Dimensionality Reduction Method Research Articles

Correlation-based outlier detection for ships’ in-service datasets

With the advent of big data, it has become increasingly difficult to obtain high-quality data. Solutions are required to remove undesired outlier samples from massively large datasets. Ship operators rely on high-frequency in-service datasets recorded onboard the ships for monitoring the performance of their fleet. The large in-service datasets are known to be highly unbalanced, making it difficult to adopt ordinary outlier detection techniques, as they would also result in the removal of rare but quite valuable data samples. Thus, the current work proposes to establish a correlation-based outlier detection scheme for ships’ in-service datasets using two well-known dimensionality reduction methods, namely, Principal Component Analysis (PCA) and Autoencoders. The correlation-based approach detects samples which do not fit the prominent correlations present in the dataset and avoids misidentifying the rare but correlation-following samples in the sparse regions of data domain. The study also attempts to provide the physical meaning of the latent variables obtained using PCA. The effectiveness of the proposed methodology is proven using an actual dataset recorded onboard a ship.

Bark frequency cepstral coefficient based sadness emotion level recognition system

Based on the adverse physiological and social consequences associated with sadness, recognizing this emotion is crucial to mitigate its negative impacts. To address this issue, an efficient system was proposed for recognizing different level of sadness using embedded technology. The system captured speech input through a microphone and then processed it on Raspberry Pi microcomputer. The key feature extraction technique used was Bark-Frequency Cepstral Coefficient (BFCC) method. After selecting a set of features, a thorough analysis of the computational algorithms was conducted, and dimensionality reduction method was applied to reduce computational costs, including noise. These features served as a pre-processing stage for Machine Learning (ML) model based on K-Nearest Neighbors (KNN) architecture. The results were then shown on a smartphone application through Bluetooth connectivity. Based on experimental results, the system showed an impressive improvement of 11.97 dB in the signal-to-noise ratio (SNR) compared to feature extraction using Mel-frequency Cepstral Coefficient (MFCC) method. The results also showed a favorable accuracy rate, implying the effectiveness of KNN with a k-value of 5 in accurately identifying different level of sadness. The system particularly excelled in correctly recognizing high and low level of sadness. Therefore, the effective categorization of sadness emotion level could be applied to the early diagnosis of mental disorders such as depression and anxiety, contributing to the reduction of the adverse impact of sadness.

Cell Painting unravels insecticidal modes of action on Spodoptera frugiperda insect cells

The “Cell Painting” technology utilizes multiplexed fluorescent staining of various cell organelles, to produce high-content microscopy images of cells for multidimensional phenotype assessment. The phenotypic profiles extracted from those images can be analyzed upon perturbations with biologically active molecules to annotate the mode of action or biological activity by comparison with reference profiles of already known mechanisms of action, ultimately enabling the determination of on-target and off-target effects. This approach is already described in various human cell cultures, the most commonly used being the U2OS cell line, yet allows broad applications in additional areas of chemical-biological research. Here we describe for the first time the application and adaptation of Cell Painting to an insect cell line, the Sf9 cells from Spodoptera frugiperda. By adjusting image acquisition and analysis models, specific phenotypic profiles were obtained in a dose-dependent manner for 20 reference compounds, including representatives for the most relevant insecticidal modes of action categories (nerve & muscle, respiration and growth & development). Through a dimensionality-reduction method, both calculations of phenotypic half maximal inhibition concentration (IC50) values as well as similarity analysis of the obtained profiles by hierarchical clustering were performed. By Cell Painting effects on the phenotype could be obtained at higher sensitivity than in other assay formats, such as cytotoxicity assessments. More importantly, these analyses provide insight into mechanistic determinants of biological activity. Compounds with similar modes of action showed a high degree of proximity in a hierarchical clustering analysis while being distinct from actives with an unrelated mode of action. In essence, we provide strong evidence on the impact of Cell Painting mechanistic understanding of insecticides with regards to determinants of efficacy and safety utilizing an insect cell model system.

