scispace - formally typeset
Search or ask a question

What are the limitations of ICA when the data dimension is much larger than the sample size? 

Best insight from top research papers

ICA faces limitations in high dimensions compared to sample size due to instability, especially when independent components vary with each run . In the high-dimensional scaling limit, the joint empirical measure of the target feature vector and algorithm estimates converges to a deterministic process, aiding performance evaluation . High dimension, low sample size data analysis lacks attention to sample integrity, potentially leading to outliers . Methodologies like Dynamic Tilted Current Correlation Screening (DTCCS) address challenges in high-dimensional statistics, offering variable screening and influence measure techniques . Fuzzy cluster scaled PCA is proposed for dimensional reduction in high dimension, low sample size data, enabling discrimination of individual subjects observed by body-worn sensors .

Answers from top 5 papers

More filters
Papers (5)Insight
ICA faces limitations with high dimension low sample size data due to incorrect solutions from the covariance matrix eigenvalues, hindering multivariate analyses, as discussed in the paper.
ICA faces challenges in 'large p, small n' settings due to spurious correlations and inadequate predictor relevance detection, necessitating new methodologies like DTCCS, HD-HIM, and Cosine PoSI for high-dimensional data analysis.
ICA faces challenges in high dimension, low sample size data due to sample integrity issues like outlier detection, which have not received sufficient attention in analysis.
ICA in high dimensions faces instability due to algorithm stochasticity and noise. Minimum Distance index limitations arise, becoming concentrated and suboptimal. Visual inspection remains crucial for effective denoising in high dimensions.
Open accessPosted Content
Chuang Wang, Yue Lu 
15 Oct 2017-arXiv: Learning
9 Citations
In the high-dimensional scaling limit, ICA's performance is analyzed, showing convergence to a deterministic process via a nonlinear PDE, offering insights for efficient algorithm design.

