Principal Component Analysis Research Articles

Morphometric analyses as a tool for the delimitation of a species complex of rupicolous Cattleya orchids from the Brazilian campos rupestres of Minas Gerais and Bahia

In the present study we perform a linear morphometric analysis to assess species delimitation in Cattleya caulescens, C. pabstii, and C. pfisteri, which constitute a species complex in Brazilian campos rupestres. For this purpose, we collected 18 linear measurement variables from flowers of 153 individuals in 11 populations from the three species in the Brazilian States of Minas Gerais and Bahia. We applied Principal Component Analysis (PCA), Canonical Variate Analysis (CVA) and cluster analysis to assess the morphological variation between populations. The analyses indicated a clear difference and cohese clusters of populations for each species, but one of the populations of C. pfisteri was divergent from the other populations. This difference is putatively explained by genetic data from other studies that suggest introgression from a species from a different series, C. sincorana, in this location. The differences between C. caulescens and C. pabstii reinforce the floristic differentiation of the orchid flora from the quartzitic mountains of Southern Minas Gerais in relation to the Espinhaço range to the north, as well as the development of a specialized orchid flora in the iron ore outcrops in Central Minas Gerais.

Phytochemical variability in essential oils of Juniperus communis var. saxatilis populations grow wild in western Himalaya, India

Needle and berry samples of Juniperus communis L. var. saxatilis Pall. were sampled separately during post rainy season to comparatively investigate the essential oil (EO) yield and phytochemical variability in eight populations grow wild in western Himalaya, India. The EOs obtained from air-dried needle and berry samples separately by hydrodistillation method using Clevenger type apparatus varied in yield with geographic origin of populations, ranged between 2.5-3.4% and 1.8-2.8% (v/w, dried weight basis), respectively. GC-MS analysis of EO profiles resulted in identification of a total ninety-four phytochemicals, representing over 95% of total oil content. Both, needle as well as berry EO samples were dominated by monoterpene hydrocarbons α-pinene (18.52-30.65% and 14.31-27.37%), D-limonene (17.01-28.96% and 15.80-29.70%), β-myrcene (3.74-5.59% and 4.12-14.23%), followed by sesquiterpene hydrocarbons β-elemene (0.86-4.13% and 0.77-3.65%) and germacrene D (0.27-2.57% and 0.20-6.15%), respectively. The oxygenated sesquiterpenes α-cadinol (0.34-5.90% and to 5.63%) and α-bisabolol (to 3.39 and 0.95-6.71%) constituted the third most abundant group of terpenes while oxidized monoterpenes with α-terpineol (0.73-2.17% and 0.10-3.51%) and α-terpinyl acetate (2.10-4.76% and 0.05-3.54%) were the least dominant group. The principal component and hierarchical cluster analysis indicated that selective local environmental forces driving the microhabitat conditions appeared to be linked to high variability in essential oil composition of different common Juniper populations instead of their geographical proximity. The present study revealed that common Juniper essential oils from western Himalaya, India fulfil minimum requirements of European Pharmacopoeia and warrants its further exploitation as a natural resource of commercial significance for dietary and therapeutic applications.

A Quasi Time-Domain Method for Fatigue Analysis of Reactor Pressure Vessels in Floating Nuclear Power Plants in Marine Environments

The reactor pressure vessel (RPV) in onshore nuclear power plants is typically analysed for fatigue life by considering the temperature, internal pressure, and seismic effects using a simplified time-domain fatigue analysis. In contrast, the frequency-domain fatigue analysis method is commonly employed to assess the fatigue life of ship structures. The RPV of a floating nuclear power plant (FNPP) is subjected to a combination of temperature, internal pressure, and wave loads in the marine environment. Consequently, it is essential to effectively integrate the frequency-domain fatigue analysis method used for hull structures with the time-domain fatigue analysis method for RPVs in FNPPs or, alternatively, to develop a suitable method that effectively accounts for the temperature, internal pressure, and wave loads. In this study, a quasi-time-domain method is proposed for the fatigue analysis of RPVs in FNPPs. In this method, secondary components of marine environmental loads are filtered out using principal component analysis. Subsequently, the stress spectrum induced by waves is transformed into a stress time history. Fatigue stress under the combined influence of temperature, internal pressure, and wave loads is then obtained through a stress component superposition method. Finally, the accuracy of the quasi-time-domain method was validated through three numerical examples. The results indicate that the calculated values obtained by the quasi-time-domain method are slightly higher than those obtained by the traditional time-domain method, with a maximum deviation of no more than 24%. Additionally, the computation time of the quasi-time-domain method is reduced by 98.67% compared to the traditional time-domain method.