A comprehensive survey of dimensionality reduction and clustering methods for single-cell and spatial transcriptomics data

Abstract In recent years, the application of single-cell transcriptomics and spatial transcriptomics analysis techniques has become increasingly widespread. Whether dealing with single-cell transcriptomic or spatial transcriptomic data, dimensionality reduction and clustering are indispensable. Both single-cell and spatial transcriptomic data are often high-dimensional, making the analysis and visualization of such data challenging. Through dimensionality reduction, it becomes possible to visualize the data in a lower-dimensional space, allowing for the observation of relationships and differences between cell subpopulations. Clustering enables the grouping of similar cells into the same cluster, aiding in the identification of distinct cell subpopulations and revealing cellular diversity, providing guidance for downstream analyses. In this review, we systematically summarized the most widely recognized algorithms employed for the dimensionality reduction and clustering analysis of single-cell transcriptomic and spatial transcriptomic data. This endeavor provides valuable insights and ideas that can contribute to the development of novel tools in this rapidly evolving field.

Conditional mean dimension reduction for tensor time series

The dimension reduction problem for a stationary tensor time series is addressed. The goal is to remove linear combinations of the tensor time series that are mean independent of the past, without imposing any parametric models or distributional assumptions. To achieve this goal, a new metric called cumulative tensor martingale difference divergence is introduced and its theoretical properties are studied. Unlike existing methods, the proposed approach achieves dimension reduction by estimating a distinctive subspace that can fully retain the conditional mean information. By focusing on the conditional mean, the proposed dimension reduction method is potentially more accurate in prediction. The method can be viewed as a factor model-based approach that extends the existing techniques for estimating central subspace or central mean subspace in vector time series. The effectiveness of the proposed method is illustrated by extensive simulations and two real-world data applications.

NipalsMCIA: Flexible Multi-Block Dimensionality Reduction in R via Non-linear Iterative Partial Least Squares.

With the increased reliance on multi-omics data for bulk and single cell analyses, the availability of robust approaches to perform unsupervised analysis for clustering, visualization, and feature selection is imperative. Joint dimensionality reduction methods can be applied to multi-omics datasets to derive a global sample embedding analogous to single-omic techniques such as Principal Components Analysis (PCA). Multiple co-inertia analysis (MCIA) is a method for joint dimensionality reduction that maximizes the covariance between block- and global-level embeddings. Current implementations for MCIA are not optimized for large datasets such such as those arising from single cell studies, and lack capabilities with respect to embedding new data. We introduce nipalsMCIA, an MCIA implementation that solves the objective function using an extension to Non-linear Iterative Partial Least Squares (NIPALS), and shows significant speed-up over earlier implementations that rely on eigendecompositions for single cell multi-omics data. It also removes the dependence on an eigendecomposition for calculating the variance explained, and allows users to perform out-of-sample embedding for new data. nipalsMCIA provides users with a variety of pre-processing and parameter options, as well as ease of functionality for down-stream analysis of single-omic and global-embedding factors. nipalsMCIA is available as a BioConductor package at https://bioconductor.org/packages/release/bioc/html/nipalsMCIA.html, and includes detailed documentation and application vignettes. Supplementary Materials are available online.

Structure preserved fast dimensionality reduction

Many graph-based unsupervised dimensionality reduction techniques have raised concerns about their high accuracy. However, there is an urgent need to address the enormous time consumption problem in large-scale data scenarios. Therefore, we present a novel approach named Structure Preserved Fast Dimensionality Reduction (SPFDR). Firstly, the parameter-insensitive, sparse, and scalable bipartite graph is constructed to build the similarity matrix. Then, employing alternating iterative optimization, the linear dimensionality reduction matrix and the optimal similarity matrix preserved cluster structure are learned. The computational complexity of the conventional graph-based dimension reduction method costs O(n2d+d3), yet the proposed approach is O(ndm+nm2), wherein n, m, and d are the number of instances, anchors, and features, respectively. Eventually, experiments conducted with multiple open datasets will provide convincing evidence for how effective and efficient the proposed method is.

Research Paper on Exploring the Landscape of Recommendation Systems: A Comparative Analysis of Techniques and Approaches

