principal curve time warping time warping finds use in many fields of time series analysis and it has been effectively implemented in many different application areas rather than focusing on a particular application area we approach the general problem definition and employ principal curves a powerful machine learning tool to improve the noise robustness of existing time warping methods the increasing noise level is the most important problem that leads to unnatural alignments therefore we tested our approach in low signal to noise ratio snr signals and obtained satisfactory results moreover for the signals denoised by principal curve projections we propose a differential equation based time warping method which has a comparable performance with lower computational complexity than the existing techniques

statistical mechanics and phase transitions in clustering a new approach to clustering based on statistical physics is presented the problem is formulated as fuzzy clustering and the association probability distribution is obtained by maximizing the entropy at a given average variance the corresponding lagrange multiplier is related to the temperature and motivates a deterministic annealing process where the free energy is minimized at each temperature critical temperatures are derived for phase transitions when existing clusters split it is a hierarchical clustering estimating the most probable cluster parameters at various average variances

stable isomorphism of dual operator spaces we prove that two dual operator spaces x and y are stably isomorphic if and only if there exist completely isometric normal representations and of x and y respectively and ternary rings of operators m1 m2 such that x m2 y m1 w and y m2 x m1 w we prove that this is equivalent to certain canonical dual operator algebras associated with the operator spaces being stably isomorphic we apply these operator space results to prove that certain dual operator algebras are stably isomorphic if and only if they are isomorphic consequently we obtain that certain complex domains are biholomorphically equivalent if and only if their algebras of bounded analytic functions are morita equivalent in our sense finally we provide examples motivated by the theory of csl algebras

a global structure based algorithm for detecting the principal graph from complex data principal curves arising as an essential construct in dimensionality reduction and pattern recognition have recently attracted much attention from theoretical as well as practical perspective existing methods usually employ the first principal component of the data as an initial estimate of principal curves however they may be ineffective when dealing with complex data with self intersecting characteristics high curvature and significant dispersion in this paper a new method based on global structure is proposed to detect the principal graph a set of principal curves from complex data first the global structure of the data called an initial principal graph is extracted based on a thinning technique which captures the approximate topological features of the complex data in terms of the characteristics of the data vertex merge step and the improved fitting and smoothing phase are then proposed to control the deviation of the principal graph and improve the process of optimizing the principal graph finally the restructuring step introduced by kegl is used to rectify imperfections of the principal graph by using synthetic and real world data sets the proposed method is compared with other existing algorithms experimental results show the effectiveness of the global structure based method

piecewise linear skeletonization using principal curves proposes an algorithm to find piecewise linear skeletons of handwritten characters by using principal curves the development of the method was inspired by the apparent similarity between the definition of principal curves smooth curves which pass through the middle of a cloud of points and medial axes smooth curves that run equidistantly from the contours of a character image the central fitting and smoothing step of the algorithm is an extension of the polygonal line algorithm which approximates principal curves of data sets by piecewise linear curves the polygonal line algorithm is extended to find principal graphs and complemented with two steps specific to the task of skeletonization an initialization method to capture the approximate topology of the character and a collection of restructuring operations to improve the structural quality of the skeleton produced by the initialization method an advantage of our approach over existing methods is that we optimize the skeleton graph by minimizing an intuitive and explicit objective function that captures the two competing criteria of smoothing the skeleton and fitting it closely to the pixels of the character image we tested the algorithm on isolated handwritten digits and images of continuous handwriting the results indicated that the proposed algorithm can find a smooth medial axis in the great majority of a wide variety of character templates and that it substantially improves the pixel wise skeleton obtained by traditional thinning methods

a morita theorem for dual operator algebras abstract we prove that two dual operator algebras are weak morita equivalent in the sense of d p blecher u kashyap morita equivalence of dual operator algebras j pure appl algebra 212 2008 2401 2412 if and only if they have equivalent categories of dual operator modules via completely contractive functors which are also weak continuous on appropriate morphism spaces moreover in a fashion similar to the operator algebra case we characterize such functors as the module normal haagerup tensor product with an appropriate weak morita equivalence bimodule we also develop the theory of the w dilation which connects the non selfadjoint dual operator algebra with the w algebraic framework in the case of weak morita equivalence this w dilation is a w module over a von neumann algebra generated by the non selfadjoint dual operator algebra the theory of the w dilation is a key part of the proof of our main theorem

