title: Clustering using finite mixture models

authors: Hunt, Lynette Anne

abstract: This thesis introduces a class of multivariate mixture models that includes latent class models and mixtures of multivariate normal distributions as special cases. Like latent class models, these models make free use of local independence to reduce the number of parameters in the model and to lead to descriptions of clusters that are easily understood. Provision is made for the introduction of within cluster associations between the variables. 

Discrete, multivariate normal and location model distributions are the ‘atoms’ with which the models are built, but where more is known about the nature of the distributions in sub-populations other types of distributions could be used in place of these. 

We use the EM algorithm to find the maximum likelihood estimates of the model parameters, however the emphasis is less on parameter estimation than on the use of the estimated component distributions to cluster the data. We implement the approach of multivariate mixture models with a Fortran 77 program. The program is used to fit models to several data sets, including a large medical data set. Analysis of the resulting clusters shows that sensible clusters have been achieved. 

The thesis shows how our ability to analyse data using multivariate mixture models can be extended to include the facility to handle situations where data are missing at random in the sense of Rubin (1976). The program written for this thesis incorporates this facility. The scope of the methods proposed is illustrated by clustering several data sets.

text: Clustering using finite mixture models This thesis introduces a class of multivariate mixture models that includes latent class models and mixtures of multivariate normal distributions as special cases. Like latent class models, these models make free use of local independence to reduce the number of parameters in the model and to lead to descriptions of clusters that are easily understood. Provision is made for the introduction of within cluster associations between the variables. 

Discrete, multivariate normal and location model distributions are the ‘atoms’ with which the models are built, but where more is known about the nature of the distributions in sub-populations other types of distributions could be used in place of these. 

We use the EM algorithm to find the maximum likelihood estimates of the model parameters, however the emphasis is less on parameter estimation than on the use of the estimated component distributions to cluster the data. We implement the approach of multivariate mixture models with a Fortran 77 program. The program is used to fit models to several data sets, including a large medical data set. Analysis of the resulting clusters shows that sensible clusters have been achieved. 

The thesis shows how our ability to analyse data using multivariate mixture models can be extended to include the facility to handle situations where data are missing at random in the sense of Rubin (1976). The program written for this thesis incorporates this facility. The scope of the methods proposed is illustrated by clustering several data sets.

year: 1996

title: Identification of fatty acid esters of pectenotoxin-2 seco acid in blue mussels (mytilus edulis) from Ireland

authors: Wilkins, Alistair L.

subjects: Dinophysis

abstract: Pectenotoxins from marine dinoflagellates of the genus Dinophysis are rapidly hydrolyzed by many shellfish to give pectenotoxin-2 seco acid, which isomerizes to 7-epi-pectenotoxin-2 seco acid. Three series of fatty acid esters of pectenotoxin-2 seco acid (PTX-2 seco acid) and 7-epi-PTX-2 seco acid were detected by LC-MS analysis of extracts from blue mussels (Mytilus edulis) from Ireland. The locations of the fatty acid ester linkages were identified by a combination of LC-MSn in positive- and negative-ion modes, LC-MS analysis of the products from reaction of the esters with sodium periodate, and NMR analysis of purified samples of the two most abundant ester derivatives. The 37-O-acyl esters of PTX-2 seco acid were the most abundant, followed by the corresponding 11-O-acyl esters, accompanied by low levels of the 33-O-acyl esters. The most abundant fatty acid esters in the fractionated sample were, in order, the 16:0, 22:6, 14:0, 16:1, 18:4, and 20:5 fatty acids, although a wide array of other PTX-2 seco acid fatty acid esters were also present at low levels.

text: Identification of fatty acid esters of pectenotoxin-2 seco acid in blue mussels (mytilus edulis) from Ireland Pectenotoxins from marine dinoflagellates of the genus Dinophysis are rapidly hydrolyzed by many shellfish to give pectenotoxin-2 seco acid, which isomerizes to 7-epi-pectenotoxin-2 seco acid. Three series of fatty acid esters of pectenotoxin-2 seco acid (PTX-2 seco acid) and 7-epi-PTX-2 seco acid were detected by LC-MS analysis of extracts from blue mussels (Mytilus edulis) from Ireland. The locations of the fatty acid ester linkages were identified by a combination of LC-MSn in positive- and negative-ion modes, LC-MS analysis of the products from reaction of the esters with sodium periodate, and NMR analysis of purified samples of the two most abundant ester derivatives. The 37-O-acyl esters of PTX-2 seco acid were the most abundant, followed by the corresponding 11-O-acyl esters, accompanied by low levels of the 33-O-acyl esters. The most abundant fatty acid esters in the fractionated sample were, in order, the 16:0, 22:6, 14:0, 16:1, 18:4, and 20:5 fatty acids, although a wide array of other PTX-2 seco acid fatty acid esters were also present at low levels.

year: 2006

title: Te Kōpura

authors: Maxwell, Te Kahautu

abstract: He Hōnore, he korōria, he maungārongo ki runga ki te whenua, he whakaaro pai ki ngā tānagata katoa.


