title: Linear dimensionality reduction in linear time: Johnson-Lindenstrauss-type guarantees for random subspace

authors: Lim, Nick Jin Sean

subjects: Machine learning

abstract: We consider the problem of efficient randomized dimensionality reduction with norm-preservation guarantees. Specifically we prove data-dependent Johnson-Lindenstrauss-type geometry preservation guarantees for Ho's random subspace method: When data satisfy a mild regularity condition -- the extent of which can be estimated by sampling from the data -- then random subspace approximately preserves the Euclidean geometry of the data with high probability. Our guarantees are of the same order as those for random projection, namely the required dimension for projection is logarithmic in the number of data points, but have a larger constant term in the bound which depends upon this regularity. A challenging situation is when the original data have a sparse representation, since this implies a very large projection dimension is required: We show how this situation can be improved for sparse binary data by applying an efficient `densifying' preprocessing, which neither changes the Euclidean geometry of the data nor requires an explicit matrix-matrix multiplication. We corroborate our theoretical findings with experiments on both dense and sparse high-dimensional datasets from several application domains.

text: Linear dimensionality reduction in linear time: Johnson-Lindenstrauss-type guarantees for random subspace We consider the problem of efficient randomized dimensionality reduction with norm-preservation guarantees. Specifically we prove data-dependent Johnson-Lindenstrauss-type geometry preservation guarantees for Ho's random subspace method: When data satisfy a mild regularity condition -- the extent of which can be estimated by sampling from the data -- then random subspace approximately preserves the Euclidean geometry of the data with high probability. Our guarantees are of the same order as those for random projection, namely the required dimension for projection is logarithmic in the number of data points, but have a larger constant term in the bound which depends upon this regularity. A challenging situation is when the original data have a sparse representation, since this implies a very large projection dimension is required: We show how this situation can be improved for sparse binary data by applying an efficient `densifying' preprocessing, which neither changes the Euclidean geometry of the data nor requires an explicit matrix-matrix multiplication. We corroborate our theoretical findings with experiments on both dense and sparse high-dimensional datasets from several application domains.

year: 2017

title: “Pushing an irritational button”: Asian psychologists making sense of racialization in psychology training in Aotearoa/New Zealand

authors: Tan, Kyle K. H.

abstract: The monocultural psychology training in Aotearoa New Zealand deliberately centers White racial framing which enables those who benefit from Whiteness to uphold an imposed hierarchy of racially inferior (Māori) and superior (Pākehā) groups. In Aotearoa, we are faced with a reality that Asian (as a diverse group from East Asia, Southeast Asia, and South Asia) knowledge sources and the intake of Asian students into psychology training are scarcely prioritized. In this study, we utilized counter-storytelling as a critical race praxis to illuminate the various forms of Asianization (Asian racialization) as a subframe of White racial framing. Employing interpretative phenomenological analysis, we explored the subjective experiences of four Asian psychologists as they made sense of racism and the formation of their racialized identity within psychology training. Our analysis uncovered three main themes with subordinate themes: (1) the White mold of psychology (encountering White ideals of psychology and pursuing perceived benefits of Whiteness); (2) bearing the brunt of Asianization (ranging from being achievers yet forgotten to being perceived as a threat and unassimilable); and (3) relating to Māori (expressing identity validation and empathy yet experiencing lateral violence). We observed the manifestation of White racial framing across various cognitive (e.g., the prioritization of western knowledge and the promotion of colorblind norms), emotional (e.g., White fragility), and behavioral aspects (e.g., expectations placed on minoritized ethnic groups to assimilate), all of which contribute to Asianization archetypes (viz., the forgotten Asian, the irritational button, and the unassimilable foreigner).

text: “Pushing an irritational button”: Asian psychologists making sense of racialization in psychology training in Aotearoa/New Zealand The monocultural psychology training in Aotearoa New Zealand deliberately centers White racial framing which enables those who benefit from Whiteness to uphold an imposed hierarchy of racially inferior (Māori) and superior (Pākehā) groups. In Aotearoa, we are faced with a reality that Asian (as a diverse group from East Asia, Southeast Asia, and South Asia) knowledge sources and the intake of Asian students into psychology training are scarcely prioritized. In this study, we utilized counter-storytelling as a critical race praxis to illuminate the various forms of Asianization (Asian racialization) as a subframe of White racial framing. Employing interpretative phenomenological analysis, we explored the subjective experiences of four Asian psychologists as they made sense of racism and the formation of their racialized identity within psychology training. Our analysis uncovered three main themes with subordinate themes: (1) the White mold of psychology (encountering White ideals of psychology and pursuing perceived benefits of Whiteness); (2) bearing the brunt of Asianization (ranging from being achievers yet forgotten to being perceived as a threat and unassimilable); and (3) relating to Māori (expressing identity validation and empathy yet experiencing lateral violence). We observed the manifestation of White racial framing across various cognitive (e.g., the prioritization of western knowledge and the promotion of colorblind norms), emotional (e.g., White fragility), and behavioral aspects (e.g., expectations placed on minoritized ethnic groups to assimilate), all of which contribute to Asianization archetypes (viz., the forgotten Asian, the irritational button, and the unassimilable foreigner).

