Relational visual cluster validity

The assessment of cluster validity plays a very important role in cluster analysis. Most commonly used cluster validity methods are based on statistical hypothesis testing or finding the best clustering scheme by computing a number of different cluster validity indices. A number of visual methods of cluster validity have been produced to display directly the validity of clusters by mapping data into two- or three-dimensional space. However, these methods may lose too much information to correctly estimate the results of clustering algorithms. Although the visual cluster validity (VCV) method of Hathaway and Bezdek can successfully solve this problem, it can only be applied for object data, i.e. feature measurements. There are very few validity methods that can be used to analyze the validity of data where only a similarity or dissimilarity relation exists – relational data. To tackle this problem, this paper presents a relational visual cluster validity (RVCV) method to assess the validity of clustering relational data. This is done by combining the results of the non-Euclidean relational fuzzy c-means (NERFCM) algorithm with a modification of the VCV method to produce a visual representation of cluster validity. RVCV can cluster complete and incomplete relational data and adds to the visual cluster validity theory. Numeric examples using synthetic and real data are presente

A sparse multinomial probit model for classification

A recent development in penalized probit modelling using a hierarchical Bayesian approach has led to a sparse binomial (two-class) probit classifier that can be trained via an EM algorithm. A key advantage of the formulation is that no tuning of hyperparameters relating to the penalty is needed thus simplifying the model selection process. The resulting model demonstrates excellent classification performance and a high degree of sparsity when used as a kernel machine. It is, however, restricted to the binary classification problem and can only be used in the multinomial situation via a one-against-all or one-against-many strategy. To overcome this, we apply the idea to the multinomial probit model. This leads to a direct multi-classification approach and is shown to give a sparse solution with accuracy and sparsity comparable with the current state-of-the-art. Comparative numerical benchmark examples are used to demonstrate the method

A kernel method for non-linear systems identification – infinite degree volterra series estimation

Volterra series expansions are widely used in analyzing and solving the problems of non-linear dynamical systems. However, the problem that the number of terms to be determined increases exponentially with the order of the expansion restricts its practical application. In practice, Volterra series expansions are truncated severely so that they may not give accurate representations of the original system. To address this problem, kernel methods are shown to be deserving of exploration. In this report, we make use of an existing result from the theory of approximation in reproducing kernel Hilbert space (RKHS) that has not yet been exploited in the systems identification field. An exponential kernel method, based on an RKHS called a generalized Fock space, is introduced, to model non-linear dynamical systems and to specify the corresponding Volterra series expansion. In this way a non-linear dynamical system can be modelled using a finite memory length, infinite degree Volterra series expansion, thus reducing the source of approximation error solely to truncation in time. We can also, in principle, recover any coefficient in the Volterra series

A_4 Symmetry and Lepton Masses and Mixing

Stimulated by Ma's idea which explains the tribimaximal neutrino mixing by assuming an A_4 flavor symmetry, a lepton mass matrix model is investigated. A Frogatt-Nielsen type model is assumed, and the flavor structures of the masses and mixing are caused by the VEVs of SU(2)_L-singlet scalars \phi_i^u and \phi_i^d (i=1,2,3), which are assigned to {\bf 3} and ({\bf 1}, {\bf 1}',{\bf 1}'') of A_4, respectively.Comment: 13 pages including 1 table, errors in Sec.7 correcte

A kernel method for non-linear systems indentification - infinite degree volerra series estimation

Volterra series expansions are widely used in analyzing and solving the problems of non-linear dynamical systems. However, the problem that the number of terms to be determined increases exponentially with the order of the expansion restricts its practical application. In practice, Volterra series expansions are truncated severely so that they may not give accurate representations of the original system. To address this problem, kernel methods are shown to be deserving of exploration. In this report, we make use of an existing result from the theory of approximation in reproducing kernel Hilbert space (RKHS) that has not yet been exploited in the systems identification field. An exponential kernel method, based on an RKHS called a generalized Fock space, is introduced, to model non-linear dynamical systems and to specify the corresponding Volterra series expansion. In this way a non-linear dynamical system can be modelled using a finite memory length, infinite degree Volterra series expansion, thus reducing the source of approximation error solely to truncation in time. We can also, in principle, recover any coefficient in the Volterra series

Fluidic packaging of microengine and microrocket devices for high pressure and high temperature operation

The fluidic packaging of Power MEMS devices such as the MIT microengine and microrocket requires the fabrication of hermetic seals capable of withstanding temperature in the range 20-600/spl deg/C and pressures in the range 100-300 atm. We describe an approach to such packaging by attaching Kovar metal tubes to a silicon device using glass seal technology. Failure due to fracture of the seals is a significant reliability concern in the baseline process: microscopy revealed a large number of voids in the glass, pre-cracks in the glass and silicon, and poor wetting of the glass to silicon. The effects of various processing and materials parameters on these phenomena were examined. A robust procedure, based on the use of metal-coated silicon substrates, was developed to ensure good wetting. The bending strength of single-tube specimens was determined at several temperatures. The dominant failure mode changed from fracture at room temperature to yielding of the glass and Kovar at 600/spl deg/C. The strength in tension at room temperature was analyzed using Weibull statistics; these results indicate a probability of survival of 0.99 at an operational pressure of 125 atm at room temperature for single tubes and a corresponding probability of 0.9 for a packaged device with 11 joints. The residual stresses were analyzed using the method of finite elements and recommendations for the improvement of packaging reliability are suggested