title: Random projections as regularizers: learning a linear discriminant from fewer observations than dimensions

authors: Durrant, Robert J.

subjects: random projections

abstract: We prove theoretical guarantees for an averaging-ensemble of randomly projected Fisher linear discriminant classifiers, focusing on the casewhen there are fewer training observations than data dimensions. The specific form and simplicity of this ensemble permits a direct and much more detailed analysis than existing generic tools in previous works. In particular, we are able to derive the exact form of the generalization error of our ensemble, conditional on the training set, and based on this we give theoretical guarantees which directly link the performance of the ensemble to that of the corresponding linear discriminant learned in the full data space. To the best of our knowledge these are the first theoretical results to prove such an explicit link for any classifier and classifier ensemble pair. Furthermore we show that the randomly projected ensemble is equivalent to implementing a sophisticated regularization scheme to the linear discriminant learned in the original data space and this prevents overfitting in conditions of small sample size where pseudo-inverse FLD learned in the data space is provably poor. Our ensemble is learned from a set of randomly projected representations of the original high dimensional data and therefore for this approach data can be collected, stored and processed in such a compressed form. We confirm our theoretical findings with experiments, and demonstrate the utility of our approach on several datasets from the bioinformatics domain and one very high dimensional dataset from the drug discovery domain, both settings in which fewer observations than dimensions are the norm.

text: Random projections as regularizers: learning a linear discriminant from fewer observations than dimensions We prove theoretical guarantees for an averaging-ensemble of randomly projected Fisher linear discriminant classifiers, focusing on the casewhen there are fewer training observations than data dimensions. The specific form and simplicity of this ensemble permits a direct and much more detailed analysis than existing generic tools in previous works. In particular, we are able to derive the exact form of the generalization error of our ensemble, conditional on the training set, and based on this we give theoretical guarantees which directly link the performance of the ensemble to that of the corresponding linear discriminant learned in the full data space. To the best of our knowledge these are the first theoretical results to prove such an explicit link for any classifier and classifier ensemble pair. Furthermore we show that the randomly projected ensemble is equivalent to implementing a sophisticated regularization scheme to the linear discriminant learned in the original data space and this prevents overfitting in conditions of small sample size where pseudo-inverse FLD learned in the data space is provably poor. Our ensemble is learned from a set of randomly projected representations of the original high dimensional data and therefore for this approach data can be collected, stored and processed in such a compressed form. We confirm our theoretical findings with experiments, and demonstrate the utility of our approach on several datasets from the bioinformatics domain and one very high dimensional dataset from the drug discovery domain, both settings in which fewer observations than dimensions are the norm.

year: 2014-08-19

title: Kid's Music Box: A Digital Music Organizer Designed with Children for Children

authors: Zhang, Edmond Yiwen

subjects: Children

abstract: This thesis is an investigation of software development for children aged six to ten years old. This is a challenging area; despite the trend for children to be exposed to computer technology at an earlier age, they often struggle to utilize it effectively. Children are not merely miniature adults; they have their own needs which are often not met by traditional software. In particular, this thesis focuses on the task of music management: a task that children take much interest in but for which they are given few tools. We address this with the design of a new music management system: the Kid's Music Box.

The development of Kid's Music Box is documented in four main parts: background research, requirements gathering, design and implementation, and evaluation. Background research identifies the strengths and weaknesses of conventional music organizers with respect to young users. Requirements gathering took the form of a focus group study, which aimed to overcome the distinct challenges of obtaining input from children. The design of Kid's Music Box builds on this work, by incorporating functionality, metaphors and design elements that suit the needs and capabilities of young children. Expert evaluations and formal evaluation from children users showed promising results, which concluded that Kid's Music Box is better than other organizers in terms of managing music for children.

text: Kid's Music Box: A Digital Music Organizer Designed with Children for Children This thesis is an investigation of software development for children aged six to ten years old. This is a challenging area; despite the trend for children to be exposed to computer technology at an earlier age, they often struggle to utilize it effectively. Children are not merely miniature adults; they have their own needs which are often not met by traditional software. In particular, this thesis focuses on the task of music management: a task that children take much interest in but for which they are given few tools. We address this with the design of a new music management system: the Kid's Music Box.

The development of Kid's Music Box is documented in four main parts: background research, requirements gathering, design and implementation, and evaluation. Background research identifies the strengths and weaknesses of conventional music organizers with respect to young users. Requirements gathering took the form of a focus group study, which aimed to overcome the distinct challenges of obtaining input from children. The design of Kid's Music Box builds on this work, by incorporating functionality, metaphors and design elements that suit the needs and capabilities of young children. Expert evaluations and formal evaluation from children users showed promising results, which concluded that Kid's Music Box is better than other organizers in terms of managing music for children.

year: 2007

title: He tangi mai i te puehu: He whakatewhatewha i te mahi whakamāori me te reo ā-tuhi a ngā tūpuna

authors: Apiata, Hāwea

subjects: Māori spirituality

abstract: Kei te pūtahi o tēnei tuhinga whakapae ko te whakatewhatewha i te whakapapa o te whakaaro Māori (Māori intellectual history) mā ēnei pātai e rua: He aha ā te Māori i tuhituhi ai i te tōmuatanga o te rautau rua tekau? Ā, he pēhea tāna wetewete i ngā huatau whakawairua nō waho i te ao Māori? 

