title: Designing similarity functions

authors: Trigg, Leonard E.

abstract: The concept of similarity is important in many areas of cognitive science, computer science, and statistics. In machine learning, functions that measure similarity between two instances form the core of instance-based classifiers. Past similarity measures have been primarily based on simple Euclidean distance. As machine learning has matured, it has become obvious that a simple numeric instance representation is insufficient for most domains. Similarity functions for symbolic attributes have been developed, and simple methods for combining these functions with numeric similarity functions were devised. This sequence of events has revealed three important issues, which this thesis addresses.

The first issue is concerned with combining multiple measures of similarity. There is no equivalence between units of numeric similarity and units of symbolic similarity. Existing similarity functions for numeric and symbolic attributes have no common foundation, and so various schemes have been devised to avoid biasing the overall similarity towards one type of attribute. The similarity function design framework proposed by this thesis produces probability distributions that describe the likelihood of transforming between two attribute values. Because common units of probability are employed, similarities may be combined using standard methods. It is empirically shown that the resulting similarity functions treat different attribute types coherently.

The second issue relates to the instance representation itself. The current choice of numeric and symbolic attribute types is insufficient for many domains, in which more complicated representations are required. For example, a domain may require varying numbers of features, or features with structural information. The framework proposed by this thesis is sufficiently general to permit virtually any type of instance representation-all that is required is that a set of basic transformations that operate on the instances be defined. To illustrate the framework’s applicability to different instance representations, several example similarity functions are developed. 

The third, and perhaps most important, issue concerns the ability to incorporate domain knowledge within similarity functions. Domain information plays an important part in choosing an instance representation. However, even given an adequate instance representation, domain information is often lost. For example, numeric features that are modulo (such as the time of day) can be perfectly represented as a numeric attribute, but simple linear similarity functions ignore the modulo nature of the attribute. Similarly, symbolic attributes may have inter-symbol relationships that should be captured in the similarity function. The design framework proposed by this thesis allows domain information to be captured in the similarity function, both in the transformation model and in the probability assigned to basic transformations. Empirical results indicate that such domain information improves classifier performance, particularly when training data is limited.

text: Designing similarity functions The concept of similarity is important in many areas of cognitive science, computer science, and statistics. In machine learning, functions that measure similarity between two instances form the core of instance-based classifiers. Past similarity measures have been primarily based on simple Euclidean distance. As machine learning has matured, it has become obvious that a simple numeric instance representation is insufficient for most domains. Similarity functions for symbolic attributes have been developed, and simple methods for combining these functions with numeric similarity functions were devised. This sequence of events has revealed three important issues, which this thesis addresses.

The first issue is concerned with combining multiple measures of similarity. There is no equivalence between units of numeric similarity and units of symbolic similarity. Existing similarity functions for numeric and symbolic attributes have no common foundation, and so various schemes have been devised to avoid biasing the overall similarity towards one type of attribute. The similarity function design framework proposed by this thesis produces probability distributions that describe the likelihood of transforming between two attribute values. Because common units of probability are employed, similarities may be combined using standard methods. It is empirically shown that the resulting similarity functions treat different attribute types coherently.

The second issue relates to the instance representation itself. The current choice of numeric and symbolic attribute types is insufficient for many domains, in which more complicated representations are required. For example, a domain may require varying numbers of features, or features with structural information. The framework proposed by this thesis is sufficiently general to permit virtually any type of instance representation-all that is required is that a set of basic transformations that operate on the instances be defined. To illustrate the framework’s applicability to different instance representations, several example similarity functions are developed. 

The third, and perhaps most important, issue concerns the ability to incorporate domain knowledge within similarity functions. Domain information plays an important part in choosing an instance representation. However, even given an adequate instance representation, domain information is often lost. For example, numeric features that are modulo (such as the time of day) can be perfectly represented as a numeric attribute, but simple linear similarity functions ignore the modulo nature of the attribute. Similarly, symbolic attributes may have inter-symbol relationships that should be captured in the similarity function. The design framework proposed by this thesis allows domain information to be captured in the similarity function, both in the transformation model and in the probability assigned to basic transformations. Empirical results indicate that such domain information improves classifier performance, particularly when training data is limited.

year: 1997

title: Universal dimensions of Islam: studies in comparative religion [Book Review]

authors: Drury, Abdullah

abstract: This article reviews the book 'Universal dimensions of Islam: studies in comparative religion', edited by Patrick Laude.

text: Universal dimensions of Islam: studies in comparative religion [Book Review] This article reviews the book 'Universal dimensions of Islam: studies in comparative religion', edited by Patrick Laude.

year: 2012-01

title: Academic success amongst a cohort of gifted and talented Māori and Pasifika secondary school boys: Elements that have contributed to their achievement

authors: Miller, Graeme Oliver

subjects: Māori

abstract: In recent years Māori and Pasifika students have been the focus of much discussion and a significant amount of research relating to underachievement. Despite this, many Māori and Pasifika secondary school boys are achieving highly in the academic sphere within the context of mainstream boys’ state secondary schools in New Zealand. Achievement aside, evidence shows that Māori and Pasifika secondary school boys are seriously under-represented in programmes for the gifted and talented. This enquiry examines factors in relation to identifying gifted and talented students, and investigates how their abilities are forged and nurtured. The reasons for student success merit serious investigation because of how the multiple elements contributing to their achievement are likely to be applicable to others, and are a pressing concern for academic attainment in the New Zealand education system. 
 