Research on the biomechanical characteristics of basketball player injuries and their application in sports rehabilitation

Basketball is a dynamic sport, characterized by fast moves, powerful hops, and constant changes in direction, which contributes to its great intensity and excitement. However, these same features elevate athletes to a risk of various types, which include the most common ones such as ligament tears, knee problems, and ankle sprains. The knowledge of the risk factors associated with particular movement patterns and environmental conditions is made possible by knowledge of the biomechanical qualities of these injuries is crucial if one has to develop effective preventive and rehabilitation strategies. The purpose of the study is to establish the biomechanical characteristics of basketball player injuries and their application in sports rehabilitation. The study proposed a novel Tunicate Swarm Optimized Flexible Extreme Boosting (TSO-FXGBoost) to predict the injuries of basketball players and their sports rehabilitation. Player’s motion data capture sessions utilize cameras and sensors to record their biomechanics during basketball activities. A Gaussian filter was employed to process the data to eliminate the noise present in the biomechanical data. Principal component analysis (PCA) served as a dimensionality reduction approach to extract relevant features from the pre-processed data. The results demonstrate that certain biomechanical features have a strong correlation with the occurrence of injuries, which indicates great potential in the strategies of prevention of injuries. In a comparative analysis, the suggested approach performs various assessment metrics such as accuracy (98%), recall (96.2%), precision (98.49%), and F1 score (97.8%). The suggested approach and rehabilitation strategies can be customized to each player’s unique biomechanical profile, improving rehabilitation times and lowering the risk of re-injury.

Social inclusion and poverty reduction in sub-Saharan Africa

PurposeThe poverty puzzle persists in sub-Saharan Africa decades after some other regional bodies have recorded substantial gains in their poverty reduction efforts. This study seeks to explore the extent to which social inclusion influences poverty outcomes in sub-Saharan Africa.Design/methodology/approachThe study constructs a social inclusion index and its sub-indices using principal component analysis and employs the Lewbel instrumental variable estimation method to test the impact of the computed social inclusion indices on poverty outcomes for 19 sub-Saharan African countries.FindingsThe results have shown that social inclusion reduces the proportion of the poor and the depth of poverty within sub-Saharan Africa significantly. We also observe a U-shaped relationship between social inclusion and poverty outcomes; thus, social inclusion’s poverty-reducing effect sees a reversal when it hits a certain threshold.Practical implicationsThe study provides the evidence needed to inform the policy discourse on the poverty problem, which continues to plague sub-Saharan Africa.Social implicationsWith sub-Saharan Africa’s position as the region with the worst poverty statistics, the results of this study will prove useful in tackling poverty to ensure improved quality of life.Originality/valueThis study presents original evidence on social inclusion and its relationship with poverty.Peer reviewThe peer review history for this article is available at: https://publons.com/publon/10.1108/IJSE-08-2023-0640

Development of methodology to support molecular endotype discovery from synovial fluid of individuals with knee osteoarthritis: The STEpUP OA consortium