Related Questions

What are the limitations of PCA when the data dimension is much larger than the sample size?5 answersPCA faces limitations when the data dimension is significantly larger than the sample size. In such scenarios, PCA can exhibit unexpected behaviors like upward bias in sample eigenvalues and inconsistency in sample eigenvectors. This phenomenon has been extensively studied under the spiked covariance model, highlighting issues such as the behavior of sample eigenvalues and the rescaled extreme sample eigenvalues. To address these challenges, alternative estimation methods have been developed, leveraging sparsity in eigenvectors or the covariance matrix. Additionally, in high-dimensional low sample size data, obtaining correct solutions through traditional multivariate analyses becomes mathematically challenging, necessitating innovative approaches like fuzzy cluster scaled PCA for effective dimensional reduction.
What methods of analysis are available for high-dimensional small sample data?5 answersMethods of analysis for high-dimensional small sample data include the pairwise Hotelling method, bias-adjustment methods, feature selection and extraction methods, max t-test-type statistics, and dynamic eigenvector estimation. The pairwise Hotelling method balances existing approaches by utilizing correlation information and provides good control over type I error rates and statistical power, especially for highly correlated covariates. Bias-adjustment methods adjust for bias in principal component scores and improve classification performance in high-dimensional situations with small sample sizes. Feature selection and extraction methods, such as Correlation Explanation (CorEx), Conditional Infomax Feature Extraction (CIFE), Maximum Relevance Minimum Redundancy (MRMR), and Kernel Entropy Component Analysis (KECA), can be used to classify high-dimensional low sample size datasets. Max t-test-type statistics, analyzed using a randomization-based approach, are suitable for analyzing high-dimensional designs with small sample sizes. Dynamic eigenvector estimation allows for modeling the change in high-dimensional data over time and can be effectively solved using manifold optimization algorithms.
What are the limitations of AI?5 answersAI has several limitations. Content-filtering AI systems used by online service providers and governments to regulate internet content are subject to limitations that affect their accuracy and transparency, potentially leading to the removal of legitimate content and the persistence of objectionable content. Implementing AI in administrative procedures requires careful consideration of the capabilities and limitations of different systems, including transparency and data availability. The validity of AI predictions relies on extensive, representative, and unbiased training data, and transparency is crucial for establishing trust and reliability in AI systems. Additionally, AI systems in healthcare, such as those used for colorectal cancer, rely on reductive reasoning and computational determinism, which can lead to inherent biases, limited evaluations, and the marginalization of socio-technical factors, posing risks to clinical decision-making and patient care. Furthermore, the proliferation of AI systems is currently benefiting those with economic power, potentially exacerbating global inequality.
Is bootstrapping ever used when performing PCA on data where the sample size is less than a dimension?4 answersBootstrapping is used in PCA to overcome the small sample problem and improve the mean centering process. It is shown that when using the bootstrap procedure, a small number of synthesized images can effectively multiply biometric data without degradation of correlations, leading to the possibility of reducing the size of the test biometric sample. Bootstrap methods are rarely used in conjunction with propensity-score matching, but two different bootstrap methods have been proposed for use in this context, with one method involving drawing bootstrap samples from the matched pairs in the propensity-score-matched sample. The bootstrap method can be used to conduct relevant causal tests on big data, such as in the field of stock market analysis.
Is the performance of ICA worse in short time series?5 answersThe performance of ICA on short time series varies depending on the specific application. In the study by Lopez et al., the performance of multifractal detrended analysis using ICA was evaluated on short time series, including the daily exchange rate between the U.S. dollar and the euro. In another study by James et al., the authors analyzed intracranial electroencephalogram recordings using ICA and found that standard ensemble ICA resulted in marginal improvements in separation for short time series, while space-time ICA using just 2 recording channels showed more distinct components. Peña et al. compared the performance of different ICA procedures on multivariate time series data and found that one of the procedures, FOTBI, provided accurate forecasts for the industrial production index time series. Lu et al. proposed an ICA-based signal reconstruction approach for financial time series forecasting and demonstrated its superiority over other models. Finally, Hou et al. used ICA for weighted filtering and extraction of common mode errors in a regional GNSS observation network, showing improved precision compared to traditional ICA.
Is it appropriate to perform a PCA when the sample size is less than the variable?4 answersPerforming PCA when the sample size is less than the number of variables can lead to spurious results and should be done with caution. Sample correlation matrices will always result in decreasing eigenvalues, even if there is no structure, making it necessary to test for real patterns. PC-scores calculated from non-distinct PC's have large standard errors and cannot be used for biological interpretations. However, there are methods that have been developed to address the issue of high dimension low sample size (HDLSS) settings, such as cross data matrix-based methods, sparse PCA, and spherical PCA. These methods have shown asymptotic normality and consistency for estimates of PC directions in HDLSS settings.

