building k edge disjoint spanning trees of minimum total length for isometric data embedding isometric data embedding requires construction of a neighborhood graph that spans all data points so that geodesic distance between any pair of data points could be estimated by distance along the shortest path between the pair on the graph this paper presents an approach for constructing k edge connected neighborhood graphs it works by finding k edge disjoint spanning trees the sum of whose total lengths is a minimum experiments show that it outperforms the nearest neighbor approach for geodesic distance estimation

state dependent scaling design for a unified approach to robust backstepping global robust stabilization of nonlinear systems is characterized as a state dependent scaling problem by choosing scaling functions recursively one can construct robust control laws for an extended class of strict feedback systems

still image coding based on vector quantization and fractal approximation in this paper we propose a coding algorithm for still images using vector quantization vq and fractal approximation in which low frequency components of an input image are approximated by vq and its residual is coded by fractal mapping the conventional fractal coding algorithms indirectly used the gray patterns of an original image with contraction mapping whereas the proposed fractal coding method employs an approximated and then decimated image as a domain pool and uses its gray patterns thus the proposed algorithm utilizes fractal approximation without the constraint of contraction mapping for approximation of an original image we employ the discrete cosine transform dct rather than conventional polynomial based transforms in addition for variable blocksize segmentation we use the fractal dimension of a block that represents the roughness of the gray surface of a region computer simulations with several test images show that the proposed method shows better performance than the conventional fractal coding methods for encoding still pictures

tta a new approach to estimate hurst exponent with less estimation error and computational time abstract investigation of long memory processes in signals can give us an important information about how signals have behaved so far and how will it behave in future hurst exponent estimation is a proper tool to show memory in signals rescaled range analysis r s detrended fluctuation analysis dfa and generalized hurst exponent ghe are most known methods for estimation of hurst exponent which introduced in literature in this paper we propose a new algorithm to estimate hurst exponent based on triangles total areas tta that can be made out of three samples of different lag in time series to test our algorithm performance we used two kinds of synthetic waveforms with known hurst exponents results indicates that the proposed method is superior with respect to data length estimation error computational time and noise sensitivity we also apply our proposed method in epilepsy detection and compare our results with previous works to show outperformance of our algorithm with accuracy of 94 5 in classification between interictal and ictal eeg signals

suboptimal minimum cluster volume cover based method for measuring fractal dimension a new method for calculating fractal dimension is developed in this paper the method is based on the box dimension concept however it involves direct estimation of a suboptimal covering of the data set of interest by finding a suboptimal cover this method is better able to estimate the required number of covering elements for a given cover size than is the standard box counting algorithm moreover any decrease in the error of the covering element count directly increases the accuracy of the fractal dimension estimation in general our method represents a mathematical dual to the standard box counting algorithm by not solving for the number of boxes used to cover a data set given the size of the box instead the method chooses the number of covering elements and then proceeds to find the placement of smallest hyperellipsoids that fully covers the data set this method involves a variant of the fuzzy c means clustering algorithm as well as the use of the minimum cluster volume clustering algorithm a variety of fractal dimension estimators using this suboptimal covering method are discussed finally these methods are compared to the standard box counting algorithm and wavelet decomposition methods for calculating fractal dimension by using one dimensional cantor dust sets and a set of standard brownian random fractal images

robust h sub spl infin control of uncertain nonlinear system via state feedback this technical note presents a solution of robust h sub spl infin control problem for an affine nonlinear system with gain bounded uncertainty it is shown that the l sub 2 induced norm of a closed loop system with the uncertainty is less than one if an extended nonlinear system with no uncertainty is dissipative with respect to a supply rate in consequence of this result a state feedback law such that the closed loop system has h sub spl infin robust performance is derived based on the hamilton jacobi inequality it is also shown that the existing results for linear systems are special cases of the presented results