Objectives To develop a protocol for largescale analysis of synovial fluid proteins, for the identification of biological networks associated with subtypes of osteoarthritis. Methods Synovial Fluid To detect molecular Endotypes by Unbiased Proteomics in Osteoarthritis (STEpUP OA) is an international consortium utilising clinical data (capturing pain, radiographic severity and demographic features) and knee synovial fluid from 17 participating cohorts. 1746 samples from 1650 individuals comprising OA, joint injury, healthy and inflammatory arthritis controls, divided into discovery (n = 1045) and replication (n = 701) datasets, were analysed by SomaScan Discovery Plex V4.1 (>7000 SOMAmers/proteins). An optimised approach to standardisation was developed. Technical confounders and batch-effects were identified and adjusted for. Poorly performing SOMAmers and samples were excluded. Variance in the data was determined by principal component (PC) analysis. Results A synovial fluid standardised protocol was optimised that had good reliability (<20% co-efficient of variation for >80% of SOMAmers in pooled samples) and overall good correlation with immunoassay. 1720 samples and >6290 SOMAmers met inclusion criteria. 48% of data variance (PC1) was strongly correlated with individual SOMAmer signal intensities, particularly with low abundance proteins (median correlation coefficient 0.70), and was enriched for nuclear and non-secreted proteins. We concluded that this component was predominantly intracellular proteins, and could be adjusted for using an ‘intracellular protein score’ (IPS). PC2 (7% variance) was attributable to processing batch and was batch-corrected by ComBat. Lesser effects were attributed to other technical confounders. Data visualisation revealed clustering of injury and OA cases in overlapping but distinguishable areas of high-dimensional proteomic space. Conclusions We have developed a robust method for analysing synovial fluid protein, creating a molecular and clinical dataset of unprecedented scale to explore potential patient subtypes and the molecular pathogenesis of OA. Such methodology underpins the development of new approaches to tackle this disease which remains a huge societal challenge.

Refinement and Validation of the SPEcies at Risk Index for Metals (SPEARmetal Index) for Assessing Ecological Impacts of Metal Contamination in the Nakdong River, South Korea

The SPEcies At Risk index for metals (SPEARmetal index) was refined using updated physiological sensitivity data and validated to assess the ecological impact of metal contamination on benthic macroinvertebrate communities in the upper Nakdong River, near a Zn smelter in Korea. Biosurvey and chemical monitoring data were collected at 18 sites surrounding the smelter and nearby mines. Acute ecotoxicity tests on 20 indigenous species from the Korean peninsula were conducted and used to update taxon-specific metal sensitivity data. The refined SPEARmetal index, based on this updated sensitivity, was significantly lower than previous versions, with most values below the severe impact threshold (0.5) in the main stream. The correlation between hazard quotients in water and the SPEAR index improved, with the correlation coefficient increasing from 0.63 to 0.70. Despite consistently high benthic macroinvertebrate indices (BMIs) across the study area, generic ecological indices, such as total richness, EPT (Ephemeroptera, Plecoptera, and Trichoptera taxa richness), and Shannon’s diversity index, showed correlations with metal contamination levels. Principal component analysis identified the SPEARmetal index as the primary indicator associated with metal contamination in both water and sediment. These findings highlight the improved performance of the refined SPEARmetal index as a more sensitive and specific tool for assessing the ecological status of metal-impacted aquatic ecosystems compared to traditional indices.

Temporal Image Sandwiches Enable Link between Functional Data Analysis and Deep Learning for Single-Plant Cotton Senescence

Abstract Senescence is a highly ordered biological process involving resource redistribution away from aging tissues that affects yield and quality in annuals and perennials. Images from 14 unmanned / unoccupied / uncrewed aerial system (UAS, UAV, drone) flights captured the senescence window across two experiments while functional principal component analysis (FPCA) effectively reduced the dimensionality of temporal visual senescence ratings (VSRs) and two vegetation indices: the red chromatic coordinate index (RCC) and transformed normalized difference green and red index (TNDGR). Convolutional neural networks (CNNs) trained on temporally concatenated, or “sandwiched,” UAS images of individual cotton plants (Gossypium hirsutum L.), allowed single-plant analysis (SPA). The first functional principal component scores (FPC1) served as the regression target across six CNN models (M1-M6). Model performance was strongest for FPC1 scores from VSRs (R2 = 0.857 and 0.886 for M1 and M4), strong for TNDGR (R2 = 0.743 and 0.745 for M3 and M6), and strong-to-moderate for RCC (R2 = 0.619 and 0.435 for M2 and M5), with deep learning attention of each model confirmed by activation of plant pixels within saliency maps. Single-plant UAS image analysis across time enabled translatable implementations of high-throughput phenotyping by linking deep learning with functional data analysis (FDA). This has applications for fundamental plant biology, monitoring orchards or other spaced plantings, plant breeding, and genetic research.

