the accuracy of change detection through bi-temporal feature interaction.FIBTNet designs a bi-temporal feature exchange architecture(EXA)and a bi-temporal difference extraction architecture(DFA).EXA improves the feature exchange ability of the model encoding process through multiple space,channel or hybrid feature exchange methods,while DFA uses the change residual(CR)module to improve the ability of the model decoding process to extract different features at multiple scales.Additionally,at the junction of encoder and decoder,channel exchange is combined with the CR module to achieve an adaptive channel exchange,which further improves the decision-making performance of model feature fusion.Experimental results on the LEVIR-CD and S2Looking datasets demonstrate that iCDNet achieves superior F1 scores,Intersection over Union(IoU),and Recall compared to mainstream building change detectionmodels,confirming its effectiveness and superiority in the field of remote sensing image change detection.

Cross-Dimension Attentive Feature Fusion Network for Unsupervised Time-Series Anomaly Detection

Time series anomaly detection is crucial in various industrial applications to identify unusual behaviors within the time series data.Due to the challenges associated with annotating anomaly events,time series reconstruction has become a prevalent approach for unsupervised anomaly detection.However,effectively learning representations and achieving accurate detection results remain challenging due to the intricate temporal patterns and dependencies in real-world time series.In this paper,we propose a cross-dimension attentive feature fusion network for time series anomaly detection,referred to as CAFFN.Specifically,a series and feature mixing block is introduced to learn representations in 1D space.Additionally,a fast Fourier transform is employed to convert the time series into 2D space,providing the capability for 2D feature extraction.Finally,a cross-dimension attentive feature fusion mechanism is designed that adaptively integrates features across different dimensions for anomaly detection.Experimental results on real-world time series datasets demonstrate that CAFFN performs better than other competing methods in time series anomaly detection.

FusionNN:A Semantic Feature Fusion Model Based on Multimodal for Web Anomaly Detection

With the rapid development of the mobile communication and the Internet,the previous web anomaly detectionand identificationmodels were built relying on security experts’empirical knowledge and attack features.Althoughthis approach can achieve higher detection performance,it requires huge human labor and resources to maintainthe feature library.In contrast,semantic feature engineering can dynamically discover new semantic featuresand optimize feature selection by automatically analyzing the semantic information contained in the data itself,thus reducing dependence on prior knowledge.However,current semantic features still have the problem ofsemantic expression singularity,as they are extracted from a single semantic mode such as word segmentation,character segmentation,or arbitrary semantic feature extraction.This paper extracts features of web requestsfrom dual semantic granularity,and proposes a semantic feature fusion method to solve the above problems.Themethod first preprocesses web requests,and extracts word-level and character-level semantic features of URLs viaconvolutional neural network(CNN),respectively.By constructing three loss functions to reduce losses betweenfeatures,labels and categories.Experiments on the HTTP CSIC 2010,Malicious URLs and HttpParams datasetsverify the proposedmethod.Results show that compared withmachine learning,deep learningmethods and BERTmodel,the proposed method has better detection performance.And it achieved the best detection rate of 99.16%in the dataset HttpParams.

Video-Based Deception Detection with Non-Contact Heart Rate Monitoring and Multi-Modal Feature Selection

Deception detection plays a crucial role in criminal investigation.Videos contain a wealth of information regarding apparent and physiological changes in individuals,and thus can serve as an effective means of deception detection.In this paper,we investigate video-based deception detection considering both apparent visual features such as eye gaze,head pose and facial action unit(AU),and non-contact heart rate detected by remote photoplethysmography(rPPG)technique.Multiple wrapper-based feature selection methods combined with the K-nearest neighbor(KNN)and support vector machine(SVM)classifiers are employed to screen the most effective features for deception detection.We evaluate the performance of the proposed method on both a self-collected physiological-assisted visual deception detection(PV3D)dataset and a public bag-oflies(BOL)dataset.Experimental results demonstrate that the SVM classifier with symbiotic organisms search(SOS)feature selection yields the best overall performance,with an area under the curve(AUC)of 83.27%and accuracy(ACC)of 83.33%for PV3D,and an AUC of 71.18%and ACC of 70.33%for BOL.This demonstrates the stability and effectiveness of the proposed method in video-based deception detection tasks.