a threshold of ln n for approximating set cover given a collection f of subsets of s 1 n setcover is the problem of selecting as few as possiblesubsets from f such that their union covers s and maxk cover is the problem of selecting k subsets from f such that their union has maximum cardinality both these problems arenp hard we prove that 1 o 1 ln n is a threshold below which setcover cannot be approximated efficiently unless np has slightlysuperpolynomial time algorithms this closes the gap up to low orderterms between the ratio of approximation achievable by the greedyalogorithm which is 1 o 1 lnn and provious results of lund and yanakakis that showed hardness ofapproximation within a ratio of log 2 n 2s0 72 ln n for max k cover we show an approximationthreshold of 1 1 e up tolow order terms under assumption that p np

similarity preserving principal curve an optimal 1 d feature extractor for data representation this paper discusses the problem of what kind of learning model is suitable for the tasks of feature extraction for data representation and suggests two evaluation criteria for nonlinear feature extractors reconstruction error minimization and similarity preservation based on the suggested evaluation criteria a new type of principal curve similarity preserving principal curve sppc is proposed sppcs minimize the reconstruction error under the condition that the similarity between similar samples are preserved in the extracted features thus giving researchers effective and reliable cognition of the inner structure of data sets the existence and properties of sppcs are analyzed a practical learning algorithm is proposed and high dimensional extensions of sppcs are also discussed experimental results show the virtues of sppcs in preserving inner structures of data sets and discovering manifolds with high nonlinearity

robust control for nonlinear systems with structured l 2 gain bounded uncertainty abstract this paper focuses on the problem of robust control design for uncertain nonlinear systems with l 2 gain bounded dynamic uncertainty and periodically time varying memoryless uncertainty the robust performance problem is solved via nonlinear h control with scaling factors it is shown that the scaling factors can be functions of state variables in contrast with linear robust control

necessary and sufficient conditions of stability a multiloop generalization of the circle criterion a linear time invariant system with a vector output and a vector input is described this system is closed by an uncertain nonlinear time varying feedback the only information on this feedback is given by several integral quadratic inequalities i e the uncertainties under consideration generalize the so called conic nonlinearities necessary and sufficient frequency domain conditions of stability are obtained an advanced version of the s procedure losslessness theorem and some other tools of the absolute stability theory are used

alignment of overlapping locally scaled patches for multidimensional scaling and dimensionality reduction data observations that lie on a manifold can be approximated by a collection of overlapping local patches the alignment of which in a low dimensional euclidean space provides an embedding of the data this paper describes an embedding method using classical multidimensional scaling as a local model based on the fact that a manifold locally resembles a euclidean space a set of overlapping neighborhoods are chosen by a greedy approximation algorithm of minimum set cover local patches derived from the set of overlapping neighborhoods by classical multidimensional scaling are aligned in order to minimize a residual measure which has a quadratic form of the resulting global coordinates and can be minimized analytically by solving an eigenvalue problem this method requires only distances within each neighborhood and provides locally isometric embedding results the size of the eigenvalue problem scales with the number of overlapping neighborhoods rather than the number of data points experiments on both synthetic and real world data sets demonstrate the effectiveness of this method extensions and variations of the method are discussed

on the hardness of approximating minimization problems we prove results indicating that it is hard to compute efficiently good approximate solutions to the graph coloring set covering and other related minimization problems specifically there is an e 0 such that graph coloring cannot be approximated with ratio n e unless p np set covering cannot be approximated with ratio c log n for any c 1 4 unless np is contained in dtime n poly log n similar results follow for related problems such as clique cover fractional chromatic number dominating set and others

can the fractal dimension of images be measured abstract fractal dimension is a popular parameter for explaining certain phenomena and for describing natural textures the problem of estimating the fractal dimension of a profile or an image is more difficult and devious than theory suggests this paper studies the accuracy and robustness of two common estimators of fractal dimension box counting and the variation method using two types of data brownian and takagi poor results are demonstrated from applying theory directly called naive estimation data is then interpreted in the most optimistic way possible by matching the estimator to the known fractal dimension experiments quantify the effects of resolution or fineness of sampling and quantization or rounding of sampled values increasing resolution enhances the estimators when true dimension d is large but may possibly due to quantization effect degrade estimators when d is small quantization simply causes shifts in estimates the results suggest that one should not place much reliance in the absolute value of a fractal estimate but that the estimates do vary monotonically with d and might be useful descriptors in tasks such as image segmentation and description

