Archetypal shapes based on landmarks and extension to handle missing data

Archetype and archetypoid analysis are extended to shapes. The objective is to find representative shapes. Archetypal shapes are pure (extreme) shapes. We focus on the case where the shape of an object is represented by a configuration matrix of landmarks. As shape space is not a vectorial space, we work in the tangent space, the linearized space about the mean shape. Then, each observation is approximated by a convex combination of actual observations (archetypoids) or archetypes, which are a convex combination of observations in the data set. These tools can contribute to the understanding of shapes, as in the usual multivariate case, since they lie somewhere between clustering and matrix factorization methods. A new simplex visualization tool is also proposed to provide a picture of the archetypal analysis results. We also propose new algorithms for performing archetypal analysis with missing data and its extension to incomplete shapes. A well-known data set is used to illustrate the methodologies developed. The proposed methodology is applied to an apparel design problem in children

Análisis de arquetipos de las respuestas del estudiantado a las encuestas docentes

Comunicació presentada al 2º Congreso Virtual Avances en Tecnologías, Innovación y Desafíos de la Educación Superior ATIDES 2018 (15-31 de octubre de 2018, En línea)Una forma habitual de valorar la docencia del profesorado es, en parte, a través de las encuestas a los estudiantes. Los datos en bruto, no resumidos, ofrecen la posibilidad de ser examinados. En este trabajo se ilustrará el uso del análisis de arquetipos con datos faltantes (no todos los estudiantes responden a todas las preguntas), una técnica estadística que nos permitirá obtener una instantánea de cómo han respondido los estudiantes a dicha encuesta ese año y asignatura, y tener una radiografía más clara de sus opiniones. También se mostrará qué factores han influido más en la satisfacción general con el profesorado, mediante el uso de bosques aleatorios. En concreto, se analizarán los datos de dos casos que muestran dos situaciones diferentes. Esta metodología puede emplearse en otros problemas de minería de datos en Educación.A common way of assessing teaching ability is, in part, through student surveys. The raw data, not summarized, offer the possibility of being examined. This paper will illustrate the use of archetype analysis with missing data (not all students answer all questions), a statistical technique that will allow us to obtain a snapshot of how students have responded to that survey that year and subject, and have a more detailed analysis of their opinions. It will also show which factors have most influenced the overall satisfaction with the teaching staff, through the use of random forests. In particular, the data of two cases that show two different situations will be analyzed. This methodology can be used in other data mining problems in Education

Archetypal analysis for ordinal data

Archetypoid analysis (ADA) is an exploratory approach that explains a set of continuous observations as mixtures of pure (extreme) patterns. Those patterns (archetypoids) are actual observations of the sample which makes the results of this technique easily interpretable, even for non-experts. Note that the observations are approximated as a convex combination of the archetypoids. Archetypoid analysis, in its current form, cannot be applied directly to ordinal data. We propose and describe a two-step method for applying ADA to ordinal responses based on the ordered stereotype model. One of the main advantages of this model is that it allows us to convert the ordinal data to numerical values, using a new data-driven spacing that better reflects the ordinal patterns of the data, and this numerical conversion then enables us to apply ADA straightforwardly. The results of the novel method are presented for two behavioural science applications. Finally, the proposed method is also compared with other unsupervised statistical learning methods

Actas del Congreso Virtual Avances en Tecnologías, Innovación y Desafíos de la Educación Superior ATIDES 2018

Actes del Congres Virtual Avances en Tecnologías, Innovación y Desafíos de la Educación Superior ATIDES 201