Effects of jogi, Micropogonias undulatus, addition on the production of volatile compounds in baechu-kimchi

Baechu-kimchi is a traditional vegetable fermented food using kimchi cabbage (Brassica rapa) as the main ingredient. A wide variety of ingredients can be used in kimchi depending on the specific region and even household. Although there have been a lot of studies examining various aspects of kimchi, there has been limited research on kimchi with added fish as a minor ingredient. Therefore, in the present work we aimed to assess changes in the volatile compounds of baechu-kimchi with the addition of seafood used as minor ingredients of kimchi. Sulfur compounds were the most commonly detected volatile compounds; 9 categories of volatile components were detected in total. Altogether, 30 sulfur compounds were detected, and among them, five sulfur compounds: (E)-1-(methyltrisulfanyl)prop-1-ene, 1-(methyldisulfanyl)-1-methylsulfanylpropane, (methyltetrasulfanyl)methane, 1-(methyldisulfanyl)-1-[(E)-prop-1-enyl]sulfanylpropane, and 1,1-bis(methyldisulfanyl)propane, were found only in jogi-added kimchi, thus confirming the influence of jogi addition. Principal component analysis revealed clear distinctions in the volatile compounds as a result of jogi addition as fermentation progressed. Moreover, when confirming the correlation with microbial populations, it was evident that the differentiation in volatile compounds was more attributable to jogi addition than microbial impact. In conclusion, the addition of jogi to baechu-kimchi led to an abundance of volatile compounds by the 20th day of fermentation.

Computational fluid dynamics and shape analysis enhance aneurysm rupture risk stratification.

Accurately quantifying the rupture risk of unruptured intracranial aneurysms (UIAs) is crucial for guiding treatment decisions and remains an unmet clinical challenge. Computational Flow Dynamics and morphological measurements have been shown to differ between ruptured and unruptured aneurysms. It is not clear if these provide any additional information above routinely available clinical observations or not. Therefore, this study investigates whether incorporating image-derived features into the established PHASES score can improve the classification of aneurysm rupture status. A cross-sectional dataset of 170 patients (78 with ruptured aneurysm) was used. Computational fluid dynamics (CFD) and shape analysis were performed on patients' images to extract additional features. These derived features were combined with PHASES variables to develop five ridge constrained logistic regression models for classifying the aneurysm rupture status. Correlation analysis and principal component analysis were employed for image-derived feature reduction. The dataset was split into training and validation subsets, and a ten-fold cross validation strategy with grid search optimisation and bootstrap resampling was adopted for determining the models' coefficients. Models' performances were evaluated using the area under the receiver operating characteristic curve (AUC). The logistic regression model based solely on PHASES achieved AUC of 0.63. All models incorporating derived features from CFD and shape analysis demonstrated improved performance, reaching an AUC of 0.71. Non-sphericity index (shape variable) and maximum oscillatory shear index (CFD variable) were the strongest predictors of a ruptured status. This study demonstrates the benefits of integrating image-based fluid dynamics and shape analysis with clinical data for improving the classification accuracy of aneurysm rupture status. Further evaluation using longitudinal data is needed to assess the potential for clinical integration.

Measuring integrated accessibility for sustainable mobility: a fuzzy set approach case study

AbstractSustainable transportation is vital to climate justice and social equity. Despite the efforts to achieve sustainability, there is still a lack of adequate measurement that integrates land use and transportation systems, which can be barriers to planning implementation. With methodological improvements in fuzzy theory application, this study develops an integrated index to measure the sustainability of multimodal accessibility. We do so by defining a fuzziness degree based on the different trip purposes and modes of transportation with a case study in Isfahan, Iran. Sustainable accessibility indicators were developed for walking, biking, and public transportation to represent the performance of each transportation system, considering the integration with land-use patterns. We analyze transportation modes and the accessibility to five main urban activities, including employment opportunities, education, healthcare, shopping, and recreation services, based on the travel distances, followed by a statistical integration method with Principal Components Analysis (PCA) for each travel mode. The outcome provides insights for urban planners and transportation planners to effectively evaluate the degree of integration between transportation and land-use systems and contribute to enhancing sustainable accessibility.