Ina koa, ko tā te tuhinga whakapae nei he whakaaranga, he whakaatu hoki i ētahi huarahi e toru hei rangahau i ngā whakapapa o te whakaaro taketake: ko te ketuketu rua mahara (archival research); ko te tātari ariā (conceptual analysis); me te reo e whakamahia ana kia wetewete i te kaupapa. Mā te mahi ketuketu rua mahara e āhei ai ki te wānanga i ngā whakaputanga a Wiremu Takana, he kaituhi, he kaiwhakamāori nō Ngāti Kahungunu. Ka whakaputaina tāna tuhinga tuatahi i te tau 1915. Ā, e rua anō i whakaputaina e ia i te tau whai muri mai i 1916. Ko ēnei tuhinga āna e whakatewhatewha ana i te whakamāoritanga o te rongopai me te āheinga o ngā pūrākau Māori kia whakamārama i ngā whakaakoranga Moromona. Kāore anō kia āta tātaritia, kia āta rangahaua āna pukapuka e tētahi atu o mua. Ko te huarahi rangahau tuarua ko te tātari i te whakamāoritanga o ētahi ariā whakawairua e kitea ana i roto i ngā karaipiture o te Hāhi o Ihu Karaiti o te Hunga Tapu o ngā Rā o Muri nei. E toru ngā ariā kua tīpakongia hei tirotiro, arā, ko heaven, hell me baptism. Ā, hei whakawhānui atu i te titiro ki tēnei kaupapa, ka huritaongia ngā hua o te tuhinga reo Māori, arā, ka matapakina ngā take kia tuhituhi i te mahi rangahau i roto i te reo Māori.

I te mutunga iho, mā te āta wānanga i ngā whakaputanga reo Māori a te Hāhi o Ihu Karaiti (LDS) e whakawhānuitia ai tō tātou māramatanga ki te hītori o te mahi whakaputa pukapuka i roto i te Hāhi, te mahi punenga a te Māori, te whakareretanga o ngā tuhituhinga reo Māori, me te hītori o te Hāhi o Ihu Karaiti i Aotearoa nei.

text: He tangi mai i te puehu: He whakatewhatewha i te mahi whakamāori me te reo ā-tuhi a ngā tūpuna Kei te pūtahi o tēnei tuhinga whakapae ko te whakatewhatewha i te whakapapa o te whakaaro Māori (Māori intellectual history) mā ēnei pātai e rua: He aha ā te Māori i tuhituhi ai i te tōmuatanga o te rautau rua tekau? Ā, he pēhea tāna wetewete i ngā huatau whakawairua nō waho i te ao Māori? 

Ina koa, ko tā te tuhinga whakapae nei he whakaaranga, he whakaatu hoki i ētahi huarahi e toru hei rangahau i ngā whakapapa o te whakaaro taketake: ko te ketuketu rua mahara (archival research); ko te tātari ariā (conceptual analysis); me te reo e whakamahia ana kia wetewete i te kaupapa. Mā te mahi ketuketu rua mahara e āhei ai ki te wānanga i ngā whakaputanga a Wiremu Takana, he kaituhi, he kaiwhakamāori nō Ngāti Kahungunu. Ka whakaputaina tāna tuhinga tuatahi i te tau 1915. Ā, e rua anō i whakaputaina e ia i te tau whai muri mai i 1916. Ko ēnei tuhinga āna e whakatewhatewha ana i te whakamāoritanga o te rongopai me te āheinga o ngā pūrākau Māori kia whakamārama i ngā whakaakoranga Moromona. Kāore anō kia āta tātaritia, kia āta rangahaua āna pukapuka e tētahi atu o mua. Ko te huarahi rangahau tuarua ko te tātari i te whakamāoritanga o ētahi ariā whakawairua e kitea ana i roto i ngā karaipiture o te Hāhi o Ihu Karaiti o te Hunga Tapu o ngā Rā o Muri nei. E toru ngā ariā kua tīpakongia hei tirotiro, arā, ko heaven, hell me baptism. Ā, hei whakawhānui atu i te titiro ki tēnei kaupapa, ka huritaongia ngā hua o te tuhinga reo Māori, arā, ka matapakina ngā take kia tuhituhi i te mahi rangahau i roto i te reo Māori.

I te mutunga iho, mā te āta wānanga i ngā whakaputanga reo Māori a te Hāhi o Ihu Karaiti (LDS) e whakawhānuitia ai tō tātou māramatanga ki te hītori o te mahi whakaputa pukapuka i roto i te Hāhi, te mahi punenga a te Māori, te whakareretanga o ngā tuhituhinga reo Māori, me te hītori o te Hāhi o Ihu Karaiti i Aotearoa nei.

year: 2021