See what other people are reading

What is the purpose of the four points bending test in structural engineering?
5 answers
The four-point bending test in structural engineering serves the purpose of evaluating various mechanical properties of materials, such as the elastic modulus, Poisson's ratio, shear modulus, and flexural strength. This testing method is particularly useful for assessing the behavior of brittle materials under flexural stress, where flaws can lead to fracture initiation. Additionally, the four-point bending test allows for a comprehensive evaluation of stress-optic coefficient measurements and their uncertainties, providing a more accurate estimation compared to other methods. Furthermore, in the case of directionally-reinforced fiber composites, the four-point bending test is crucial for studying fracture mechanisms and ensuring accurate results by subjecting a larger portion of the beam to a constant bending moment.
What's the definition of generative ai?
5 answers
Generative artificial intelligence (AI), often referred to as Gen-AI, is a form of AI that autonomously creates new content like text, images, audio, and video. It leverages deep neural networks to simulate Bayesian models, enabling high-dimensional regression with feature selection and deep learning capabilities. Gen-AI excels in pattern recognition and content generation, showcasing potential applications in various industries such as product design, metaverse technology, and Bayesian computation. This technology is rapidly evolving, with the generative AI market projected to grow significantly, from 1.5 billion dollars in 2021 to 6.5 billion dollars by 2026, at a compound annual growth rate of 34.9%.
What are some of the most commonly used sustainability indicators in manufacturing scheduling?
4 answers
In the realm of manufacturing scheduling, sustainability indicators play a crucial role in evaluating and enhancing the sustainability of production processes. These indicators are essential for assessing the environmental, economic, and social impacts of manufacturing activities. Among the most commonly used sustainability indicators in manufacturing scheduling, energy consumption and greenhouse gas emissions stand out due to their significant relevance to environmental sustainability. Energy consumption is a critical factor, given the industrial sector's substantial share in global energy use, highlighting the importance of energy-aware scheduling practices for sustainable development. Similarly, greenhouse gas emissions are a primary concern for their role in climate change, necessitating their consideration in sustainable manufacturing practices. Furthermore, the socio-economic indicators of sustainability, such as profit margin and makespan, are frequently employed to assess the economic viability and efficiency of manufacturing operations. These indicators help in quantifying the success of sustainability practices within organizations, ensuring that manufacturing processes are not only environmentally friendly but also economically sound. Additionally, the process sustainability index (ProcSI) architecture provides a structured approach to evaluating sustainability, incorporating a comprehensive set of performance indicators across different dimensions of sustainability. The adoption of advanced manufacturing paradigms, such as Industry 4.0 and smart manufacturing, further emphasizes the importance of integrating sustainability indicators into scheduling decisions. These technologies enable the continuous monitoring of manufacturing processes, facilitating the identification of areas for improvement in terms of sustainability. Moreover, the exploration of ecological cooling/lubrication methods in sustainable manufacturing highlights the industry's shift towards minimizing the environmental impact of production processes. In summary, the most commonly used sustainability indicators in manufacturing scheduling include energy consumption, greenhouse gas emissions, socio-economic factors like profit margin and makespan, and comprehensive evaluation frameworks like the ProcSI architecture. These indicators are pivotal in guiding the manufacturing industry towards more sustainable and efficient production practices.
What are the potential failures that occur in wind turbine power plants?
5 answers
Potential failures in wind turbine power plants include component damage due to complex environments and long-term operational cycles, blade damage from lightning, fatigue loads, icing, and airborne particulates, and faults that can lead to false or missed alarms due to data characteristics like large volumes, correlations, and fluctuating SCADA data. Early detection of these failures is crucial to prevent breakdowns, extend turbine service life, and optimize project efficiency. Methods like deep residual networks for fault detectionand fuzzy Multi-Criteria Decision Making for failure prioritizationare proposed to enhance monitoring and maintenance. Additionally, innovative testing concepts using inverters for automated fault detection in generators are suggested to efficiently schedule maintenance and ensure reliability.
What are the differences between intermodal transport and multimodal transport?
5 answers
Intermodal transport involves using multiple modes of transport under a single contract, typically combining road, rail, sea, or air transport. It focuses on the seamless transfer of goods between different modes. On the other hand, multimodal transport refers to the use of at least two different modes of transport without the requirement of a single contract. It emphasizes the integration of various transport modes to ensure efficient and sustainable urban mobility. Intermodal transport often involves specific loading units like containers, swap bodies, and semi-trailers, with containers being the most commonly used unit. In contrast, multimodal transport systems are described as multilayer networks, where different transport modes are interconnected, enabling individuals to navigate urban systems using various modes.
Can the Quantitative Diversity Index be combined with other portfolio optimization techniques to improve investment performance?