Classification of Dog Breeds Using Convolutional Neural Network Models and Support Vector Machine

When classifying breeds of dogs, the accuracy of classification significantly affects breed identification and dog research. Using images to classify dog breeds can improve classification efficiency; however, it is increasingly challenging due to the diversities and similarities among dog breeds. Traditional image classification methods primarily rely on extracting simple geometric features, while current convolutional neural networks (CNNs) are capable of learning high-level semantic features. However, the diversity of dog breeds continues to pose a challenge to classification accuracy. To address this, we developed a model that integrates multiple CNNs with a machine learning method, significantly improving the accuracy of dog images classification. We used the Stanford Dog Dataset, combined image features from four CNN models, filtered the features using principal component analysis (PCA) and gray wolf optimization algorithm (GWO), and then classified the features with support vector machine (SVM). The classification accuracy rate reached 95.24% for 120 breeds and 99.34% for 76 selected breeds, respectively, demonstrating a significant improvement over existing methods using the same Stanford Dog Dataset. It is expected that our proposed method will further serve as a fundamental framework for the accurate classification of a wider range of species.

Direct reprogramming of fibroblasts into spiral ganglion neurons by defined transcription factors

AbstractDegeneration of the cochlear spiral ganglion neurons (SGNs) is one of the major causes of sensorineural hearing loss and significantly impacts the outcomes of cochlear implantation. Functional regeneration of SGNs holds great promise for treating sensorineural hearing loss. In this study, we systematically screened 33 transcriptional regulators implicated in neuronal and SGN fate. Using gene expression array and principal component analyses, we identified a sequential combination of Ascl1, Pou4f1 and Myt1l (APM) in promoting functional reprogramming of SGNs. The neurons induced by APM expressed mature neuronal and SGN lineage‐specific markers, displayed mature SGN‐like electrophysiological characteristics and exhibited single‐cell transcriptomes resembling the endogenous SGNs. Thus, transcription factors APM may serve as novel candidates for direct reprogramming of SGNs and hearing recovery due to SGN damages.

Development and Validation of a Measure of the Resolution Phase of the Sexual Response Cycle: The Sexual Resolution Scale (SRS)

ABSTRACT We developed and validated a measure of the depth of the resolution experience – the Sexual Resolution Scale (SRS). Portuguese-speaking participants responded to an online survey including the SRS whose eight items were derived from the literature on post-sex states: 1) deeply relaxed, 2) with elevated heart rate, 3) with intensified emotions, 4) more aware of body, 5) in a profound peace, 6) more imaginative, 7) more predisposed to talk about emotionally charged topics, 8) more predisposed to listen to emotionally charged topics. They also reported the intensity of satisfaction, desire, arousal, and orgasm, during the last sexual activity, and completed the Perceived Relationship Quality Components Inventory, and the Female Sexual Function Index or the International Index of Erectile Function. Principal Component Analysis and Confirmatory Factor Analysis revealed two dimensions: Internal Experience (items 1 to 6) and Openness to Communication (items 7 and 8). The two dimensions had good reliability. Invariance was confirmed between women and men. Nomological validity evidence was demonstrated: the two dimensions correlated with better sexual function during the last sexual activity and over the past 4 weeks. The SRS appears to be usable to measure the enjoyable aspects of the resolution phase of sexual intercourse.