embedding formulae in diffraction theory embedding formulae are remarkable as they allow one to decompose scattering problems apparently dependent upon several angular variables angles of incidence and observation into those dependent upon fewer angular variables in terms of facilitating rapid computations across considerable parameter regimes this is a considerable advantage our aim is to derive embedding formulae for scattering and diffraction problems in acoustics electromagnetism and elasticity here we construct a general approach to formulating and using embedding formulae we do this using complementary approaches overly singular states and a physical interpretation in terms of sources the crucial point we identify is the form of the auxiliary state used in the reciprocal theorem this is unphysically singular at the edge and is reminiscent of weight function methods used in fracture mechanics illustrative implementations of our approach are given using wiener hopf techniques for semi infinite model problems in both elasticity and acoustics we also demonstrate our approach using a numerical example from acoustics and we make connections with high frequency asymptotic methods

learning and design of principal curves principal curves have been defined as self consistent smooth curves which pass through the middle of a d dimensional probability distribution or data cloud they give a summary of the data and also serve as an efficient feature extraction tool we take a new approach by defining principal curves as continuous curves of a given length which minimize the expected squared distance between the curve and points of the space randomly chosen according to a given distribution the new definition makes it possible to theoretically analyze principal curve learning from training data and it also leads to a new practical construction our theoretical learning scheme chooses a curve from a class of polygonal lines with k segments and with a given total length to minimize the average squared distance over n training points drawn independently convergence properties of this learning scheme are analyzed and a practical version of this theoretical algorithm is implemented in each iteration of the algorithm a new vertex is added to the polygonal line and the positions of the vertices are updated so that they minimize a penalized squared distance criterion simulation results demonstrate that the new algorithm compares favorably with previous methods both in terms of performance and computational complexity and is more robust to varying data models

an algorithm for data driven bandwidth selection the analysis of a feature space that exhibits multiscale patterns often requires kernel estimation techniques with locally adaptive bandwidths such as the variable bandwidth mean shift proper selection of the kernel bandwidth is however a critical step for superior space analysis and partitioning this paper presents a mean shift based approach for local bandwidth selection in the multimodal multivariate case the method is based on a fundamental property of normal distributions regarding the bias of the normalized density gradient this paper demonstrates that within the large sample approximation the local covariance is estimated by the matrix that maximizes the magnitude of the normalized mean shift vector using this property the paper develops a reliable algorithm which takes into account the stability of local bandwidth estimates across scales the validity of the theoretical results is proven in various space partitioning experiments involving the variable bandwidth mean shift

operator synthesis i synthetic sets bilattices and tensor algebras abstract the interplay between the invariant subspace theory and spectral synthesis for locally compact abelian group discovered by arveson ann of math 2 100 1974 433 is extended to include other topics as harmonic analysis for varopoulos algebras and approximation by projection valued measures we propose a coordinate approach which nevertheless does not use the technique of pseudo integral operators as well as a coordinate free one which allows to extend to non separable spaces some important results and constructions of arveson we solve some problems posed in arveson 1974

stochastic global optimization methods part 1 clustering methods in this stochastic approach to global optimization clustering techniques are applied to identify local minima of a real valued objective function that are potentially global three different methods of this type are described their accuracy and efficiency are analyzed in detail

