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The goal of clustering is to detect the presence of distinct groups in a data set and assign group labels to the observations. Nonparametric clustering is based on the premise that the observations may be regarded as a sample from some underlying density in feature space and that groups correspond to modes of this density. The goal then is to find the modes(More)
High density clusters can be characterized by the connected components of a level set L(λ) = {x : p(x) > λ} of the underlying probability density function p generating the data, at some appropriate level λ ≥ 0. The complete hierarchical clustering can be characterized by a cluster tree T = λ L(λ). In this paper, we study the behavior of a density level set(More)
  • Rebecca Nugent, Alex Reinhart, Francesca Matano, Brendan McVeigh, Jerzy Wieczorek
  • 2015
General Course Plan: This course is the second half of a year long course in probability and mathematical statistics. Using the probability theory developed in a mathematical probability class, such as 36-225, this course turns to the basic ideas and methods of analyzing data and making inferences about an unknown population based on information contained(More)
In educational research, a fundamental goal is identifying which skills students have mastered, which skills they have not, and which skills they are in the process of mastering. As the number of examinees, items, and skills increases, the estimation of even simple cognitive diagnosis models becomes difficult. To address this, we introduce a capability(More)
While students' skill set profiles can be estimated with formal cognitive diagnosis models [8], their computational complexity makes simpler proxy skill estimates attractive [1, 4, 6]. These estimates can be clustered to generate groups of similar students. Often hierarchical agglomerative clustering or k-means clustering is utilized, requiring, for K(More)
This special issue of JEDM was dedicated to bridging work done in the disciplines of educational and psychological assessment and educational data mining (EDM) via the assessment design and implementation framework of evidence-centered design (ECD). It consisted of a series of five papers: one conceptual paper on ECD, three applied case studies that use ECD(More)
In educational research, a fundamental goal is identifying which skills students have mastered, which skills they have not, and which skills they are in the process of mastering. As the number of examinees, items, and skills increases, the estimation of even simple cognitive diagnosis models becomes difficult. We adopt a faster, simpler approach: cluster a(More)
In recent years the educational community has increasingly embraced digital technologies for the purposes of developing alternative learning environments, providing diagnostic feedback, and fostering the development of so-called 21 st-century skills. This special issue is dedicated to bridging recent work from the disciplines of educational and(More)