Characterization of Groundwater Geochemistry in an Esker Aquifer in Western Finland Based on Three Years of Monitoring Data

This study investigated the hydrogeochemistry of a shallow Quaternary sedimentary aquifer in an esker deposition in western Finland, where distinct spatial and temporal variability in groundwater hydrogeochemistry has been observed. Field investigation and hydrogeochemical data were obtained from autumn 2010 to autumn 2013. The data were analyzed using the multivariate statistical methods principal component analysis (PCA) and hierarchical cluster analysis (HCA), in conjunction with groundwater classification based on the main ionic composition. The stable isotope ratios of δ18O and δD were used to determine the origin of the groundwater and its connection to surface water bodies. The groundwater geochemistry is characterized by distinct redox zones caused by the influence of organic matter, pyrite oxidation, and preferential flow pathways due to different hydrogeological conditions. The groundwater is of the Ca-HCO3 type and locally of the Ca-HCO3-SO4 type, with low TDS, alkalinity, and pH, but elevated Fe and Mn concentrations, KMnO4 consumption, and, occasionally, Ni concentrations. The decomposition of organic matter adds CO2 to the groundwater, and in this study, the dissolution of CO2 was found to increase the pH and enhance the buffering capacity of the groundwater. The mobility of redox-sensitive elements and trace metals is controlled by pH and redox conditions, which are affected by the pumping rate, precipitation, and temperature. With the expected future increases in precipitation and temperature, the buffering capacity of the aquifer system will enhance the balance between alkalinity from bioactivity and acidity from recharge and pyrite oxidation.

Comparison of the performance of classical and quantum machine‐learning methods on the detection of sugar beet Cercospora leaf disease

AbstractImage processing and machine‐learning (ML) techniques are essential for the detection of diseases and pests in plants. This study explored the application of quantum ML (QML) algorithms for the early detection of Cercospora beticola leaf disease in sugar beet, which causes significant impact on global sugar production. Using a dataset of 1065 images (739 diseased and 326 healthy), we extracted 70 ML statistical features, including 10 from the grey‐level co‐occurrence matrix (GLCM) and 60 colour‐related features. Performance evaluations of classical ML algorithms, such as random forest (RF; 91.95% accuracy) and extreme gradient boosting (91.95% accuracy), demonstrated strong results compared to quantum approaches. Notably, the quantum support vector classifier (QSVC) achieved an accuracy of 85% with perfect recall of 1.00, while the variational quantum classifier (VQC) recorded an accuracy of 88.73%. Dimensionality reduction via principal component analysis reduced features from 70 to 5, enabling effective classification with competitive results: ML (RF) 91.41%, VQC with limited‐memory Broyden–Fletcher–Goldfarb–Shanno with box constraints (L_BFGS_B) 88.73% and QSVC 85%. These findings highlight the potential of QML algorithms in improving agricultural disease identification and aiding in the advancement of more efficient, sustainable farming techniques.

Assessment of Terminal Heat Stress Tolerance in Doubled Haploids Derived from Synthetic Hexaploid Wheat (Triticum aestivum L.) Using Genetic Variability and PCA-based Cluster Analyses

A comprehensive study was conducted on germplasm derived from two synthetic wheats and two hexaploid wheats i.e., SHW14102 x BWL4444, SHW14102 x BWL3531, and SHW3761 x BWL4444 to identify the potential doubled haploids that can withstand high temperatures, particularly at the reproductive stage during crop seasons viz., 2020–2021 and 2021–2022. The doubled haploid lines were selected based on phenotypic characteristics using genetic variability analysis. In the preliminary field trial evaluation, 100 lines were selected based on high phenotypic uniformity for further testing against terminal heat stress conditions and high yield potential. Among these, 17 lines had relatively higher values for days to biomass yield, grain yield, thousand-grain weight, and harvest index and relatively lower values for maturity, and grain filling duration based on principal component and cluster analyses. Principal component analysis (PCA) based cluster analysis exhibited that, clusters II and III had clear separation compared to cluster I. All three clusters were analyzed according to their means and standard deviations. The mean values for GYP (385.07), BMYP (1162.37), and TGW (38.13) were relatively higher in cluster 1 than in other clusters. Cluster 2 exhibited a higher value for DH (89.14), SL with awns (18.21), and GFD (18.19) while cluster 3 showed a higher value for HI (41.02). Thus, it was concluded that cluster I demonstrated superior performance in grain yield per plant, biomass yield per plant, and thousand-grain weight, indicating its overall higher productivity compared to the other clusters under terminal heat stress conditions and suggesting them as potential germplasm for future breeding programs.