Ko te tāhu o tēnei tuhituhinga he titiro ki Te Hāhi Ringatū i runga o Whitianga marae. E rua noa iho ngā Rā Ringatū ka tū ki runga i tēnei marae, arā, ko Te Huamata, hei te tahi o Hune tēnā me Te Pure, hei te tahi o Nōema tēnā. I roto i te tuhituhingaroa nei ka titiro he aha I tae atu ai wēnei tikanga ki tēnei o ngā marae. Ka whakatakoto haere, i pēhea hoki ngā whakahaeretanga i te wā o ngā pakeke. Kātahi ka titiro ki ngā whakarerekētanga ki ngā tikanga i roto i te wā, ā, he aha i pērā ai. 
Kua tata ki te toru tekau tau mai i te whakakoretanga o Te Māratapu a Te Ringatū i roto i wāna whakahaerenga i Te Huamata me Te Pure. Ko tērā tūāhuatanga o Te Ringatū e kore nei e kitea e tēnei reanga tangata.
Tokoiti noa nei, me kī, ngā mōrehu o tērā whakatipuranga pakeke i kitea wērā tūāhuatanga e ora tonu ana. Nō reira i toko ake te whakaaro ki te rangahau, ki te kohikohi hoki i ngā kōrero i te hunga i rongo, i kite, i tipu ake hoki i roto i tērā Ao. He pekanga nui o te tuhinga nei kua titiro ki Te Huamata me Te Pure me wōna tapu, me wōna whakahaerenga ki runga o te marae o Whitianga.
Ki te whakawhāriki i ngā kōrero nei mō Te Ringatū ki runga o Whitianga kua tātaritia kia waru ngā pekanga o te tuhinga kia mārama ai ki te karu pānui i ngā kōrero; i pēhea tae atu ai Te Ringatū ki runga o Whitianga, i pēhea tāna kawe i ngā tikanga, ā, he aha i whakarerekēngia ai tāna kawe i Te Huamata me Te Pure i roto I te wā.

Tuatahi: Ki te kōrero mō Te Ringatū me hoki ki te tīmata maitanga o Te Ringatū. Ka tirohia, nā wai i tīmata, ā, he aha i tīmataria ai, me te whakaatu i wētahi āhuatanga i pā ki tōna Poropiti me wāna pononga i te tīmatatanga rā anō o Te Ringatū.

Tuarua: Ko te whai haere tēnei i ngā takahanga waewae o ngā tīpuna o Te Whānau-a-Apanui, ki te whai i Te Ringatū. Ka titiro he aha te take i huri ai a Te Whānau-a-Apanui ki ngā tikanga o Te Ringatū. Ka titiro anō hoki ki te taenga atu o Te Kooti me tana iwi Ringatū ki roto o Te Whānau-a-Apanui me wāna mahi ki a rātou i reira.