The field of recommendation systems has witnessed a profound evolution since its inception with Grundy, the first computer-based librarian, in 1979. From its humble beginnings, recommendation systems have become integral to various facets of daily life, particularly in e-commerce, thanks to breakthroughs like Amazon’s Collaborative Filtering in the late 1990s. This led to widespread adoption across diverse sectors, prompting significant research interest and investment, exemplified by Netflix’s renowned recommendation system contest in 2006. Today, recommendation systems employ various techniques such as Hybrid Filtering, Content-Based Filtering, Demographic Filtering, and Collaborative Filtering catering to personalized information needs across industries like entertainment, education, and healthcare. Moreover, emerging types of recommendation systems, including Knowledge-Based, RiskAware, Social-Networking, and Context-Aware, further broaden their applicability, addressing specific user needs and preferences. Leveraging machine learning and AI algorithms on big data, recommendation systems have become a quintessential application of big data analytics, enhancing user experience and engagement in domains like e-learning, tourism, and news dissemination. However, scaling recommendation systems present challenges due to the exponential growth of input data, necessitating strategies like Dimensionality Reduction and cluster-based methods. Integrating multiple recommendation algorithms enhances system complexity, requiring careful consideration of algorithm selection, performance monitoring, and maintenance. Transparency and explanation mechanisms become crucial in complex systems to foster user trust and understanding. Despite challenges, recommendation systems continue to drive innovation, delivering personalized recommendations and enriching user experiences across various domains.

Precise Molecular Subtyping Reveals Heterogeneity of Lung Adenocarcinoma Based on DNA Methylation

Background: Due to the high heterogeneity of lung adenocarcinoma (LUAD), which restricts the effectiveness of therapy, precise molecular subgrouping of LUAD is of great significance. Clinical research has demonstrated the significant potential of DNA methylation as a classification indicator for human malignancies. Methods: WGML framework (which was developed based on weighted gene correlation network analysis (WGCNA), Gene Ontology (GO), and machine learning) was developed to precisely subgroup molecular subtypes of LUAD. This framework included two parts: the WG algorithm and the machine learning part. The WG algorithm part was an original algorithm used to obtain a crucial module, which was characterized by weighted correlation network analysis, functional annotation, and mathematical algorithms. The machine learning part utilized the Boruta algorithm, random forest algorithm, and Gradient Boosting Regression Tree algorithm to select feature genes. Then, based on the results of the WGML framework, subtypes were computed by the hierarchical clustering algorithm. A series of analyses, including dimensionality reduction methods, survival analysis, clinical stage analysis, immune infiltration analysis, tumor environment analysis, immune checkpoints analysis, TIDE analysis, CYT analysis, somatic mutation analysis, and drug sensitivity analysis, were utilized to demonstrate the effectiveness of subgrouping. GEO datasets were used to externally validate the results. Meanwhile, another subgrouping method of LUAD from another study was employed to compare with the WGML framework. Result: By importing DNA methylation data into the WGML framework, nine genes were obtained to further subgroup LUAD. Three subtypes, the Carcinogenesis subtype, Immune-infiltration subtype, and Chemoresistance subtype, were identified. The dimensionality reduction method exhibited great distinctness between subtypes. A series of analyses were employed to exhibit the difference among the three subtypes and to demonstrate the accuracy of the definition of subtypes. Besides, the WGML framework was compared with a LUAD subgrouping method from another research, which demonstrated that WGML had better efficiency for subgrouping LUAD. Conclusion: This study provides a novel LUAD subgrouping framework named WGML for the accurate subgrouping of lung adenocarcinoma. result: By importing DNA methylation data into WGML framework, nine genes were obtained to further subgroup LUAD. Three subtypes, Carcinogenesis subtype, Immune-infiltration subtype, and Chemoresistance subtype were identified. Dimensionality reduction method exhibited great distinctness between subtypes. A series analyses were employed to exhibit the difference of three subtypes and to demonstrate accuracy of definition of subtypes. Besides, WGML framework was compared with a LUAD subgrouping method from another research, which demonstrated WGML had better efficiency for subgrouping LUAD.

Construction of a large-scale maritime element semantic schema based on knowledge graph models for unmanned automated decision-making

In maritime logistics optimization, considerable research efforts are focused on the extraction of deep behavioral characteristics from comprehensive shipping data to discern patterns in maritime vessel behavior. The effective linkage of these characteristics with maritime infrastructure, such as berths, is critical for the enhancement of ship navigation systems. This endeavor is paramount not only as a research focus within maritime information science but also for the progression of intelligent maritime systems. Traditional methodologies have primarily emphasized the analysis of navigational paths of vessels without an extensive consideration of the geographical dynamics between ships and port infrastructure. However, the introduction of knowledge graphs has enabled the integration of disparate data sources, facilitating new insights that propel the development of intelligent maritime systems. This manuscript presents a novel framework using knowledge graph technology for profound analysis of maritime data. Utilizing automatic identification system (AIS) data alongside spatial information from port facilities, the framework forms semantic triplet connections among ships, anchorages, berths, and waterways. This enables the semantic modeling of maritime behaviors, offering precise identification of ships through their diverse semantic information. Moreover, by exploiting the semantic relations between ships and berths, a reverse semantic knowledge graph for berths is constructed, which is specifically tailored to ship type, size, and category. The manuscript critically evaluates a range of graph embedding techniques, dimensionality reduction methods, and classification strategies through experimental frameworks to determine the most efficacious methodologies. The findings reveal that the maritime knowledge graph significantly enhances the semantic understanding of unmanned maritime equipment, thereby improving decision-making capabilities. Additionally, it establishes a semantic foundation for the development of expansive maritime models, illustrating the potential of knowledge graph technology in advancing intelligent maritime systems.