Image-processing-based model for surface roughness evaluation in titanium based alloys using dual tree complex wavelet transform and radial basis function neural networks.

In this study, we examine the assessment of surface roughness on turned surfaces of Ti 6Al 4V using a computer vision system. We utilize the Dual-Tree Complex Wavelet Transform (DTCWT) to break down the images of the turned surface into sub-images oriented in directions. Three different methods of feature generation have been compared, i.e., the use of Gray-Level Co-Occurrence Matrix (GLCM) and DTCWT-based extraction of second-order statistical features, DTCWT Image fusion, and the use of GLCM for feature extraction, and DTCWT image fusion using Particle Swarm Optimization (PSO) based GLCM features. Principal Component Analysis (PCA) was utilized to identify and select features. The model was developed using a Radial Basis Function Neural Network (RBFNN). Accordingly, six models were designed based on the three feature generation methods, considering all features and features selected using PCA. The RBFNN model, which incorporates DTCWT Image fusion and utilizes PSO with PCA features, achieved a training data prediction accuracy of 100% and a test data prediction accuracy of 99.13%.

Mathematical foundation of High-Dimensional Data Analysis: Leveraging Topology and Geometry for Enhanced Model Interpretability in AI

One of the most important challenges for modern AI and machine learning is the analysis of high-dimensional data. Traditional methods face serious complications in such cases due to high complexity of datasets: the curse of dimensionality, overfitting, and lack of transparency of model behavior. In this paper, we adopt a novel approach to analyze high-dimensional data; topological and geometric techniques will be exploited, taking advantage of better model interpretability and deeper insights into the structure. Precisely, we discuss Topological Data Analysis, mainly Persistent Homology (Edelsbrunner et al., 2002), which allows the extraction of topological features-like loops and connected components that enable the extracting knowledge about the global structure of data. We also see how some concepts of differential geometry and Riemannian geometry (Do Carmo, 1976) can be used to cast light on manifold data structure lying at the heart of any attempt at modeling intrinsic patterns in high-dimensional spaces. We will review how these mathematical pillars, combined with state-of-the-art techniques for dimensionality reduction like t-SNE, UMAP, Principal Component Analysis, are able to provide interpretable and low-dimensional representations of high-dimensional data that can be used to understand models and make decisions. Case studies are also included, which explain the practical working of these methods in AI systems and show how much complex models can be made transparent using these, especially in domains that are very critical, such as healthcare (Caruana et al., 2015), finance (Chen et al., 2018), and autonomous systems ( Wang et al., 2019). We also discuss some of the difficulties in using these methods for practical applications: computational complexity; the need for large-scale data processing (Bengio et al., 2007); and integration of topological and geometric intuition with the rest of the machine learning pipeline (Zhu et al., 2020). We conclude with possible future directions of research toward fine-tuning these methods and exploring their broader applicability to AI in its quest for more robust, interpretable, and reliable AI models. Given this work, we focus on how linking topology, geometry, and AI bears great promise for solving one of today's critical challenges: model interpretability in high-dimensional data analysis.

PW-FBPNN: A Hybrid Fault Diagnosis Method for Power Circuit Systems Combining Principal Component Analysis, Wavelet Packet Transform, and Fuzzy Neural Networks

Due to the complexity of fault states and the non-linear relationship between input and output responses, fault diagnosis in complex power circuit systems faces significant challenges. This study proposes a novel hybrid method, PW-FBPNN, which integrates principal component analysis (PCA), wavelet packet transform (WPT), and fuzzy back propagation neural network (FBPNN) to enhance fault diagnosis. The effectiveness of this method was demonstrated through experiments on the voltage divider basic operational amplifier and the second-order filter circuit of the four operational amplifiers. PW-FBPNN achieved 100% accuracy in diagnosing most types of faults, with a minimum accuracy of 91.67% for challenging faults. This method was significantly superior to existing methods such as FCM-HMM-SVM and KICA-DNN in terms of accuracy and computational efficiency and could complete the diagnosis in just 0.01 seconds. These results indicate that PW-FBPNN has the potential to improve fault diagnosis in power circuit systems, providing a promising solution for enhancing system reliability and maintenance efficiency.