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: Compression-based template matching

authors: Inglis, Stuart J.

subjects: Machine learning

abstract: Textual image compression is a method of both lossy and lossless image compression that is particularly effective for images containing repeated sub-images, notably pages of text (Mohiuddin et al., 1984; Witten et al., 1992). The process comprises three main steps:
• Extracting all the characters from an image;
• Building a library that contains one representative for each character class;
• Compressing the image with respect to the library.

text: Compression-based template matching Textual image compression is a method of both lossy and lossless image compression that is particularly effective for images containing repeated sub-images, notably pages of text (Mohiuddin et al., 1984; Witten et al., 1992). The process comprises three main steps:
• Extracting all the characters from an image;
• Building a library that contains one representative for each character class;
• Compressing the image with respect to the library.

year: 1993

title: Ngāti Whakaue Māngai Nui

authors: Hiini, Anaha Te Wheoro

subjects: Ngāti Whakaue Māngai Nui

abstract: Ko Ngāti Whakaue tētehi iwi ahurei o te waka o Te Arawa.  Ko tētehi taha ōna kei ngā tahataha o te kōroto moana o Te Rotorua-nui-a-Kahumatamomoe, i Waingaehe ki Waimihia.  Ko tētehi atu taha ōna kei te ūnga o te waka rongomaiwhiti o Te Arawa, arā ki Maketū.  
Kua whai mana a Ngāti Whakaue i ngā rautau e tū whakahīhī ai rātau hei iwi mana nui i ō rātau pūkenga me ō rātau pūmanawa kia mau tonu tō rātau Whakauetanga, tō rātau ahurea me ā rātau tikanga.   Ko tētehi pūkenga pēnei i te āheinga ki te whakairo i te kupu rōreka, ki te tuitui i te kōrero i whakaputaina ai te kōrero ‘Te Arawa Māngai Nui’.  He mea whakapuaki te kōrero rā e iwi kē ki te whakanui i ngā pūkōrero o ngā paepae o Te Arawa, ka mutu, koirā hoki tētehi pūkenga i hau ai te rongo o Ngāti Whakaue.  
Nā, ko te pūkenga e kōrerohia nei, ko te reo o Ngāti Whakaue.  Ko tōna oranga tonutanga te kaupapa matua o tēnei tuhinga e rangahaua ana i te putanga o te kōrero a tētehi o ngā koroua matatau o te iwi i te tau 1992, arā a Hamuera Mitchell, nāna tonu nei i whakapuaki ‘Ka mate te reo o Ngāti Whakaue ā te tekau tau’.  

Nō reira, he whakatewhatewhahanga tēnei tuhinga o te reo o Ngāti Whakaue o tua, o mohoa noa nei hoki kia mōhiotia ai te oranga, te matenga haeretanga rānei o te reo o te iwi, o ngā hapū, o te hapori, o te kāinga o nāianei, kia tau hoki mehemea āe rānei kua whai hua ngā rautaki reo o mua a Ngāti Whakaue ki te whakarauora i tōna ake reo, ā, ka aha te iwi e anga whakamua ai.  Ka mātaitia te āhua o te reo o Ngāti Whakaue kia mōhiotia mehemea i tika tā Hamera Mitchell i kī ai i te tau 1992, karekau rānei, mehemea rānei he wero kē nāna kia kaua e tukuna e te iwi o Ngāti Whakaue tō rātau reo kia mate.

Ko te tikanga rangahau Pākehā, ko te tikanga rangahau Māori, me ngā tikanga ako reo ka kaha mātaitia i tēnei tuhinga kia tika ai te kohinga o ngā raraunga o tēnei momo rangahau, ngā tikanga matatika a te wānanga, ngā tukanga tātari me te whakahōrapatanga atu i ngā whakataunga o te rangahau.  

