Ward's Hierarchical Clustering Method: Clustering Criterion and Agglomerative Algorithm

The Ward error sum of squares hierarchical clustering method has been very widely used since its first description by Ward in a 1963 publication. It has also been generalized in various ways. However there are different interpretations in the literature and there are different implementations of the Ward agglomerative algorithm in commonly used software systems, including differing expressions of the agglomerative criterion. Our survey work and case studies will be useful for all those involved in developing software for data analysis using Ward's hierarchical clustering method.Comment: 20 pages, 21 citations, 4 figure

Identifying Prototypical Components in Behaviour Using Clustering Algorithms

Quantitative analysis of animal behaviour is a requirement to understand the task solving strategies of animals and the underlying control mechanisms. The identification of repeatedly occurring behavioural components is thereby a key element of a structured quantitative description. However, the complexity of most behaviours makes the identification of such behavioural components a challenging problem. We propose an automatic and objective approach for determining and evaluating prototypical behavioural components. Behavioural prototypes are identified using clustering algorithms and finally evaluated with respect to their ability to represent the whole behavioural data set. The prototypes allow for a meaningful segmentation of behavioural sequences. We applied our clustering approach to identify prototypical movements of the head of blowflies during cruising flight. The results confirm the previously established saccadic gaze strategy by the set of prototypes being divided into either predominantly translational or rotational movements, respectively. The prototypes reveal additional details about the saccadic and intersaccadic flight sections that could not be unravelled so far. Successful application of the proposed approach to behavioural data shows its ability to automatically identify prototypical behavioural components within a large and noisy database and to evaluate these with respect to their quality and stability. Hence, this approach might be applied to a broad range of behavioural and neural data obtained from different animals and in different contexts

Visualization of Hidden Node Activity in Neural Networks: I. Visualization Methods

Quality of neural network mappings may be evaluated by visual inspection of hidden and output node activities for the training dataset. This paper discusses how to visualize such multidimensional data, introducing a new projection on a lattice of hypercube nodes. It also discusses what type of information one may expect from visualization of the activity of hidden and output layers. Detailed analysis of the activity of RBF hidden nodes using this type of visualization is presented in the companion paper

Law and Finance: Common Law and Civil Law Countries Compared-An Empirical Critique

The 'theory of law and finance' argues that the common law system provides a better framework for financial development and economic growth than the civil law tradition. This paper identifies a number of problems that cast doubt on the soundness of the empirical basis of this literature. However, this analysis supports the idea that the legal tradition is a major factor in shaping corporate law. In particular, while there is not much evidence that common law countries protect financial investors "better" than civil law countries I find support for the assumption that financial investors are treated "differently" across legal families. Copyright (c) The London School of Economics and Political Science 2007.