5 answers
Yes, the Quantitative Diversity Index (QDI) can be effectively combined with other portfolio optimization techniques to enhance investment performance. Research has shown that incorporating diversity measures, such as QDI, alongside traditional risk measures like Value-at-Risk (VaR) and Expected Shortfall (ES) can lead to improved portfolio optimization outcomes. Additionally, models that utilize entropy and mutual information instead of variance and covariance for risk assessment have demonstrated enhanced portfolio diversity measures, especially in terms of portfolio weight entropy, which can contribute to better performance. Moreover, techniques like dimension reduction and increased sparsity in the covariance matrix have been proposed to efficiently solve large portfolio optimization problems, resulting in improved optimizer performance while maintaining expected risk and return levels. By integrating QDI with these approaches, investors can achieve a more robust and diversified investment portfolio, ultimately enhancing investment performance.
Can the portfolio risk minimization be combined with portfolio entropy maximization?chniques to improve investment performance?
4 answers
Portfolio risk minimization can indeed be combined with portfolio entropy maximization to enhance investment performance. Research has shown that mean-entropy (ME) models, which focus on maximizing entropy instead of minimizing variance and covariance, can offer benefits in terms of portfolio diversity measures and stability under increasing return constraints. Additionally, incorporating entropy-based dynamic portfolio selection models, which utilize the exponential Rényi entropy criterion to measure risk, has been found to significantly improve portfolio performance compared to traditional mean-variance models. Furthermore, utilizing Tsallis entropy as a risk measure in portfolio optimization problems through mean-entropy models has been highlighted as a flexible approach to address uncertainty and enhance decision-making processes. By integrating these approaches, investors can potentially achieve a more balanced and efficient portfolio allocation strategy.
Article about mathematical modeling of obesity hormons and colon cancer?
5 answers
Obesity is intricately linked to colon cancer development through various mechanisms, including epigenetic alterations and hormonal influences. Mathematical modeling, particularly utilizing artificial intelligence principles like fuzzy inference, has been proposed to analyze the complex factors contributing to colon cancer development. Hormones, growth factors, and cytokines produced by adipocytes in obesity play a role in cancer progression, affecting colon epithelial cells and promoting cancer through dysregulation of the local environment. Understanding the interplay between obesity-related hormonal changes and colon cancer progression is crucial for identifying potential treatment and prevention targets. Mathematical modeling can aid in predicting and preventing the occurrence of obesity-associated colon cancer, providing a valuable tool for future research and interventions.
What are the key stages in the life cycle of a generative AI project?
5 answers
The key stages in the life cycle of a generative AI project involve various critical steps. Initially, the project starts with the Design phase, where the problem is contextualized, drawing on state-of-the-art AI applications and ethics guidelines. Subsequently, in the Develop phase, data and algorithms are transformed into AI models, which are then benchmarked, evaluated, and explained. Following this, in the Deploy phase, computational performance is assessed, leading to the operationalization of AI models and the hyperautomation of the system as a complete AI solution. Additionally, generative AI methods for Bayesian Computation involve generating training datasets, dimensionality reduction, and using deep neural networks to uncover the inverse Bayes map between parameters and data. These stages collectively form the comprehensive life cycle of a generative AI project.
How does global classification of age differ from other age classification systems?
5 answers
Global classification of age, as discussed in the contexts, involves considering the overall functional network or features of an individual to classify age groups. This method often includes analyzing the entire brain or intra-hemispheric connectivity strength for classification parameters, without focusing on specific facial or gait features. In contrast, other age classification systems, such as facial-based methods using features like Local Directional Pattern (LDP) and Gabor wavelet transform, or gait-based approaches like Gait energy image Projection model (GPM), concentrate on specific physical characteristics for age estimation. Global classification aims to capture broader patterns in functional networks, while other systems focus on localized features like facial expressions, poses, or gait parameters for age group determination.
What are the current best practices for quality control in the fruit industry?
5 answers
Current best practices for quality control in the fruit industry encompass a variety of innovative techniques. These include the utilization of optical methods for non-invasive fruit quality control, such as soft tactile sensors that can detect small forces without damaging the fruit. Additionally, multidimensional statistical analysis methods are employed for classifying apples based on hyperspectral imaging, allowing for accurate identification of defects and sorting by quality. To monitor the presence of pollutants in fruits, IoT technology is utilized to measure pesticide concentrations and send data to a cloud platform for analysis and dissemination to users via mobile applications. Furthermore, non-destructive monitoring methods like visible/near-infrared spectroscopy and electronic nose are employed for quality assessment without damaging the fruit. These integrated approaches ensure efficient and reliable quality control in the fruit industry.