Linear dimensionality reduction: Survey, insights, and generalizations

© 2015 John P. Cunningham and Zoubin Ghahramani. Linear dimensionality reduction methods are a cornerstone of analyzing high dimensional data, due to their simple geometric interpretations and typically attractive computational properties. These methods capture many data features of interest, such as covariance, dynamical structure, correlation between data sets, input-output relationships, and margin between data classes. Methods have been developed with a variety of names and motivations in many fields, and perhaps as a result the connections between all these methods have not been highlighted. Here we survey methods from this disparate literature as optimization programs over matrix manifolds. We discuss principal component analysis, factor analysis, linear multidimensional scaling, Fisher's linear discriminant analysis, canonical correlations analysis, maximum autocorrelation factors, slow feature analysis, sufficient dimensionality reduction, undercomplete independent component analysis, linear regression, distance metric learning, and more. This optimization framework gives insight to some rarely discussed shortcomings of well-known methods, such as the suboptimality of certain eigenvector solutions. Modern techniques for optimization over matrix manifolds enable a generic linear dimensionality reduction solver, which accepts as input data and an objective to be optimized, and returns, as output, an optimal low-dimensional projection of the data. This simple optimization framework further allows straightforward generalizations and novel variants of classical methods, which we demonstrate here by creating an orthogonal-projection canonical correlations analysis. More broadly, this survey and generic solver suggest that linear dimensionality reduction can move toward becoming a blackbox, objective-agnostic numerical technology.

Proceedings of an international workshop on the value of computer-based engineering tools, held in Cambridge in April 1997

There is increasing adoption of computer-based tools to support the product development process. Tolls include computer-aided design, computer-aided manufacture, systems engineering and product data management systems. The fact that companies choose to invest in tools might be regarded as evidence that tools, in aggregate, are perceived to possess business value through their application to engineering activities. Yet the ways in which value accrues from tool technology are poorly understood.

This report records the proceedings of an international workshop during which some novel approaches to improving our understanding of this problem of tool valuation were presented and debated. The value of methods and processes were also discussed. The workshop brought together British, Dutch, German and Italian researchers. The presenters included speakers from industry and academia (the University of Cambridge, the University of Magdeburg and the Politechnico de Torino)

The work presented showed great variety. Research methods include case studies, questionnaires, statistical analysis, semi-structured interviews, deduction, inductive reasoning, the recording of anecdotes and analogies. The presentations drew on financial investment theory, the industrial experience of workshop participants, discussions with students developing tools, modern economic theories and speculation on the effects of company capabilities.

Articulating current service development practices: a qualitative analysis of eleven mental health projects.

BACKGROUND: The utilisation of good design practices in the development of complex health services is essential to improving quality. Healthcare organisations, however, are often seriously out of step with modern design thinking and practice. As a starting point to encourage the uptake of good design practices, it is important to understand the context of their intended use. This study aims to do that by articulating current health service development practices. METHODS: Eleven service development projects carried out in a large mental health service were investigated through in-depth interviews with six operation managers. The critical decision method in conjunction with diagrammatic elicitation was used to capture descriptions of these projects. Stage-gate design models were then formed to visually articulate, classify and characterise different service development practices. RESULTS: Projects were grouped into three categories according to design process patterns: new service introduction and service integration; service improvement; service closure. Three common design stages: problem exploration, idea generation and solution evaluation - were then compared across the design process patterns. Consistent across projects were a top-down, policy-driven approach to exploration, underexploited idea generation and implementation-based evaluation. CONCLUSIONS: This study provides insight into where and how good design practices can contribute to the improvement of current service development practices. Specifically, the following suggestions for future service development practices are made: genuine user needs analysis for exploration; divergent thinking and innovative culture for idea generation; and fail-safe evaluation prior to implementation. Better training for managers through partnership working with design experts and researchers could be beneficial.