Tuatoru: Ka whakaatu i konei, he aha te take ko wātahi marae tokoiti noa iho o Te Whānau-a-Apanui ka noho hei marae Ringatū, mai i te taenga atu o Te Ringatū, aā, tae noa ki tēnei rā.
Tuawhā: I konei ka tae ki te pūtake o te tuhinga. Ka titiro i konei ki te taenga o ngā whakahaere Ringatū, arā, Te Huamata me Te Pure ki runga i te marae o Whitianga. Ka whakaatu i konei, he aha i tae atu ai wēnei tikanga ki tērā marae. Ka kite anē hoki he aha i karangatia ko Whitianga te marae pou mō Te Ringatū ki roto o Te Whānau-a-Apanui.
Tuarima: Ka tiro haeretia i konei ngā tikanga e pā ana ki Te Huamata me wōna whakahaere I ngā. tapu katoa e pā ana ki Te Huamata. Ka whakarārangitia ko ngā karakia me wōna kaupapa katoa kia kite ai te kaipānui i te hōhonutanga o tēnei tikanga a Te Ringatū. I konei ka kite anō hoki te kaipānui i ngā kōrero a ngā pakeke, nāna nei i kite, i tipu ake i roto i tērā tikanga.
Tuaono: Ka titiro i konei ko ngā whakahaere a Te Ringatū i tēnei tikanga, arā, Te Pure. Pērā anō ki te tipuranga tuarima, ka whakarārangitia ai ko ngā karakia me wōna kaupapa katoa kia kite ai te kaipānui i te tikanga o Te Pure, ā, he aha i pērā rawa ai te kaha whakapono o ngā pakeke ki tēnei tūāhuatanga, ko Te Pure.
Tuawhitu: I konei ka titiro ki a Paora Delamere me te take i whakarerekēngia ai e ia ngā tikanga tapu o Te Huamata me Te Pure. Ka titiro anō hoki ki wētahi āhuatanga hou i tīmataria ai e ia i waenganui i Te Ringatū whanui huri i Aotearoa.
Tuawaru: Ka tuituia ngā pekanga katoa ki te whakamārama i ngā kōrero kia eke katoa ki runga i te tāhūhū o te kōrero. Ka kitea te take i tīmataria ai Te Ringatu, arā ngā kairiri a Māori ki a tauiwi. Ā, pērā anō te take i huri ai a Te Whānau-a-Apanui ki ngā tikanga a Te Ringatū. Koira i hanake hoki ai ngā pakeke ki Ōtewa ki te pōhiri i a Te Kooti ki te rohe o Te Whānau-a-Apanui, nā te rauwhaitanga o te patu i ngā papatipu. Ko te hokitanga ki te haumoana o Te Whānau-a-Apanui, ko te hokinga anō hoki o Te Māratapu o Te Huamata, o Te Pure ki reira toka atu ai. Ka haere te wā, ā, nāwai rā ka poua wēnei tikanga a Te Ringatū ki Te Māratapu ki runga o Whitianga, ana, i tipu ake he tipu hou, he oranga hou, ā, he tikanga hou i te huringa o te wā.
Katoa wēnei kōrero hei whakaatu i te āhua o te taenga o Te Huamata me Te Pure ki runga o Whitianga marae, mai i te kunenga ake o te whakaaro ki te whai I wēnei tikanga, ā, tae noa ki te whakatinanatanga e haere ake nei, e haere ake. He rautau kua taha, he raurau tau e haere mai nei.

text: Te Kōpura He Hōnore, he korōria, he maungārongo ki runga ki te whenua, he whakaaro pai ki ngā tānagata katoa.


Ko te tāhu o tēnei tuhituhinga he titiro ki Te Hāhi Ringatū i runga o Whitianga marae. E rua noa iho ngā Rā Ringatū ka tū ki runga i tēnei marae, arā, ko Te Huamata, hei te tahi o Hune tēnā me Te Pure, hei te tahi o Nōema tēnā. I roto i te tuhituhingaroa nei ka titiro he aha I tae atu ai wēnei tikanga ki tēnei o ngā marae. Ka whakatakoto haere, i pēhea hoki ngā whakahaeretanga i te wā o ngā pakeke. Kātahi ka titiro ki ngā whakarerekētanga ki ngā tikanga i roto i te wā, ā, he aha i pērā ai. 
Kua tata ki te toru tekau tau mai i te whakakoretanga o Te Māratapu a Te Ringatū i roto i wāna whakahaerenga i Te Huamata me Te Pure. Ko tērā tūāhuatanga o Te Ringatū e kore nei e kitea e tēnei reanga tangata.
Tokoiti noa nei, me kī, ngā mōrehu o tērā whakatipuranga pakeke i kitea wērā tūāhuatanga e ora tonu ana. Nō reira i toko ake te whakaaro ki te rangahau, ki te kohikohi hoki i ngā kōrero i te hunga i rongo, i kite, i tipu ake hoki i roto i tērā Ao. He pekanga nui o te tuhinga nei kua titiro ki Te Huamata me Te Pure me wōna tapu, me wōna whakahaerenga ki runga o te marae o Whitianga.
Ki te whakawhāriki i ngā kōrero nei mō Te Ringatū ki runga o Whitianga kua tātaritia kia waru ngā pekanga o te tuhinga kia mārama ai ki te karu pānui i ngā kōrero; i pēhea tae atu ai Te Ringatū ki runga o Whitianga, i pēhea tāna kawe i ngā tikanga, ā, he aha i whakarerekēngia ai tāna kawe i Te Huamata me Te Pure i roto I te wā.