feature selection in the pattern classification problem of digital chest radiograph segmentation in pattern classification problems the choice of variables to include in the feature vector is a difficult one the authors have investigated the use of stepwise discriminant analysis as a feature selection step in the problem of segmenting digital chest radiographs in this problem locally calculated features are used to classify pixels into one of several anatomic classes the feature selection step was used to choose a subset of features which gave performance equivalent to the entire set of candidate features while utilizing less computational resources the impact of using the reduced selected feature set on classifier performance is evaluated for two classifiers a linear discriminator and a neural network the results from the reduced selected feature set were compared to that of the full feature set as well as a randomly selected reduced feature set the results of the different feature sets were also compared after applying an additional postprocessing step which used a rule based spatial information heuristic to improve the classification results this work shows that in the authors pattern classification problem using a feature selection step reduced the number of features used reduced the processing time requirements and gave results comparable to the full set of features

texture roughness analysis and synthesis via extended self similar ess model the 2d fractional brownian motion fbm model provides a useful tool to model textured surfaces whose roughness is scale invariant to represent textures whose roughness is scale dependent we generalize the fbm model to the extended self similar ess model in this research we present an estimation algorithm to extract the model parameters from real texture data furthermore a new incremental fourier synthesis algorithm is proposed to generate the 2d realizations of the ess model finally the estimation and rendering methods are combined to synthesize real textured surfaces

parameterized lmis in control theory a wide variety of problems in control system theory fall within the class of parameterized linear matrix inequalities lmis that is lmis whose coefficients are functions of a parameter confined to a compact set such problems though convex involve an infinite set of lmi constraints and hence are inherently difficult to solve numerically this paper investigates relaxations of parameterized lmi problems into standard lmi problems using techniques relying on directional convexity concepts an in depth discussion of the impact of the proposed techniques in quadratic programming lyapunov based stability and performance analysis mu analysis and linear parameter varying control is provided illustrative examples are given to demonstrate the usefulness and practicality of the approach

hessian eigenmaps locally linear embedding techniques for high dimensional data we describe a method for recovering the underlying parametrization of scattered data m i lying on a manifold m embedded in high dimensional euclidean space the method hessian based locally linear embedding derives from a conceptual framework of local isometry in which the manifold m viewed as a riemannian submanifold of the ambient euclidean space r n is locally isometric to an open connected subset of euclidean space r d because does not have to be convex this framework is able to handle a significantly wider class of situations than the original isomap algorithm the theoretical framework revolves around a quadratic form h f m h f m f dm defined on functions f m r here hf denotes the hessian of f and h f averages the frobenius norm of the hessian over m to define the hessian we use orthogonal coordinates on the tangent planes of m the key observation is that if m truly is locally isometric to an open connected subset of r d then h f has a d 1 dimensional null space consisting of the constant functions and a d dimensional space of functions spanned by the original isometric coordinates hence the isometric coordinates can be recovered up to a linear isometry our method may be viewed as a modification of locally linear embedding and our theoretical framework as a modification of the laplacian eigenmaps framework where we substitute a quadratic form based on the hessian in place of one based on the laplacian

state dependent scaling problems and stability of interconnected iiss and iss systems this paper addresses the problem of establishing stability of nonlinear interconnected systems this paper introduces a mathematical formulation of the state dependent scaling problems whose solutions directly provide lyapunov functions proving stability properties of interconnected dissipative systems in a unified manner stability criteria are interpreted as sufficient conditions for the existence of solutions to the state dependent scaling problems computing solutions to the problems is straightforward for systems covered by classical stability criteria it however could be too difficult for systems with strong nonlinearity the main purpose of this paper is to demonstrate the effectiveness beyond formal applicability by focusing on interconnected integral input to state stable iiss systems and input to state stable iss systems this paper derives small gain type theorems for interconnected systems involving iiss systems from the state dependent scaling formulation this paper provides solutions and lyapunov functions explicitly the new framework seamlessly generalizes the iss small gain theorem and classical stability criteria such as the lp small gain theorem the passivity theorems the circle and popov criteria state dependence of the scaling is crucial for effective treatment of essential nonlinearities while constants are sufficient for classical nonlinearities

