title: Improving finite sample estimates of principal components

authors: Weeraratne, Nuwan

abstract: Principal Component Analysis (PCA) is a method of compressing high-dimensional data into a lower-dimensional format that captures the essence of the original structure. PCA is a matrix decomposition technique based on eigen decomposition. It quantifies relationships between variables using covariance matrices, captures the shape of the data distribution, and evaluates the importance of directions using eigenvalues. Therefore, the accuracy of the variance-covariance estimation is crucial for reliable PCA. In high-dimensional settings where the number of observations (n) is much smaller than the number of variables (p) (i.e., n << p), the conventional Maximum Likelihood Estimator (MLE) of covariance becomes poorly conditioned and yields unreliable principal components. To address these limitations, we propose a novel estimation framework called Pairwise Differences Covariance (PDC), along with four regularized extensions: Standardized PDC (SPDC), Local Scaled PDC (LSPDC), Maximum Absolute Scaled PDC (MAXPDC), and Range
Scaled PDC (RPDC). These estimators increase the effective sample size by utilizing all pairwise differences within the data, thereby enhancing estimation stability without requiring additional data collection. Extensive experiments on synthetic and real datasets demonstrate that the proposed
estimators, particularly SPDC, significantly reduce the over-dispersion of the first principal component and improve directional accuracy. On average, SPDC reduced cosine similarity error by approximately 10–30% and narrowed eigenvalue spread by 10–20% compared to MLE and Ledoit-Wolf estimators in n << p HDLSS scenarios. Real-world applications confirm the practical utility and robustness of these methods for analyzing high-dimensional data.

text: Improving finite sample estimates of principal components Principal Component Analysis (PCA) is a method of compressing high-dimensional data into a lower-dimensional format that captures the essence of the original structure. PCA is a matrix decomposition technique based on eigen decomposition. It quantifies relationships between variables using covariance matrices, captures the shape of the data distribution, and evaluates the importance of directions using eigenvalues. Therefore, the accuracy of the variance-covariance estimation is crucial for reliable PCA. In high-dimensional settings where the number of observations (n) is much smaller than the number of variables (p) (i.e., n << p), the conventional Maximum Likelihood Estimator (MLE) of covariance becomes poorly conditioned and yields unreliable principal components. To address these limitations, we propose a novel estimation framework called Pairwise Differences Covariance (PDC), along with four regularized extensions: Standardized PDC (SPDC), Local Scaled PDC (LSPDC), Maximum Absolute Scaled PDC (MAXPDC), and Range
Scaled PDC (RPDC). These estimators increase the effective sample size by utilizing all pairwise differences within the data, thereby enhancing estimation stability without requiring additional data collection. Extensive experiments on synthetic and real datasets demonstrate that the proposed
estimators, particularly SPDC, significantly reduce the over-dispersion of the first principal component and improve directional accuracy. On average, SPDC reduced cosine similarity error by approximately 10–30% and narrowed eigenvalue spread by 10–20% compared to MLE and Ledoit-Wolf estimators in n << p HDLSS scenarios. Real-world applications confirm the practical utility and robustness of these methods for analyzing high-dimensional data.

year: 2025

title: A novel two stage scheme utilizing the test set for model selection in text classification

authors: Pfahringer, Bernhard

subjects: computer science

abstract: Text classification is a natural application domain for semi-supervised learning, as labeling documents is expensive, but on the other hand usually an abundance of unlabeled documents is available. We describe a novel simple two stage scheme based on dagging which allows for utilizing the test set in model selection. The dagging ensemble can also be used by itself instead of the original classifier. We evaluate the performance of a meta classifier choosing between various base learners and their respective dagging ensembles. The selection process seems to perform robustly especially for small percentages of available labels for training.

text: A novel two stage scheme utilizing the test set for model selection in text classification Text classification is a natural application domain for semi-supervised learning, as labeling documents is expensive, but on the other hand usually an abundance of unlabeled documents is available. We describe a novel simple two stage scheme based on dagging which allows for utilizing the test set in model selection. The dagging ensemble can also be used by itself instead of the original classifier. We evaluate the performance of a meta classifier choosing between various base learners and their respective dagging ensembles. The selection process seems to perform robustly especially for small percentages of available labels for training.

year: 2005

title: He Manu-Iri-i-te-Rangi - Bird of the Heavens: Tūrake Manuirirangi 1896 - 1969

authors: Manuirirangi, Hōri

abstract: Tūrake Manuirirangi was an influential tupuna of the Manuirirangi whānau. He was a devoted member of the Church of Jesus Christ of Latter-day Saints, and was instrumental in its establishment in the South Taranaki region. This chapter looks at his beliefs and leadership qualities within the Church, and within his hapū of Ngāti Tū, of Ngā Ruahine Iwi. The main focus here is to report on information collated from interviews, church records and Mormon missionary diaries.

text: He Manu-Iri-i-te-Rangi - Bird of the Heavens: Tūrake Manuirirangi 1896 - 1969 Tūrake Manuirirangi was an influential tupuna of the Manuirirangi whānau. He was a devoted member of the Church of Jesus Christ of Latter-day Saints, and was instrumental in its establishment in the South Taranaki region. This chapter looks at his beliefs and leadership qualities within the Church, and within his hapū of Ngāti Tū, of Ngā Ruahine Iwi. The main focus here is to report on information collated from interviews, church records and Mormon missionary diaries.

year: 2014