finding curvilinear features in spatial point patterns principal curve clustering with noise clustering about principal curves combines parametric modeling of noise with nonparametric modeling of feature shape this is useful for detecting curvilinear features in spatial point patterns with or without background noise applications include the detection of curvilinear minefields from reconnaissance images some of the points in which represent false detections and the detection of seismic faults from earthquake catalogs our algorithm for principal curve clustering is in two steps the first is hierarchical and agglomerative hpcc and the second consists of iterative relocation based on the classification em algorithm cem pcc hpcc is used to combine potential feature clusters while cem pcc refines the results and deals with background noise it is important to have a good starting point for the algorithm this can be found manually or automatically using for example nearest neighbor clutter removal or model based clustering we choose the number of features and the amount of smoothing simultaneously using approximate bayes factors

strong morita equivalence of operator spaces abstract we introduce and examine the notions of strong equivalence and strong tro equivalence for operator spaces we show that they behave in an analogous way to how strong morita equivalence does for the category of c algebras in particular we prove that strong equivalence coincides with stable isomorphism under the expected countability hypothesis and that strongly tro equivalent operator spaces admit a correspondence between particular representations furthermore we show that strongly equivalent operator spaces have stably isomorphic second duals and strongly equivalent tro envelopes in the case of unital operator spaces strong equivalence implies stable isomorphism of the c envelopes

responses of partially immersed elastic structures using a symmetric formulation for coupled boundary element and finite element methods using a coupled bem fem this work describes a numerical method to compute the response and acoustic radiation for structures partially immersed in fluid the structures and their responses are assumed to be symmetric about a symmetric plane a symmetric complex matrix derived from the bem and a reciprocal principle for surface acoustics is also used to represent the acoustic loading against the structures in addition selecting a proper green s function based on image source method satisfies the boundary conditions of pressure release on the fluid surface and null normal velocity on the symmetric plane moreover a boundary integral equation emerges when the field point approaches the structural surface where the normal derivative of the green s function over partial infinitesimal spheres is evaluated these limiting values depend on locations of the field point on the surface owing to the symmetry of the acoustic loading matrix the matrix for the coupled bem fem is a banded symmetric one thereby allowing us to employ a variable banded storage method and invert of the matrix doing so markedly increases computational efficiency furthermore an analytical solution of a spherical thin shell with the lower semi sphere immersed in water is carried out by characteristic function expansions for shell equation and acoustic loading these analytical solutions compare with the results obtained from the proposed numerical method a good correlation for low frequencies is obtained and minor discrepancies are observed with an increasing frequency

stably isomorphic dual operator algebras we prove that two unital dual operator algebras a b are stably isomorphic if and only if they are equivalent eleftherakis in j pure appl algebra arxiv math oa 0607489v4 2007 if and only if they have completely isometric normal representations on hilbert spaces h k respectively and there exists a ternary ring of operators mathcal m subset b h k such that alpha a mathcal m beta b mathcal m w and beta b mathcal m alpha a mathcal m w

an acoustic boundary integral formulation for open shells allowing different impedance conditions top and bottom surfaces abstract in the automotive aerospace industries as well as the underwater acoustics defense applications the addition of coatings to modify the response of the vibrating structure is commonplace the formulation developed is an extension of the existing thin body formulation currently found in commercial noise prediction codes such as sysnoise in order to allow problems requiring different boundary condition on both sides of the thin shell to be solved for instance a generalised thin body acoustic formulation would allow for a local impedance boundary condition to be specified on the top surface and a hard neumann boundary condition to be specified on the bottom surface such a formulation would allow for different local impedance coatings to be specified on the top and bottom surfaces due to the lack of analytical solutions for such problems even for the simplest geometries it is difficult to validate such a formulation however three test cases are presented two flat plate examples and a open cylinder with a point monopole source excitation at its centre

locally defined principal curves and surfaces principal curves are defined as self consistent smooth curves passing through the middle of the data and they have been used in many applications of machine learning as a generalization dimensionality reduction and a feature extraction tool we redefine principal curves and surfaces in terms of the gradient and the hessian of the probability density estimate this provides a geometric understanding of the principal curves and surfaces as well as a unifying view for clustering principal curve fitting and manifold learning by regarding those as principal manifolds of different intrinsic dimensionalities the theory does not impose any particular density estimation method can be used with any density estimator that gives continuous first and second derivatives therefore we first present our principal curve surface definition without assuming any particular density estimation method afterwards we develop practical algorithms for the commonly used kernel density estimation kde and gaussian mixture models gmm results of these algorithms are presented in notional data sets as well as real applications with comparisons to other approaches in the principal curve literature all in all we present a novel theoretical understanding of principal curves and surfaces practical algorithms as general purpose machine learning tools and applications of these algorithms to several practical problems