Hei āpiti atu, ka kōrerohia ngā kaupapa mātauranga a Ngāti Whakaue, tae noa atu ki ngā tini kaupapa whakarauora reo a te iwi kua whakahaerehia mai i te tau 2005 ki ēnei rangi tonu nei mō te oranga o te reo o Ngāti Whakaue te take e anga tōtika atu ai ki te wetenga o te rautaki reo o mua a Ngāti Whakaue i whakahaerehia ai i ngā tau 2013 ki te tau 2017 i kitea ai ōna pikinga, ōna hekenga, ōna ngoikoretanga me ōna hua.  

Heoi anō, hei whaiwhai noa ake i te rautaki o mua nei, ko ngā mātātuhi kua mahue iho rā, ko te korenga o ngā arotakenga, ko te korenga o ngā pūrongo, ko te korenga o ētehi taunakitanga ā-tuhi nei, ko te korenga o tētehi aha kē atu rānei kia kitea he hua, he pikinga, he hekenga, he aha rānei.  Ahakoa tērā raru, nā te kitenga me te rongotanga o te pikinga haeretanga o te āhua o te reo, nā ngā kōrero ā-waha me ngā kauhau a ētehi mō ngā hua i puta ai i te rautaki reo o mua a Ngāti Whakaue i mana ai te whakahaumanutanga o te reo o ngā paepae o te iwi.

Nā te mea ko te reo Māori te remurere o te kaituhi nei, kua tekau mā waru tau ia e whai ana i te kaupapa i a ia e whakaako ana, i a ia e wānanga ana, i a ia hoki e whakapau kaha ana ki te whakaora anō i te reo Māori, kua whakaritea e ia tētehi rautaki reo hou e toru tekau tau te roa hei kōkiri mā te iwi e ora rawa atu anō ai te reo o Ngāti Whakaue, e whai hua anō ai hoki te whakapuakitanga o te kōrero rā ‘Te Arawa Māngai Nui’, hei tohu whakanui i ngā pūkenga kōrero o te iwi.

E ai ki te kōrero, ‘he tīmohea kua pakari’.  Nā roto i te āta rangahaua o te kaupapa nei i mōhio ai e ora tonu nei te reo o Ngāti Whakaue, heoi, kāore e pērā rawa te kaha o te oranga i te wā i a kui mā, i a koro mā.  Ahakoa te kōrero mō te matenga haeretanga o te reo o Ngāti Whakaue, nā ngā kaupapa whakaora reo a te iwi i ngā tau i piki anō ai te oranga o te reo, ka mutu, mā te whakahaerenga tonutanga o ngā wānanga nei e ora tonu anō ai te reo.

text: Ngāti Whakaue Māngai Nui Ko Ngāti Whakaue tētehi iwi ahurei o te waka o Te Arawa.  Ko tētehi taha ōna kei ngā tahataha o te kōroto moana o Te Rotorua-nui-a-Kahumatamomoe, i Waingaehe ki Waimihia.  Ko tētehi atu taha ōna kei te ūnga o te waka rongomaiwhiti o Te Arawa, arā ki Maketū.  
Kua whai mana a Ngāti Whakaue i ngā rautau e tū whakahīhī ai rātau hei iwi mana nui i ō rātau pūkenga me ō rātau pūmanawa kia mau tonu tō rātau Whakauetanga, tō rātau ahurea me ā rātau tikanga.   Ko tētehi pūkenga pēnei i te āheinga ki te whakairo i te kupu rōreka, ki te tuitui i te kōrero i whakaputaina ai te kōrero ‘Te Arawa Māngai Nui’.  He mea whakapuaki te kōrero rā e iwi kē ki te whakanui i ngā pūkōrero o ngā paepae o Te Arawa, ka mutu, koirā hoki tētehi pūkenga i hau ai te rongo o Ngāti Whakaue.  
Nā, ko te pūkenga e kōrerohia nei, ko te reo o Ngāti Whakaue.  Ko tōna oranga tonutanga te kaupapa matua o tēnei tuhinga e rangahaua ana i te putanga o te kōrero a tētehi o ngā koroua matatau o te iwi i te tau 1992, arā a Hamuera Mitchell, nāna tonu nei i whakapuaki ‘Ka mate te reo o Ngāti Whakaue ā te tekau tau’.  