maximal linear embedding for dimensionality reduction over the past few decades dimensionality reduction has been widely exploited in computer vision and pattern analysis this paper proposes a simple but effective nonlinear dimensionality reduction algorithm named maximal linear embedding mle mle learns a parametric mapping to recover a single global low dimensional coordinate space and yields an isometric embedding for the manifold inspired by geometric intuition we introduce a reasonable definition of locally linear patch maximal linear patch mlp which seeks to maximize the local neighborhood in which linearity holds the input data are first decomposed into a collection of local linear models each depicting an mlp these local models are then aligned into a global coordinate space which is achieved by applying mds to some randomly selected landmarks the proposed alignment method called landmarks based global alignment lga can efficiently produce a closed form solution with no risk of local optima it just involves some small scale eigenvalue problems while most previous aligning techniques employ time consuming iterative optimization compared with traditional methods such as isomap and lle our mle yields an explicit modeling of the intrinsic variation modes of the observation data extensive experiments on both synthetic and real data indicate the effectivity and efficiency of the proposed algorithm

representing curves at their natural scales abstract the shapes of curves generally contain several structures at different scales an expressive curve representation should explicitly describe each structure at its appropriate scale this greatly simplifies any reasoning processes e g matching applied to the curve rather than exhaustively represent the curve over a full range of scales just the most significant ones should be retained for a compact and useful representation a technique is presented that identifies the significant or natural scales in a curve

local fractal and multifractal features for volumic texture characterization for texture analysis several features such as co occurrence matrices gabor filters and the wavelet transform are used recently fractal geometry appeared to be an effective feature to analyze texture but it is often restricted to 2d images while 3d information can be very important especially in medical image processing moreover applications are limited to the use of fractal dimension this study focuses on the benefits of fractal geometry in a classification method based on volumic texture analysis the proposed methods make use of fractal and multifractal features for a 3d texture analysis of a voxel neighborhood they are validated with synthetic data before being applied on real images their efficiencies are proved by comparison to some other texture features in supervised classification processes adaboost and support vector machine classifiers the results showed that features based on fractal geometry by combining fractal and multifractal features contributed to new texture characterization information on new features was useful and complementary for a classification method this study suggests that fractal geometry can provide a new useful information in 3d texture analysis especially in medical imaging

multiple resolution texture analysis and classification textures are classified based on the change in their properties with changing resolution the area of the gray level surface is measured at serveral resolutions this area decreases at coarser resolutions since fine details that contribute to the area disappear fractal properties of the picture are computed from the rate of this decrease in area and are used for texture comparison and classification the relation of a texture picture to its negative and directional properties are also discussed

robust stability with time varying structured uncertainty considers the problem of assessing robust stability in the presence of block diagonally structured time varying dynamic uncertainty it is shown that robust stability holds only if there exist constant scalings which lead to a small gain condition the notion of stability here is finite gain stability over finite energy signals in sharp contrast to the case of time invariant dynamic uncertainty this result is not limited by the number uncertainty blocks these results parallel previous results regarding finite gain stability over persistent bounded signals