This qualitative study examines why 30 academically successful Māori and Pasifika secondary school boys achieved highly in the mainstream education system. The boys ranged from 13 to 19 years, the youngest being in his first year at high school as a Year 9 student, and the oldest being in his second year at university. The thesis argues their academic success was due to the complex interplay of home and school environmental elements, and the boys’ intrapersonal characteristics. The study explored the boys’ and parents’ narratives to explain why students had achieved highly, and examined both the parents’ and boys’ perceptions of how well the schools had provided for their intellectual, emotional and cultural needs. Sociocultural learning theory is the main theoretical lens through which the findings are viewed. The methodology is primarily built upon narrative inquiry. The main method of data collection was by semi-structured interview, both individually and in focus groups. Supplementary methods utilised were questionnaires and observation.  
  
An issue in the research was the disparity between the cultural and ethnic background of the participants and myself as the researcher. However, an endeavour was made to mitigate this by consulting with Māori and Pasifika educators, a kaumatua (elder) and iwi (tribal) representative prior to the research commencing. In addition, models developed through this study were submitted to Māori and Pasifika educators for their comment and approval prior to being included. 
 
With its focus specifically on highly-achieving Māori and Pasifika secondary school boys, this thesis makes an original contribution to the national and international discussion about raising student achievement. It provides a platform for further research to 	address the particular concerns around the underachievement of Māori and Pasifika secondary school boys. 
 
While there are several implications arising from the research, all are linked to the need for policy makers and educators to address the issue of the underrepresentation of Māori and Pasifika students in programmes for the gifted and talented. Policies, practices and relationships need to be examined to evaluate how effectively they contribute to gifted and talented Māori and Pasifika students receiving the academic opportunities they deserve. A key part of this examination will need to include consultation with students and their whānau.

text: Academic success amongst a cohort of gifted and talented Māori and Pasifika secondary school boys: Elements that have contributed to their achievement In recent years Māori and Pasifika students have been the focus of much discussion and a significant amount of research relating to underachievement. Despite this, many Māori and Pasifika secondary school boys are achieving highly in the academic sphere within the context of mainstream boys’ state secondary schools in New Zealand. Achievement aside, evidence shows that Māori and Pasifika secondary school boys are seriously under-represented in programmes for the gifted and talented. This enquiry examines factors in relation to identifying gifted and talented students, and investigates how their abilities are forged and nurtured. The reasons for student success merit serious investigation because of how the multiple elements contributing to their achievement are likely to be applicable to others, and are a pressing concern for academic attainment in the New Zealand education system. 
 
This qualitative study examines why 30 academically successful Māori and Pasifika secondary school boys achieved highly in the mainstream education system. The boys ranged from 13 to 19 years, the youngest being in his first year at high school as a Year 9 student, and the oldest being in his second year at university. The thesis argues their academic success was due to the complex interplay of home and school environmental elements, and the boys’ intrapersonal characteristics. The study explored the boys’ and parents’ narratives to explain why students had achieved highly, and examined both the parents’ and boys’ perceptions of how well the schools had provided for their intellectual, emotional and cultural needs. Sociocultural learning theory is the main theoretical lens through which the findings are viewed. The methodology is primarily built upon narrative inquiry. The main method of data collection was by semi-structured interview, both individually and in focus groups. Supplementary methods utilised were questionnaires and observation.  
  
An issue in the research was the disparity between the cultural and ethnic background of the participants and myself as the researcher. However, an endeavour was made to mitigate this by consulting with Māori and Pasifika educators, a kaumatua (elder) and iwi (tribal) representative prior to the research commencing. In addition, models developed through this study were submitted to Māori and Pasifika educators for their comment and approval prior to being included. 
 
With its focus specifically on highly-achieving Māori and Pasifika secondary school boys, this thesis makes an original contribution to the national and international discussion about raising student achievement. It provides a platform for further research to 	address the particular concerns around the underachievement of Māori and Pasifika secondary school boys. 
 
While there are several implications arising from the research, all are linked to the need for policy makers and educators to address the issue of the underrepresentation of Māori and Pasifika students in programmes for the gifted and talented. Policies, practices and relationships need to be examined to evaluate how effectively they contribute to gifted and talented Māori and Pasifika students receiving the academic opportunities they deserve. A key part of this examination will need to include consultation with students and their whānau.

year: 2015