Nō reira, he whakatewhatewhahanga tēnei tuhinga o te reo o Ngāti Whakaue o tua, o mohoa noa nei hoki kia mōhiotia ai te oranga, te matenga haeretanga rānei o te reo o te iwi, o ngā hapū, o te hapori, o te kāinga o nāianei, kia tau hoki mehemea āe rānei kua whai hua ngā rautaki reo o mua a Ngāti Whakaue ki te whakarauora i tōna ake reo, ā, ka aha te iwi e anga whakamua ai.  Ka mātaitia te āhua o te reo o Ngāti Whakaue kia mōhiotia mehemea i tika tā Hamera Mitchell i kī ai i te tau 1992, karekau rānei, mehemea rānei he wero kē nāna kia kaua e tukuna e te iwi o Ngāti Whakaue tō rātau reo kia mate.

Ko te tikanga rangahau Pākehā, ko te tikanga rangahau Māori, me ngā tikanga ako reo ka kaha mātaitia i tēnei tuhinga kia tika ai te kohinga o ngā raraunga o tēnei momo rangahau, ngā tikanga matatika a te wānanga, ngā tukanga tātari me te whakahōrapatanga atu i ngā whakataunga o te rangahau.  

Hei āpiti atu, ka kōrerohia ngā kaupapa mātauranga a Ngāti Whakaue, tae noa atu ki ngā tini kaupapa whakarauora reo a te iwi kua whakahaerehia mai i te tau 2005 ki ēnei rangi tonu nei mō te oranga o te reo o Ngāti Whakaue te take e anga tōtika atu ai ki te wetenga o te rautaki reo o mua a Ngāti Whakaue i whakahaerehia ai i ngā tau 2013 ki te tau 2017 i kitea ai ōna pikinga, ōna hekenga, ōna ngoikoretanga me ōna hua.  

Heoi anō, hei whaiwhai noa ake i te rautaki o mua nei, ko ngā mātātuhi kua mahue iho rā, ko te korenga o ngā arotakenga, ko te korenga o ngā pūrongo, ko te korenga o ētehi taunakitanga ā-tuhi nei, ko te korenga o tētehi aha kē atu rānei kia kitea he hua, he pikinga, he hekenga, he aha rānei.  Ahakoa tērā raru, nā te kitenga me te rongotanga o te pikinga haeretanga o te āhua o te reo, nā ngā kōrero ā-waha me ngā kauhau a ētehi mō ngā hua i puta ai i te rautaki reo o mua a Ngāti Whakaue i mana ai te whakahaumanutanga o te reo o ngā paepae o te iwi.

Nā te mea ko te reo Māori te remurere o te kaituhi nei, kua tekau mā waru tau ia e whai ana i te kaupapa i a ia e whakaako ana, i a ia e wānanga ana, i a ia hoki e whakapau kaha ana ki te whakaora anō i te reo Māori, kua whakaritea e ia tētehi rautaki reo hou e toru tekau tau te roa hei kōkiri mā te iwi e ora rawa atu anō ai te reo o Ngāti Whakaue, e whai hua anō ai hoki te whakapuakitanga o te kōrero rā ‘Te Arawa Māngai Nui’, hei tohu whakanui i ngā pūkenga kōrero o te iwi.

E ai ki te kōrero, ‘he tīmohea kua pakari’.  Nā roto i te āta rangahaua o te kaupapa nei i mōhio ai e ora tonu nei te reo o Ngāti Whakaue, heoi, kāore e pērā rawa te kaha o te oranga i te wā i a kui mā, i a koro mā.  Ahakoa te kōrero mō te matenga haeretanga o te reo o Ngāti Whakaue, nā ngā kaupapa whakaora reo a te iwi i ngā tau i piki anō ai te oranga o te reo, ka mutu, mā te whakahaerenga tonutanga o ngā wānanga nei e ora tonu anō ai te reo.

year: 2020