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: Parasthetica: Artworks for GA2025

authors: Soo, Chin-En Keith

abstract: Parasthetica transforms eBooks into abstract visual artworks through a character-matching system that maps literary text into chromatic geometric forms. The program positions itself at the crossroads of digital humanities, generative art, and data visualisation. Each text becomes a living artwork, where words are translated into dynamic, colour-based grids that reveal hidden linguistic and structural patterns. Rather than statistical summaries, the visualisations offer immersive aesthetic experiences that mirror the rhythm, genre, and emotional intensity of the source material.

text: Parasthetica: Artworks for GA2025 Parasthetica transforms eBooks into abstract visual artworks through a character-matching system that maps literary text into chromatic geometric forms. The program positions itself at the crossroads of digital humanities, generative art, and data visualisation. Each text becomes a living artwork, where words are translated into dynamic, colour-based grids that reveal hidden linguistic and structural patterns. Rather than statistical summaries, the visualisations offer immersive aesthetic experiences that mirror the rhythm, genre, and emotional intensity of the source material.

year: 2025-12

title: Tūrangawaewae mō te Kīngitanga

authors: Takerei, Mamae Rangiaroha Tuānewa

subjects: Tūrangawaewae

abstract: Tūrangawaewae is an iconic marae located at the heart of the Kīngitanga. Established by Te Pūea Hērangi and other whānau, this marae has come to represent the struggles, successes and history of the Kīngitanga movement. Tūrangawaewae is therefore the embodiment of the Kīngitanga and the people of Waikato.
From very humble beginnings, and forged on the tireless efforts of Te Pūea and her followers, this marae has hosted world leaders, monarchs and aristocracy from across the world. All have come to Tūrangawaewae to forge relationships with the Kīngitanga, with Māori and with the New Zealand government. It has become a hallowed place when histories are shared and futures are created.
This thesis looks at how Tūrangawaewae encapsulates the Kīngitanga and all that it means. It explores this history of its establishment and highlight the central figures and the motivations behind the building of this marae and complex. In addition, this thesis will show how the different building and features of the marae showcase the ideology of the Kīngitanga movement and its leaders. Based on a traditional approach to Waikato knowledge, and founded on firsthand experience, this thesis reveals an insides perspective of the kīngitanga, the people, various events and the marae of Tūrangawaewae.

text: Tūrangawaewae mō te Kīngitanga Tūrangawaewae is an iconic marae located at the heart of the Kīngitanga. Established by Te Pūea Hērangi and other whānau, this marae has come to represent the struggles, successes and history of the Kīngitanga movement. Tūrangawaewae is therefore the embodiment of the Kīngitanga and the people of Waikato.
From very humble beginnings, and forged on the tireless efforts of Te Pūea and her followers, this marae has hosted world leaders, monarchs and aristocracy from across the world. All have come to Tūrangawaewae to forge relationships with the Kīngitanga, with Māori and with the New Zealand government. It has become a hallowed place when histories are shared and futures are created.
This thesis looks at how Tūrangawaewae encapsulates the Kīngitanga and all that it means. It explores this history of its establishment and highlight the central figures and the motivations behind the building of this marae and complex. In addition, this thesis will show how the different building and features of the marae showcase the ideology of the Kīngitanga movement and its leaders. Based on a traditional approach to Waikato knowledge, and founded on firsthand experience, this thesis reveals an insides perspective of the kīngitanga, the people, various events and the marae of Tūrangawaewae.

year: 2019