influence of image resolution and thresholding on the apparent mass fractal characteristics of preferential flow patterns in field soils preferential flow is ubiquitous in field soils where it has important practical implications for water and contaminant transport dyes are frequently used to visualize preferential flow pathways the fact that stain patterns in pictures of soil profiles often exhibit convoluted geometries reminiscent of fractals has encouraged a number of authors to use the principles of fractal geometry to describe stain patterns this description typically involves two numbers a mass and a surface fractal dimension the evaluation of either one via image analysis requires numerous subjective choices to be made including choices regarding image resolution the definition adopted for the fractal dimension and the thresholding algorithm used to generate binary images the present article analyzes in detail the influence of these various choices on the mass fractal dimension of stained preferential flow patterns a theoretical framework in which to envisage these choices is developed using the classical quadratic von koch island as an example this framework is then applied to a set of pictures of an actual stain pattern in an orchard soil the results suggest that the apparent mass fractal dimension of the stain pattern varies between 1 56 and 1 88 depending on choices made at different stages in the evaluation of the fractal dimension in each case considered the dimension determined by a straight line fit in a log log plot has extremely high statistical significance with r 0 999 of the various parameters subject to choice image resolution seems to have the most pronounced influence on the value of the fractal dimension which increases markedly at higher resolution smaller pixel size by analogy with the case of the quadratic von koch island this dependence on image resolution as well as the fact that the surface area of the stain pattern does not decrease with pixel size suggests that the stain pattern is not a mass fractal that is there is no reason to believe that its various dimensions differ from 2 the approach adopted in the present article could be useful whenever fractal dimensions are evaluated via image analysis

dimensionality reduction an interpretation from manifold regularization perspective in this paper we propose to unify various dimensionality reduction algorithms by interpreting the manifold regularization mr framework in a new way although the mr framework was originally proposed for learning we utilize it to give a unified treatment for many dimensionality reduction algorithms from linear to nonlinear supervised to unsupervised and single class to multi class approaches in addition the framework can provide a general platform to design new dimensionality reduction algorithms the framework is expressed in the form of a regularized fitting problem in a reproducing kernel hilbert space it consists of one error part and two regularization terms the complexity term and the smoothness term the error part measures the difference between the estimated low dimensional data distribution and the true high dimensional data distribution or the difference between the estimated and targeted low dimensional representations of data the complexity term is a measurement of the complexity of the feature mapping for dimensionality reduction and the smoothness term reflects the intrinsic structure of data based on the framework we propose a manifold regularized kernel least squares mr kls method which can efficiently learn an explicit feature mapping in the semi supervised sense experiments show that our approach is effective for out of sample extrapolation c 2014 elsevier inc all rights reserved

evaluating the fractal dimension of surfaces fractal objects derive from many interface phenomena as they arise in for example materials science chemistry and geology hence the problem of estimating fractal dimension becomes of both theoretical and practical importance existing algorithms implement the standard definitions of fractal dimension directly but as we show often give unreliable results when applied to digitized and quantized data we present a new algorithm for estimating the fractal dimension of surfaces the variation method that is more reliable and robust than the standard ones it is based on a new definition of fractal dimension particularly suited for graphs of functions the variation method is validated with both fractional brownian surfaces and takagi surfaces two classes of mathematical objects with known fractal dimension and is shown to give more accurate results than the classical algorithms finally our new algorithm is applied to data from sand blasted metal surfaces

the complex structured singular value a tutorial introduction to the complex structured singular value is presented with an emphasis on the mathematical aspects of the based methods discussed here have been useful for analysing the performance and robustness properties of linear feedback systems several tests for robust stability and performance with computable bounds for transfer functions and their state space realizations are compared and a simple synthesis problem is studied uncertain systems are represented using linear fractional transformations lfts which naturally unify the frequency domain and state space methods

complexity confusion and perceptual grouping part ii mapping complexity intermediate level vision is central to form perception and we outline an approach to intermediate level segmentation based on complexity analysis in this second of a pair of papers we continue the focus on edge element grouping and the motivating example of an edge element inferred from an unknown image is this local edge part of a long curve or part of a texture if the former which is the next element along the curve if the latter is the texture like a well combed hair pattern in which nearby elements are oriented similarly or more chaotic as in a spaghetti pattern in the previous paper we showed how these questions raise issues of complexity and dimensionality and how context in both position and orientation are important we now propose a measure based on tangential and normal complexities and illustrate its computation tangential complexity is related to extensions normal complexity to density taken together they define four canonical classes of tangent distributions those arising from curves from texture flows from turbulent textures and from isolated dust examples are included

