Moving window kernel PCA for adaptive monitoring of nonlinear processes

This paper discusses the monitoring of complex nonlinear and time-varying processes. Kernel principal component analysis (KPCA) has gained significant attention as a monitoring tool for nonlinear systems in recent years but relies on a fixed model that cannot be employed for time-varying systems. The contribution of this article is the development of a numerically efficient and memory saving moving window KPCA (MWKPCA) monitoring approach. The proposed technique incorporates an up- and downdating procedure to adapt (i) the data mean and covariance matrix in the feature space and (ii) approximates the eigenvalues and eigenvectors of the Gram matrix. The article shows that the proposed MWKPCA algorithm has a computation complexity of O(N2), whilst batch techniques, e.g. the Lanczos method, are of O(N3). Including the adaptation of the number of retained components and an l-step ahead application of the MWKPCA monitoring model, the paper finally demonstrates the utility of the proposed technique using a simulated nonlinear time-varying system and recorded data from an industrial distillation column.

Living arrangements, relationship to people in the household and admission to care homes for older people

Objective: to assess the separate contributions of marital status, living arrangements and the presence of children to subsequent admission to a care home.

Design and methods: a longitudinal study derived from the health card registration system and linked to the 2001 Census, comprising 28% of the Northern Ireland population was analysed using Cox regression to assess the likelihood of admission for 51,619 older people in the 6 years following the census. Cohort members’ age, sex, marital and health status and relationship to other household members were analysed.

Results: there were 2,138 care home admissions; a rate of 7.4 admissions per thousand person years. Those living alone had the highest likelihood of admission [hazard ratio (HR) compared with living with partner 1.66 (95% CI 1.48, 1.87)] but there was little difference between the never-married and the previously married. Living with children offered similar protection as living with a partner (HR 0.97; 95% CI 0.81, 1.16). The presence of children reduced admissions especially for married couples (HR 0.67 95% CI 0.54, 0.83; models adjusting for age, gender and health). Women were more likely to be admitted, though there were no gender differences for people living alone or those co-habiting with siblings.

Implications: presence of potential caregivers within the home, rather than those living elsewhere, is a major factor determining admission to care home. Further research should concentrate on the health and needs of these co-residents.