GP‐FMLNet:A feature matrix learning network enhanced by glyph and phonetic information for Chinese sentiment analysis

Sentiment analysis is a fine‐grained analysis task that aims to identify the sentiment polarity of a specified sentence.Existing methods in Chinese sentiment analysis tasks only consider sentiment features from a single pole and scale and thus cannot fully exploit and utilise sentiment feature information,making their performance less than ideal.To resolve the problem,the authors propose a new method,GP‐FMLNet,that integrates both glyph and phonetic information and design a novel feature matrix learning process for phonetic features with which to model words that have the same pinyin information but different glyph information.Our method solves the problem of misspelling words influencing sentiment polarity prediction results.Specifically,the authors iteratively mine character,glyph,and pinyin features from the input comments sentences.Then,the authors use soft attention and matrix compound modules to model the phonetic features,which empowers their model to keep on zeroing in on the dynamic‐setting words in various positions and to dispense with the impacts of the deceptive‐setting ones.Ex-periments on six public datasets prove that the proposed model fully utilises the glyph and phonetic information and improves on the performance of existing Chinese senti-ment analysis algorithms.

A Heuristic Radiomics Feature Selection Method Based on Frequency Iteration and Multi-Supervised Training Mode

Radiomics is a non-invasive method for extracting quantitative and higher-dimensional features from medical images for diagnosis.It has received great attention due to its huge application prospects in recent years.We can know that the number of features selected by the existing radiomics feature selectionmethods is basically about ten.In this paper,a heuristic feature selection method based on frequency iteration and multiple supervised training mode is proposed.Based on the combination between features,it decomposes all features layer by layer to select the optimal features for each layer,then fuses the optimal features to form a local optimal group layer by layer and iterates to the global optimal combination finally.Compared with the currentmethod with the best prediction performance in the three data sets,thismethod proposed in this paper can reduce the number of features fromabout ten to about three without losing classification accuracy and even significantly improving classification accuracy.The proposed method has better interpretability and generalization ability,which gives it great potential in the feature selection of radiomics.

Feature extraction and learning approaches for cancellable biometrics:A survey

Biometric recognition is a widely used technology for user authentication.In the application of this technology,biometric security and recognition accuracy are two important issues that should be considered.In terms of biometric security,cancellable biometrics is an effective technique for protecting biometric data.Regarding recognition accuracy,feature representation plays a significant role in the performance and reliability of cancellable biometric systems.How to design good feature representations for cancellable biometrics is a challenging topic that has attracted a great deal of attention from the computer vision community,especially from researchers of cancellable biometrics.Feature extraction and learning in cancellable biometrics is to find suitable feature representations with a view to achieving satisfactory recognition performance,while the privacy of biometric data is protected.This survey informs the progress,trend and challenges of feature extraction and learning for cancellable biometrics,thus shedding light on the latest developments and future research of this area.

Curve Classification Based onMean-Variance Feature Weighting and Its Application

The classification of functional data has drawn much attention in recent years.The main challenge is representing infinite-dimensional functional data by finite-dimensional features while utilizing those features to achieve better classification accuracy.In this paper,we propose a mean-variance-based(MV)feature weighting method for classifying functional data or functional curves.In the feature extraction stage,each sample curve is approximated by B-splines to transfer features to the coefficients of the spline basis.After that,a feature weighting approach based on statistical principles is introduced by comprehensively considering the between-class differences and within-class variations of the coefficients.We also introduce a scaling parameter to adjust the gap between the weights of features.The new feature weighting approach can adaptively enhance noteworthy local features while mitigating the impact of confusing features.The algorithms for feature weighted K-nearest neighbor and support vector machine classifiers are both provided.Moreover,the new approach can be well integrated into existing functional data classifiers,such as the generalized functional linear model and functional linear discriminant analysis,resulting in a more accurate classification.The performance of the mean-variance-based classifiers is evaluated by simulation studies and real data.The results show that the newfeatureweighting approach significantly improves the classification accuracy for complex functional data.