building k connected neighborhood graphs for isometric data embedding isometric data embedding using geodesic distance requires the construction of a connected neighborhood graph so that the geodesic distance between every pair of data points can be estimated this paper proposes an approach for constructing k connected neighborhood graphs the approach works by applying a greedy algorithm to add each edge in a nondecreasing order of edge length to a neighborhood graph if end vertices of the edge are not yet k connected on the graph the k connectedness between vertices is tested using a network flow technique by assigning every vertex a unit flow capacity this approach is applicable to a wide range of data experiments show that it gives better estimation of geodesic distances than other approaches especially when the data are undersampled or nonuniformly distributed

laplacian eigenmaps for dimensionality reduction and data representation one of the central problems in machine learning and pattern recognition is to develop appropriate representations for complex data we consider the problem of constructing a representation for data lying on a low dimensional manifold embedded in a high dimensional space drawing on the correspondence between the graph laplacian the laplace beltrami operator on the manifold and the connections to the heat equation we propose a geometrically motivated algorithm for representing the high dimensional data the algorithm provides a computationally efficient approach to nonlinear dimensionality reduction that has locality preserving properties and a natural connection to clustering some potential applications and illustrative examples are discussed

shape based invariant texture indexing this paper introduces a new texture analysis scheme which is invariant to local geometric and radiometric changes the proposed methodology relies on the topographic map of images obtained from the connected components of level sets this morphological tool providing a multi scale and contrast invariant representation of images is shown to be well suited to texture analysis we first make use of invariant moments to extract geometrical information from the topographic map this yields features that are invariant to local similarities or local affine transformations these features are invariant to any local contrast change we then relax this invariance by computing additional features that are invariant to local affine contrast changes and investigate the resulting analysis scheme by performing classification and retrieval experiments on three texture databases the obtained experimental results outperform the current state of the art in locally invariant texture analysis

classification and segmentation of rotated and scaled textured images using texture tuned masks abstract a rotation and scale invariant texture classifier function is described for effective classification and segmentation of images involving textures of unknown rotation and scale changes the classifier used is the texture energy associated with a mask that has been tuned to be both discriminant between different textures and to be invariant to rotation and scale changes the mask tuning scheme utilized is based on task oriented criterion optimization via a guided random search procedure to incorporate the changes both a dynamic texture sample set using a two dimensional 2d linked list and a re ranking procedure are applied for training maximum feature dispersion of inter texture classes and high feature convergence of inner texture class samples associated with other statistical measures are suggested as key criteria in training in a study based on 15 distinct brodatz textures it is found that the tuning process although computationally intensive converges efficiently the mean classifier values of the classifier for a particular texture at different orientation and different scales are tightly clustered an objective measure of classification capability is determined by computing the standard deviation of the classifier over pure texture at definite orientation and scale examples are presented of the classifier function applied to the segmentation of collages of brodatz textures comprising regions of various orientation and scale

an evaluation of intrinsic dimensionality estimators the intrinsic dimensionality of a data set may be useful for understanding the properties of classifiers applied to it and thereby for the selection of an optimal classifier in this paper the authors compare the algorithms for two estimators of the intrinsic dimensionality of a given data set and extend their capabilities one algorithm is based on the local eigenvalues of the covariance matrix in several small regions in the feature space the other estimates the intrinsic dimensionality from the distribution of the distances from an arbitrary data vector to a selection of its neighbors the characteristics of the two estimators are investigated and the results are compared it is found that both can be applied successfully but that they might fail in certain cases the estimators are compared and illustrated using data generated from chromosome banding profiles

