Mixtures of Common Skew-t Factor Analyzers

A mixture of common skew-t factor analyzers model is introduced for model-based clustering of high-dimensional data. By assuming common component factor loadings, this model allows clustering to be performed in the presence of a large number of mixture components or when the number of dimensions is too large to be well-modelled by the mixtures of factor analyzers model or a variant thereof. Furthermore, assuming that the component densities follow a skew-t distribution allows robust clustering of skewed data. The alternating expectation-conditional maximization algorithm is employed for parameter estimation. We demonstrate excellent clustering performance when our model is applied to real and simulated data.This paper marks the first time that skewed common factors have been used

Base Size Sets and Determining Sets

Bridging the work of Cameron, Harary, and others, we examine the base size set B(G) and determining set D(G) of several families of groups. The base size set is the set of base sizes of all faithful actions of the group G on finite sets. The determining set is the subset of B(G) obtained by restricting the actions of G to automorphism groups of finite graphs. We show that for finite abelian groups, B(G)=D(G)={1,2,...,k} where k is the number of elementary divisors of G. We then characterize B(G) and D(G) for dihedral groups of the form D_{p^k} and D_{2p^k}. Finally, we prove B(G) is not equal to D(G) for dihedral groups of the form D_{pq} where p and q are distinct odd primes.Comment: 10 pages, 1 figur

Mixtures of Skew-t Factor Analyzers

In this paper, we introduce a mixture of skew-t factor analyzers as well as a family of mixture models based thereon. The mixture of skew-t distributions model that we use arises as a limiting case of the mixture of generalized hyperbolic distributions. Like their Gaussian and t-distribution analogues, our mixture of skew-t factor analyzers are very well-suited to the model-based clustering of high-dimensional data. Imposing constraints on components of the decomposed covariance parameter results in the development of eight flexible models. The alternating expectation-conditional maximization algorithm is used for model parameter estimation and the Bayesian information criterion is used for model selection. The models are applied to both real and simulated data, giving superior clustering results compared to a well-established family of Gaussian mixture models

Adolescents' and parents' views of Child and Adolescent Mental Health Services (CAMHS) in Ireland

Aim: To explore adolescents’ and parents’ experiences of CAMHS in relation to accessibility, approachability, and appropriateness. Methods: Using a descriptive qualitative design, a combination of focus group and single interviews were conducted with adolescents (n=15) and parents (n=32) from three mental health clinics. Data were transcribed verbatim and analysed using thematic analysis. Results: Accessing mental health services was a challenging experience due to knowledge deficit, lack of information and limited availability of specialist services. Participants desired more information, involvement in decision-making, single and shared consultations, flexible scheduling of appointments, continuity with clinicians, school support and parent support groups. Participants seem to be generally satisfied, however adolescents felt less involved in decision making than they would have liked. Frequent staff changes was problematic as it disrupted continuity of care and hindered the formation of a trusting relationship. Implications for practice: Parents and adolescents expressed similar views of the positive and negative aspects of mental health services. Their need for more information-sharing and involvement in decision-making underline the importance of collaborative practice. Clinician continuity contributed to trusting therapeutic relationships and was valued. These are key principles that with attention, could lead to quality service provision for adolescents and families