a unique coupled boundary element finite element method for the elastoacoustic analysis of fluid filled thin shells a coupled boundary element finite element technique originally developed for the analysis of open thin shell problems such as propeller blades is used in this paper for the analysis of the fluid filled elastic structures for open thin shell problems the question of nonuniqueness does not arise however it was thought at the time that such a formulation would prove to be nonunique for the analysis of closed fluid filled submerged bodies the work presented in this paper will demonstrate that for submerged fluid filled closed elastic bodies this coupled formulation is unique throughout the entire frequency range an advantage in implementing the variational form of the acoustic integral operator is that the resulting fluid matrix is symmetric as such the fluid structural coupling is simplified and the computational efficiency enhanced

scattering by cracks beneath fluid solid interfaces abstract the scattering of incident plane elastic or fluid body waves and interfacial waves by an arbitrarily orientated subsurface crack is considered the crack lies in an infinite elastic half space that is coupled to an overlying fluid half space material parameters relevant for water metal and water rock combinations are taken and far field scattering patterns are given these demonstrate beam formation along critical angles for light or moderate fluid coupling it is shown that the beams form along different critical angles depending upon the magnitude of the coupling in addition reciprocity relations relating the far field scattering coefficients viewed along an angle and generated by one type of plane wave incident along to the scattering coefficient viewed along generated by another plane wave incident along are found reciprocity relations involving interfacial waves are also given power flow theorems are derived these relate the time averaged scattered power to a combination of far field scattering coefficients this is used to determine the proportion of scattered power converted into the different types of scattered wave the reciprocity and power flow theorems provide a powerful consistency check upon the numerical accuracy of the results the boundary value problem is recast as a system of coupled integro differential equations for the unknown jump in displacement across the crack faces these integral equations are solved in an efficient and fast numerical manner by performing the integrations over the crack faces analytically thus reducing the computational effort substantially

density estimation with confidence sets exemplified by superclusters and voids in the galaxies abstract a method is presented for forming both a point estimate and a confidence set of semiparametric densities the final product is a three dimensional figure that displays a selection of density estimates for a plausible range of smoothing parameters the boundaries of the smoothing parameter are determined by a nonparametric goodness of fit test that is based on the sample spacings for each value of the smoothing parameter our estimator is selected by choosing the normal mixture that maximizes a function of the sample spacings a point estimate is selected from this confidence set by using the method of cross validation an algorithm to find the mixing distribution that maximizes the spacings functional is presented these methods are illustrated with a data set from the astronomy literature the measurements are velocities at which galaxies in the corona borealis region are moving away from our galaxy if the galaxies are clustered the velocity density will be multimodal with clusters correspond

a reciprocity relation for fluid loaded elastic plates that contain rigid defects a reciprocity relation between the farfield behaviour of the scattered fields generated by incident waves either flexural plate waves or incident from the fluid upon rigid defects embedded in a thin elastic fluid loaded plate is derived this reciprocity result is then illustrated upon model problems for which the explicit solution can be determined and the relation demonstrated

mean shift mode seeking and clustering mean shift a simple interactive procedure that shifts each data point to the average of data points in its neighborhood is generalized and analyzed in the paper this generalization makes some k means like clustering algorithms its special cases it is shown that mean shift is a mode seeking process on the surface constructed with a shadow kernal for gaussian kernels mean shift is a gradient mapping convergence is studied for mean shift iterations cluster analysis if treated as a deterministic problem of finding a fixed point of mean shift that characterizes the data applications in clustering and hough transform are demonstrated mean shift is also considered as an evolutionary strategy that performs multistart global optimization