year: 2025

title: Blood Quantum  “A Pūrākau approach to understanding the impact of ‘Blood Quantum’ in Māori Identity”

authors: Edwards, Alvina Jean

subjects: Blood quantum

abstract: “The master’s tools will never dismantle the master’s house” (Lorde, 1984, p.94)

This thesis begins and ends with being Ngāi Tahu, the two fundamental questions that generated this topic are: Who determines Indigenous legal identity? Who defines tribal membership and affiliation? Although the idea of defining Indigenous Peoples, for political purposes originated in colonial times, the complications, and complexities of defining who an Indigenous individual remains a truly contentious issue. This thesis will draw on the Indigenous Māori methodology of pūrākau, or story work for its structure and method to explore the above questions relating to Indigenous identity. The pūrākau approach enables the research to harness mātauranga Māori knowledge such as whakapapa and korero tuku iho alongside western thought, which is now inked in academic disciplines such as in the study of law. This thesis explores notions such as Indigenous ‘blood’ and our Indigenous ‘DNA.’ It is argued that to understand the history, the politics, the laws of blood quantum and DNA, it is important to understand the mind of the coloniser and the tools they continue to use. 

The study of blood quantum has become an important aspect of the tino rangatiratanga (self-determination) of many Indigenous peoples. From a historical and cultural perspective, blood quantum standards divide and alienate communities, and perpetuate a discourse that promotes internalised self-hatred, alienation, and fractionation. This research will develop pūrākau as a pedagogy through creating learning tools. These new learning tools will counteract the possibility of our Indigenous Peoples from being trapped within these social constructions. The thesis will explore possible self-determination techniques which emphasize pūrākau in establishing identity through creating a journey of recovery through the application of pūrākau in decolonising blood quantum ideology. Ultimately, Indigenous Peoples of Canada, New Zealand and the United States of America need to be the ones in control of their identity, tribal affiliation, cultural continuity, destiny, and the way they are legally defined.

Let's reclaim our stolen tools (Lorde, 1979)

text: Blood Quantum  “A Pūrākau approach to understanding the impact of ‘Blood Quantum’ in Māori Identity” “The master’s tools will never dismantle the master’s house” (Lorde, 1984, p.94)

This thesis begins and ends with being Ngāi Tahu, the two fundamental questions that generated this topic are: Who determines Indigenous legal identity? Who defines tribal membership and affiliation? Although the idea of defining Indigenous Peoples, for political purposes originated in colonial times, the complications, and complexities of defining who an Indigenous individual remains a truly contentious issue. This thesis will draw on the Indigenous Māori methodology of pūrākau, or story work for its structure and method to explore the above questions relating to Indigenous identity. The pūrākau approach enables the research to harness mātauranga Māori knowledge such as whakapapa and korero tuku iho alongside western thought, which is now inked in academic disciplines such as in the study of law. This thesis explores notions such as Indigenous ‘blood’ and our Indigenous ‘DNA.’ It is argued that to understand the history, the politics, the laws of blood quantum and DNA, it is important to understand the mind of the coloniser and the tools they continue to use. 

The study of blood quantum has become an important aspect of the tino rangatiratanga (self-determination) of many Indigenous peoples. From a historical and cultural perspective, blood quantum standards divide and alienate communities, and perpetuate a discourse that promotes internalised self-hatred, alienation, and fractionation. This research will develop pūrākau as a pedagogy through creating learning tools. These new learning tools will counteract the possibility of our Indigenous Peoples from being trapped within these social constructions. The thesis will explore possible self-determination techniques which emphasize pūrākau in establishing identity through creating a journey of recovery through the application of pūrākau in decolonising blood quantum ideology. Ultimately, Indigenous Peoples of Canada, New Zealand and the United States of America need to be the ones in control of their identity, tribal affiliation, cultural continuity, destiny, and the way they are legally defined.

Let's reclaim our stolen tools (Lorde, 1979)

year: 2020