Semisupervised learning of hierarchical latent trait models for data visualization

Recently, we have developed the hierarchical Generative Topographic Mapping (HGTM), an interactive method for visualization of large high-dimensional real-valued data sets. In this paper, we propose a more general visualization system by extending HGTM in three ways, which allows the user to visualize a wider range of data sets and better support the model development process. 1) We integrate HGTM with noise models from the exponential family of distributions. The basic building block is the Latent Trait Model (LTM). This enables us to visualize data of inherently discrete nature, e.g., collections of documents, in a hierarchical manner. 2) We give the user a choice of initializing the child plots of the current plot in either interactive, or automatic mode. In the interactive mode, the user selects "regions of interest," whereas in the automatic mode, an unsupervised minimum message length (MML)-inspired construction of a mixture of LTMs is employed. The unsupervised construction is particularly useful when high-level plots are covered with dense clusters of highly overlapping data projections, making it difficult to use the interactive mode. Such a situation often arises when visualizing large data sets. 3) We derive general formulas for magnification factors in latent trait models. Magnification factors are a useful tool to improve our understanding of the visualization plots, since they can highlight the boundaries between data clusters. We illustrate our approach on a toy example and evaluate it on three more complex real data sets. © 2005 IEEE.

Illustrating Cognitive Connections between Math and Language in Pre-Service Teachers’ Perceptions of Common or Everyday Terms

This paper introduces a new construct that we term Math Mediated Language (MML) focusing on the notion that common or everyday terms with mathematical meanings are important building blocks for students’ mathematical reasoning. A survey given to 96 pre-service early childhood educators indicated clear patterns of perceptions of these terms.

Modelos linear e não linear em análises genéticas para sobrevivência de crias de ovinos da raça Santa Inês.

Resumo: Registros de sobrevivência do nascimento ao desmame de 3846 crias de ovinos da raça Santa Inês foram analisados por modelos de reprodutor linear e não linear (modelo de limiar), para estimar componentes de variância e herdabilidade. Os modelos usados para sobrevivência, analisada como característica da cria, incluíram os efeitos fixos de sexo, da combinação tipo de nascimento-criação da cria e da idade da ovelha ao parto, efeito da covariável peso da cria ao nascer e efeitos aleatórios de reprodutor, da classe rebanho-ano-estação e do resíduo. Componentes de variância para o modelo linear foram estimados pelo método da máxima verossimilhança restrita (REML) e para o modelo não linear por uma aproximação da máxima verossimilhança marginal (MML), pelo programa CMMAT2. O coeficiente de herdabilidade (h2) estimado pelo modelo de limiar foi de 0,29, e pelo modelo linear, 0,14. A correlação de ordem de Spearman entre as capacidades de transmissão dos reprodutores, com base nos dois modelos foi de 0,96. As estimativas de h2 obtidas indicam a possibilidade de se obter, por seleção, ganho genético para sobrevivência. [Linear and nonlinear models in genetic analyses of lamb survival in the Santa Inês hair sheep breed]. Abstract: Records of 3,846 lambs survival from birth to weaning of Santa Inês hair sheep breed, were analyzed by linear and non linear sire models (threshold model) to estimate variance components and heritability (h2). The models that were used to analyze survival, considered in this study as a lamb trait, included the fixed effects of sex of the lamb, combination of type of birth-rearing of lamb, and age of ewe, birth weight of lamb as covariate, and random effects of sire, herd-year-season and residual. Variance components were obtained using restricted maximum likelihood (REML), in linear model and marginal maximum likelihood in threshold model through CMMAT2 program. Estimate of heritability (h2) obtained by threshold model was 0.29 and by linear model was 0.14. Rank correlation of Spearman, between sire solutions based on the two models was 0.96. The obtained estimates in this study indicate that it is possible to acquire genetic gain to survival by selection.