Tuatahi: Ki te kōrero mō Te Ringatū me hoki ki te tīmata maitanga o Te Ringatū. Ka tirohia, nā wai i tīmata, ā, he aha i tīmataria ai, me te whakaatu i wētahi āhuatanga i pā ki tōna Poropiti me wāna pononga i te tīmatatanga rā anō o Te Ringatū.

Tuarua: Ko te whai haere tēnei i ngā takahanga waewae o ngā tīpuna o Te Whānau-a-Apanui, ki te whai i Te Ringatū. Ka titiro he aha te take i huri ai a Te Whānau-a-Apanui ki ngā tikanga o Te Ringatū. Ka titiro anō hoki ki te taenga atu o Te Kooti me tana iwi Ringatū ki roto o Te Whānau-a-Apanui me wāna mahi ki a rātou i reira.

Tuatoru: Ka whakaatu i konei, he aha te take ko wātahi marae tokoiti noa iho o Te Whānau-a-Apanui ka noho hei marae Ringatū, mai i te taenga atu o Te Ringatū, aā, tae noa ki tēnei rā.
Tuawhā: I konei ka tae ki te pūtake o te tuhinga. Ka titiro i konei ki te taenga o ngā whakahaere Ringatū, arā, Te Huamata me Te Pure ki runga i te marae o Whitianga. Ka whakaatu i konei, he aha i tae atu ai wēnei tikanga ki tērā marae. Ka kite anē hoki he aha i karangatia ko Whitianga te marae pou mō Te Ringatū ki roto o Te Whānau-a-Apanui.
Tuarima: Ka tiro haeretia i konei ngā tikanga e pā ana ki Te Huamata me wōna whakahaere I ngā. tapu katoa e pā ana ki Te Huamata. Ka whakarārangitia ko ngā karakia me wōna kaupapa katoa kia kite ai te kaipānui i te hōhonutanga o tēnei tikanga a Te Ringatū. I konei ka kite anō hoki te kaipānui i ngā kōrero a ngā pakeke, nāna nei i kite, i tipu ake i roto i tērā tikanga.
Tuaono: Ka titiro i konei ko ngā whakahaere a Te Ringatū i tēnei tikanga, arā, Te Pure. Pērā anō ki te tipuranga tuarima, ka whakarārangitia ai ko ngā karakia me wōna kaupapa katoa kia kite ai te kaipānui i te tikanga o Te Pure, ā, he aha i pērā rawa ai te kaha whakapono o ngā pakeke ki tēnei tūāhuatanga, ko Te Pure.
Tuawhitu: I konei ka titiro ki a Paora Delamere me te take i whakarerekēngia ai e ia ngā tikanga tapu o Te Huamata me Te Pure. Ka titiro anō hoki ki wētahi āhuatanga hou i tīmataria ai e ia i waenganui i Te Ringatū whanui huri i Aotearoa.
Tuawaru: Ka tuituia ngā pekanga katoa ki te whakamārama i ngā kōrero kia eke katoa ki runga i te tāhūhū o te kōrero. Ka kitea te take i tīmataria ai Te Ringatu, arā ngā kairiri a Māori ki a tauiwi. Ā, pērā anō te take i huri ai a Te Whānau-a-Apanui ki ngā tikanga a Te Ringatū. Koira i hanake hoki ai ngā pakeke ki Ōtewa ki te pōhiri i a Te Kooti ki te rohe o Te Whānau-a-Apanui, nā te rauwhaitanga o te patu i ngā papatipu. Ko te hokitanga ki te haumoana o Te Whānau-a-Apanui, ko te hokinga anō hoki o Te Māratapu o Te Huamata, o Te Pure ki reira toka atu ai. Ka haere te wā, ā, nāwai rā ka poua wēnei tikanga a Te Ringatū ki Te Māratapu ki runga o Whitianga, ana, i tipu ake he tipu hou, he oranga hou, ā, he tikanga hou i te huringa o te wā.
Katoa wēnei kōrero hei whakaatu i te āhua o te taenga o Te Huamata me Te Pure ki runga o Whitianga marae, mai i te kunenga ake o te whakaaro ki te whai I wēnei tikanga, ā, tae noa ki te whakatinanatanga e haere ake nei, e haere ake. He rautau kua taha, he raurau tau e haere mai nei.

year: 1998