We argue that there are many clustering algorithms, because the notion of "cluster" cannot be precisely defined. Clustering is in the eye of the beholder, and as such, researchers have proposed many induction principles and models whose corresponding optimization problem can only be approximately solved by an even larger number of algorithms. Therefore, comparing clustering algorithms, must take into account a careful understanding of the inductive principles involved.

The design and analysis of adaptive sorting algorithms has made important contributions to both theory and practice. The main contributions from the theoretical point of view are: the description of the complexity of a sorting algorithm not only in terms of the size of a problem instance but also in terms of the disorder of the given problem instance; the establishment of new relationships among measures of disorder; the introduction of new sorting algorithms that take advantage of the existing order in the input sequence; and, the proofs that several of the new sorting algorithms achieve maximal (optimal) adaptivity with respect to several measures of disorder. The main contributions from the practical point of view are: the demonstration that several algorithms currently in use are adaptive; and, the development of new algorithms, similar to currently used algorithms that perform competitively on random sequences and are significantly faster on nearly sorted sequences. In this survey, we present the basic notions and concepts of adaptive sorting and the state of the art of adaptive sorting algorithms.

The development of companion animal robots is of growing interest. These robots have recently been marketed to older adults with dementia as a means of encouraging social engagement and reducing behavioural and psychological symptoms of dementia. This paper outlines the results of a pilot study that sought to assess the feasibility and effect of using a robotic companion animal called CuDDler on engagement and emotional states of five older adults with dementia living in nursing home care. CuDDler is a prototype robot developed in Singapore. Despite their cognitive decline, the study participants raised a number of concerns regarding the feasibility and tolerability of CuDDler. The effectiveness of CuDDler was also limited in these participants, although one participant with visual agnosia benefited greatly from the one-on-one experience. The findings demonstrate the importance of companion robots being developed that are of an appropriate size, weight and shape for older people, including those with dementia, and a realistic animal shape that does not encourage thoughts of it being a toy. Our conclusions indicate the need for further studies on the development and use of companion robots, and investigation of the comparative benefits of social robots both compared to and in association with human interactions.

Knowledge discovery from data demands that it shall be the data themselves that reveal the groups (i.e. the data elements in each group) and the number of groups. For the ubiquitous task of clustering, K-MEANS is the most used algorithm applied in a broad range of areas to identify groups where intra-group distances are much smaller than inter-group distances. As a representative-based clustering approach, K-MEANS offers an extremely efficient gradient descent approach to the total squared error of representation; however, it not only demands the parameter k, but it also makes assumptions about the similarity of density among the clusters. Therefore, it is profoundly affected by noise. Perhaps more seriously, it can often be attracted to local optima despite its immersion in a multi-start scheme. We present an effective genetic algorithm that combines the capacity of genetic operators to conglomerate different solutions of the search space with the exploitation of the hill-climber. We advance a previous genetic-searching approach called GENCLUST, with the intervention of fast hill-climbing cycles of K-MEANS and obtain an algorithm that is faster than its predecessor and achieves clustering results of higher quality. We demonstrate this across a series of 18 commonly researched datasets.

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