Discriminative embedded multi-view fuzzy C-means clustering for feature-redundant and incomplete data

Multi-view clustering is a widely-used technique that seeks to categorize data obtained from various sources. As a representative method, multi-view fuzzy clustering has attracted growing attention. However, it becomes quite challenging when feature-redundant and incomplete data is presented. Despite the existing studies on dimension reduction and imputation methods, several issues remain unresolved. There is an excessive concern on the imputation, without considering that interpolation methods lead to accuracy degradation. Moreover, most of the methods usually process these two steps separately, resulting in inefficiency. To address these issues, we propose a discriminative embedded incomplete multi-view fuzzy c-means clustering method. We construct the indicator matrix to guide the learning of the common membership function, and design the projection matrix to construct embedding spaces. Subsequently, we develop an iterative optimization algorithm that solves the resultant problem. We demonstrate that the projection matrix can be achieved through the utilization of eigenvalue decomposition. Through extensive experimental studies on various benchmark datasets, the proposed method demonstrates the effectiveness and efficiency compared to the existing state-of-the-art clustering algorithms.

Helix Formation from Hydrogen Bond Kinetics in Alanine Homopeptides

We present an analysis of α-helix folding in the coarse-grained coordinate of number of formed helical hydrogen bonds (NHBs) for four alanine peptides (ALA)n, with n = 5, 8, 15, and 21 residues. Starting with multi-microsecond all-atom molecular dynamics trajectories in aqueous solution, we represent the system dynamics in a space of between four (for ALA5) and twenty (for ALA21) hydrogen-bonding microstates. In all cases, transitions changing the hydrogen bond count by 1–2 dominate and the coil formation, NHB 1 → 0, is the fastest process. The calculation of global maximum weight paths shows that, when analyzed at a sufficiently long lag time, folding in the NHB coordinate is consecutive, with direct folding, 0 → 3, for ALA5 and bottlenecks at transitions 4 → 6 for ALA8, 0 → 5 for ALA15, and 0 → 9 for ALA21. Further coarse-graining to 2–4 dimensions was performed with the optimal dimensionality reduction method, allowing the identification of crucial folding intermediates and time scales of their formation in ALA8, ALA15, and ALA21. The detailed analysis of hydrogen bonding patterns revealed that folding is initiated preferentially at both peptide termini. The kinetic model was also used to estimate diffusion and friction coefficients for helix propagation. The description of the helix formation process in the hydrogen bonding coordinate NHB was in good general agreement with the experimental data and qualitatively similar to previous kinetic models of higher dimensions based on structural clustering. Use of the low-dimensional hydrogen bonding picture thus provides a different, complementary way of describing the complex and fascinating mechanism of helix formation.

Review Paper on Machine Learning Algorithms

This paper comprehensively reviews widely used machine learning algorithms across supervised, unsupervised, and reinforcement learning paradigms. It covers linear models, decision trees, support vector machines, neural networks, clustering techniques, dimensionality reduction methods, and ensemble approaches. For each algorithm, theoretical foundations, mathematical formulations, practical considerations like parameter tuning and computational complexity, and real-world applications across domains like computer vision and finance are discussed. Challenges and limitations such as overfitting and scalability are explored. Recent advancements like deep learning and transfer learning are highlighted. Finally, a comparative analysis evaluating strengths, weaknesses, and suitable problem domains for the algorithms is provided, serving as a guide for effective utilization of machine learning techniques. Keywords:- Machine learning · Deep learning, Gradient Descent, Logistic Regression, Support Vector Machine, K Nearest Neighbor, Predictive analytics,

Using Data Visualization Techniques to Assess Perception of Professionalism, Professional Identity and Development: A Case Study on Closed-Type Questionnaires

