Singular neutrosophic extended triplet groups and generalized groups

Neutrosophic extended triplet group (NETG) is an interesting extension of the concept of classical group, which can be used to express general symmetry. This paper further studies the structural characterizations of NETG. First, some examples are given to show that some results in literature are false. Second, the differences between generalized groups and neutrosophic extended triplet groups are investigated in detail. Third, the notion of singular neutrosophic extended triplet group (SNETG) is introduced, and some homomorphism properties are discussed and a Lagrange-like theorem for finite SNETG is proved. Finally, the following important result is proved: a semigroup is a singular neutrosophic extended triplet group (SNETG) if and only if it is a generalized group.     

Similarity, kernels, and the triangle inequality

Similarity is used as an explanatory construct throughout psychology and multidimensional scaling (MDS) is the most popular way to assess similarity. In MDS, similarity is intimately connected to the idea of a geometric representation of stimuli in a perceptual space. Whilst connecting similarity and closeness of stimuli in a geometric representation may be intuitively plausible, Tversky and Gati [Tversky, A., & Gati, I. (1982). Similarity, separability, and the triangle inequality. Psychological Review, 89(2), 123-154] have reported data which are inconsistent with the usual geometric representations that are based on segmental additivity. We show that similarity measures based on Shepard’s universal law of generalization [Shepard, R. N. (1987). Toward a universal law of generalization for psychologica science. Science, 237(4820), 1317-1323] lead to an inner product representation in a reproducing kernel Hilbert space. In such a space stimuli are represented by their similarity to all other stimuli. This representation, based on Shepard’s law, has a natural metric that does not have additive segments whilst still retaining the intuitive notion of connecting similarity and distance between stimuli. Furthermore, this representation has the psychologically appealing property that the distance between stimuli is bounded.     

A tutorial on kernel methods for categorization

The abilities to learn and to categorize are fundamental for cognitive systems, be it animals or machines, and therefore have attracted attention from engineers and psychologists alike. Modern machine learning methods and psychological models of categorization are remarkably similar, partly because these two fields share a common history in artificial neural networks and reinforcement learning. However, machine learning is now an independent and mature field that has moved beyond psychologically or neurally inspired algorithms towards providing foundations for a theory of learning that is rooted in statistics and functional analysis. Much of this research is potentially interesting for psychological theories of learning and categorization but also hardly accessible for psychologists. Here, we provide a tutorial introduction to a popular class of machine learning tools, called kernel methods. These methods are closely related to perceptrons, radial-basis-function neural networks and exemplar theories of categorization. Recent theoretical advances in machine learning are closely tied to the idea that the similarity of patterns can be encapsulated in a positive definite kernel. Such a positive definite kernel can define a reproducing kernel Hilbert space which allows one to use powerful tools from functional analysis for the analysis of learning algorithms. We give basic explanations of some key concepts—the so-called kernel trick, the representer theorem and regularization—which may open up the possibility that insights from machine learning can feed back into psychology.     

Multiple Kernel Contraction

This paper focuses on the extension of AGM that allows change for a belief base by a set of sentences instead of a single sentence. In [FH94], Fuhrmann and Hansson presented an axiomatic for Multiple Contraction and a construction based on the AGM Partial Meet Contraction. We propose for their model another way to construct functions: Multiple Kernel Contraction, that is a modification of Kernel Contraction, proposed by Hansson [Han94] to construct classical AGM contractions and belief base contractions. This construction works out the unsolved problem pointed out by Hansson in [Han99, pp. 369]. This revised version was published online in August 2006 with corrections to the Cover Date.     

Spatio-temporal pattern of vulnerable road user’s collisions hot spots and related risk factors for injury severity in Tunisia

High risk of vulnerable road users (VRUs) injuries and fatalities have received higher interest nowadays in Tunisia. By using VRUs crash record (from January 1, 2001 to December 31, 2013), we describe the spatial pattern of VRUs collisions according to different temporal scales such as (a.m. vs p.m. rush hours VRUs collisions, working days vs non-working days VRUs collisions, daytime vs nighttime VRUs collisions) and investigate the influence of personal and environmental factors for VRUs injuries severity within the Center-East region in Tunisia. The empirical results are of great variety: spatial clustering pattern of each subtype of VRUs collisions according to temporal scale were clearly observed with the exception of daytime VRUs collisions, which shows a random tendency. All time-based subtypes of VRUs collisions also were found to be clustered along the national highways and regional highways especially in the regions of Sousse and Sfax. Results from VRUs severity model suggest that the degree of injury severity is higher for male than for female victim. The Tunisian VRUs are more likely to be involved in severe collision than non-Tunisian VRUs. Among driver contributory factors, the change of direction and hazardous overtaking increase the probability of sustaining fatal accidents compared to other driver contributory factors. The season factor shows that accident severity during the summer season is higher. From a policy view point, this kind of analysis can certainly help Tunisian public authorities to develop appropriate safety measures that can possibly reduce the number of VRUs injuries and fatalities.     

Recognising faces but not traits: Accurate personality judgment from faces is unrelated to superior face memory

It is suggested that accurate personality judgments of faces are driven by a morphological ‘kernel of truth’ from face shape. We hypothesised that this relationship could lead to those with better face identification ability being better at personality judgments. We investigated the relationship between face memory, face matching, Big Five personality traits, and accuracy in recognising Big Five personality traits from 50 photographs of unknown faces. In our sample (n = 792) there was overall good (but varying) face memory and personality judgment accuracy. However, there was convincing evidence that these two skills do not correlate (all r < 0.06). We also replicate the known relationship between extraversion and face memory ability in the largest sample to date.     

Kernel principal component analysis combining rotation forest method for linearly inseparable data

Rotation forest (RoF) is an ensemble classifier combining linear analysis theories and decision tree algorithms. In recent existing works, RoF was widely applied to various fields with outstanding performance compared to traditional machine learning techniques, given that a reasonable number of base classifiers is provided. However, the conventional RoF algorithm suffers from classifying linearly inseparable datasets. In this study, a hybrid algorithm integrating kernel principal component analysis (KPCA) and the conventional RoF algorithm is proposed to overcome the classification difficulty for linearly inseparable datasets. The radial basis function (RBF) is selected as the kernel for the KPCA method to establish the nonlinear mapping for linearly inseparable data. Moreover, we evaluate various kernel parameters for better performance. Experimental results show that our algorithm improves the performance of RoF with linearly inseparable datasets, and therefore provides higher classification accuracy rates compared with other ensemble machine learning methods.