Introduction. Professional identity, professionalism, and professional development are concepts that attract research interest over the years. The concepts are complex, multi-faceted, evolving over time, and varying depending on the pre-primary teachers’ (i.e., preschool educators’) and primary school teachers’ context. The conceptualization by teachers themselves is of particular interest. Goal. Explore the use of artificial intelligence techniques and specifically dimensionality reduction methods, in analyzing in-service teachers’ perceptions of the three concepts as captured in closed-type questions with Likert-scale responses. Methods of the Research. Model Likert-scale responses of closed-type questionnaire as multi-dimensional question space. Apply dimensionality reduction techniques to visualize responses in two dimensions. Translate back question distances into theoretical concepts and identify unexplored topics. Results. The dimensionality reduction disclosed novel correlations between the concepts and their components, not previously reported in published literature, where classical statistical analysis was employed. Conclusions. We confirm the applicability and usefulness of the dimensionality reduction method for the analysis of human responses in closed-type questionnaires. Further, we identify through dimensionality reduction two novel research questions that should be further studied in the future.

Irregular optogenetic stimulation waveforms can induce naturalistic patterns of hippocampal spectral activity

Objective. Therapeutic brain stimulation is conventionally delivered using constant-frequency stimulation pulses. Several recent clinical studies have explored how unconventional and irregular temporal stimulation patterns could enable better therapy. However, it is challenging to understand which irregular patterns are most effective for different therapeutic applications given the massively high-dimensional parameter space. Approach. Here we applied many irregular stimulation patterns in a single neural circuit to demonstrate how they can enable new dimensions of neural control compared to conventional stimulation, to guide future exploration of novel stimulation patterns in translational settings. We optogenetically excited the septohippocampal circuit with constant-frequency, nested pulse, sinusoidal, and randomized stimulation waveforms, systematically varying their amplitude and frequency parameters. Main results. We first found equal entrainment of hippocampal oscillations: all waveforms provided similar gamma-power increase, whereas no parameters increased theta-band power above baseline (despite the mechanistic role of the medial septum in driving hippocampal theta oscillations). We then compared each of the effects of each waveform on high-dimensional multi-band activity states using dimensionality reduction methods. Strikingly, we found that conventional stimulation drove predominantly ‘artificial’ (different from behavioral activity) effects, whereas all irregular waveforms induced activity patterns that more closely resembled behavioral activity. Significance. Our findings suggest that irregular stimulation patterns are not useful when the desired mechanism is to suppress or enhance a single frequency band. However, novel stimulation patterns may provide the greatest benefit for neural control applications where entraining a particular mixture of bands (e.g. if they are associated with different symptoms) or behaviorally-relevant activity is desired.

Manifold learning-based UMAP method for geochemical anomaly identification

Geochemical data are usually high-dimensional data that could contain dozens of elements. Geochemical distribution patterns and anomalies related to mineralization and lithological features are always hidden in these high-dimensional data, which cannot be directly observed from the data. To solve this problem, a manifold learning-based uniform manifold approximation and projection (UMAP) method, was introduced to recognize mineralization-related geochemical anomalies from high-dimensional geochemical data in this study. The UMAP method is a nonlinear dimensionality reduction method, which is suitable for dimensionality reduction and visualization of high-dimensional data. A case study was conducted to demonstrate the advantages of the UMAP method for identifying ion-adsorbed rare-earth-element (REE) mineralization-related anomalies from high-dimensional data in the Nanling region, China. Factor analysis was used to determine ion-adsorbed REE mineralization-related element combination that consists of 10 elements. High-dimensional geochemical data were reduced to two dimensions based on the UMAP method. The results indicated that the UMAP method can effectively characterize the spatial distributions of ion-adsorbed REE mineralization-related anomalies by dimensionality reduction analysis and visualization analysis of high-dimensional geochemical data in the study area. To illustrate the superiority of the UMAP method, a comparative study was conducted between the UMAP and other three manifold learning methods, namely locally linear embedding (LLE), isometric feature mapping (Isomap) and t-distributed stochastic neighbor embedding (t-SNE). The performance of the four manifold learning methods was evaluated by receiver operating characteristic (ROC) curve and prediction-area (P-A) plot, showing that the performance of the UMAP method is superior to that of the LLE, Isomap and t-SNE methods in terms of recognizing ion-adsorbed REE mineralization-related anomalies and the spatial distributions of the REE-bearing geological bodies in the Nanling belt.

Dimensionality Reduction in Structural Health Monitoring: A Case Study on Damaged Wind Turbine Blades

AbstractIn recent years, advances in structural health monitoring (SHM) of composite materials have been observed, driven by the adoption of intelligent diagnostic techniques. Vibration signals, which embed valuable structural health information, have been increasingly utilized in SHM. However, the high dimensionality of this data has necessitated significant computational resources and has made the differentiation between health states more complex. Highlighting the need for effective feature extraction and dimensionality reduction (DR), a study is conducted. In this research, advanced DR techniques, i.e., principal component analysis (PCA), locally linear embedding (LLE), t‐distributed stochastic neighbors embedding (t‐SNE), and uniform manifold approximation and projection (UMAP), are applied to an experimental dataset from a wind turbine blade under various health and environmental conditions (controlled‐environment vibration signals). The extracted features are then processed for the classification phase, and it is found that UMAP provides the best performance, albeit with a slightly increased computational demand. The findings from this research offer invaluable insights for researchers and engineers, assisting in the selection of the most appropriate DR method for SHM, and weighing up accuracy against computational time.

Asteroid reflectance spectra from Gaia DR3: Near-UV in primitive asteroids

Context. In the context of charge-coupled devices (CCDs), the ultraviolet (UV) region has mostly remained unexplored after the 1990s. Gaia DR3 offers the community a unique opportunity to explore tens of thousands of asteroids in the near-UV as a proxy of the UV absorption. This absorption has been proposed in previous works as a diagnostic of hydration, organics, and space weathering. Aims. In this work, we aim to explore the potential of the NUV as a diagnostic region for primitive asteroids using Gaia DR3. Methods. We used a corrective factor over the blue part of Gaia spectra to erase the solar analog selection effect. We identified an artificial relation between the band noise and slope and applied a signal-to-noise ratio (S/N) threshold for Gaia bands. Meeting the quality standards, we employed a Markov chain Monte Carlo (MCMC) algorithm to compute the albedo threshold, maximizing primitive asteroid inclusion. Utilizing one- and two-dimensional (1D and 2D) projections, along with dimensionality-reduction methods (such as PCA and UMAP), we identified primitive asteroid populations. Results. We uncovered: (a) the first observational evidence linking UV absorption to the 0.7 µm band, tied to hydrated iron-rich phyllosilicates; and (b) a 2D space revealing a split in C-type asteroids based on spectral features, including UV absorption. The computed average depth (3.5 ± 1.0 %) and center (0.70 ± 0.03 µm) of the 0.7 µm absorption band for primitive asteroids observed with Gaia is in agreement with the literature values. Conclusions. In this paper, we shed light on the importance of the UV absorption feature to discriminate among different mineralogies (i.e., iron-rich phyllosilicates vs. iron-poor) or to identify taxonomies that are conflated in the visible (i.e., F-types vs. B-types). We have shown that this is a promising region for diagnostic studies of the composition of primitive asteroids.

Exploring Dimensionality Reduction Techniques for Improved Breast Cancer Diagnosis

Breast cancer diagnosis is a critical area in medical research, where the challenge lies not only in accurate identification but also in managing the inherent complexity of high-dimensional datasets. This paper navigates this challenge by exploring dimensionality reduction techniques to enhance diagnostic accuracy. The primary objective of this research was to employ dimensionality reduction methods to refine breast cancer diagnosis, with a focus on improving accuracy and interpretability. The study investigates the impact of preprocessing techniques on a high-dimensional dataset, aiming to uncover meaningful patterns for effective diagnostic models. Starting with a dataset including 569 observations and 30 attributes, careful examination reveals imbalances in the dataset (63% benign, 37% malignant). To deal with multicollinearity, we use the coefficients of Pearson correlation to find and eliminate highly correlated features. Subsequent data transformation, utilizing min-max normalization, ensures uniform weighting. Principal Component Analysis (PCA) is then leveraged for comprehensive dimensionality reduction. Visualizations through scree plots and bi-plots underscore the efficacy of early principal components in distinguishing benign from malignant cases. Our results demonstrate a notable 24% reduction in data dimensionality, affirming the process's efficiency. This abstract beckon the exploration of detailed findings, emphasizing dimensionality reduction's pivotal role in refining breast cancer diagnosis for more accurate, efficient, and interpretable models.

A new sufficient dimension reduction method via rank divergence

A new sufficient dimension reduction method via rank divergence