robust disturbance attenuation of nonlinear systems using output feedback and state dependent scaling this paper presents an approach to output feedback stabilization with l 2 disturbance attenuation for nonlinear systems in the presence of dynamic uncertainties a new formulation of state dependent scaling is introduced into the output feedback design which unifies treatment of nonlinear and linear gains the effect of disturbance on the controlled output which is allowed to be any function of output measurements can be always attenuated to an arbitrarily small level with global asymptotic stability if the plant belongs to a wide class of triangular systems whose uncertainties do not necessarily have finite linear gains the uncertain dynamics is not limited to input to state stable systems either the approach is not only a natural extension of popular approaches in robust linear control but also advantageous to numerical computation which is applicable to non triangular systems as well as triangular systems

error bounds on the estimation of fractal dimension the use of fractal dimension as an index of complexity is widely used in natural science studies related to the significance of the estimates obtained have rarely been presented in the past this paper is intended to present an error analysis in the estimation of the fractal dimension of a particular class of objects namely graphs of knopp functions the algorithm used to estimate the fractal dimension is the variation method various numerical approximations of the variation will be presented using functional properties of the chosen parametric family of sets we derive error bounds useful in the assessment of the accuracy that can be achieved in the numerical approximation of the dimension at a given scale and resolution

robust stabilization of nonlinear systems with pointwise norm bounded uncertainties a control lyapunov function approach the authors give a necessary and sufficient condition for globally stabilizing a nonlinear system robustly with respect to unstructured uncertainties spl phi spl tilde u x t norm bounded for each fixed x and u this condition requires one to find a smooth proper and positive definite solution v x of a suitable partial differential inequality depending only on the system data a procedure based on the knowledge of v x is outlined for constructing almost smooth robustly stabilizing controllers our approach based on lyapunov functions generalizes previous results for linear uncertain systems and establishes a precise connection between robust stabilization on one hand and h sub spl infin control sector conditions and input to state stabilization on the other

local coordinates alignment with global preservation for dimensionality reduction dimensionality reduction is vital in many fields and alignment based methods for nonlinear dimensionality reduction have become popular recently because they can map the high dimensional data into a low dimensional subspace with the property of local isometry however the relationships between patches in original high dimensional space cannot be ensured to be fully preserved during the alignment process in this paper we propose a novel method for nonlinear dimensionality reduction called local coordinates alignment with global preservation we first introduce a reasonable definition of topology preserving landmarks tpls which not only contribute to preserving the global structure of datasets and constructing a collection of overlapping linear patches but they also ensure that the right landmark is allocated to the new test point then an existing method for dimensionality reduction that has good performance in preserving the global structure is used to derive the low dimensional coordinates of tpls local coordinates of each patch are derived using tangent space of the manifold at the corresponding landmark and then these local coordinates are aligned into a global coordinate space with the set of landmarks in low dimensional space as reference points the proposed alignment method called landmarks based alignment can produce a closed form solution without any constraints while most previous alignment based methods impose the unit covariance constraint which will result in the deficiency of global metrics and undesired rescaling of the manifold experiments on both synthetic and real world datasets demonstrate the effectiveness of the proposed algorithm

texture features for classification of ultrasonic liver images the classification of ultrasonic liver images is studied making use of the spatial gray level dependence matrices the fourier power spectrum the gray level difference statistics and the laws texture energy measures features of these types are used to classify three sets of ultrasonic liver images normal liver hepatoma and cirrhosis 30 samples each the bayes classifier and the hotelling trace criterion are employed to evaluate the performance of these features from the viewpoint of speed and accuracy of classification it is found that these features do not perform well enough hence a new texture feature set multiresolution fractal features based on multiple resolution imagery and the fractional brownian motion model is proposed to detect diffuse liver diseases quickly and accurately fractal dimensions estimated at various resolutions of the image are gathered to form the feature vector texture information contained in the proposed feature vector is discussed a real time implementation of the algorithm produces about 90 correct classification for the three sets of ultrasonic liver images

dimensionality reduction by mixed kernel canonical correlation analysis in this paper we propose a novel method named mixed kernel cca mkcca to achieve easy yet accurate implementation of dimensionality reduction mkcca consists of two major steps first the high dimensional data space is mapped into the reproducing kernel hilbert space rkhs rather than the hilbert space with a mixture of kernels i e a linear combination between a local kernel and a global kernel meanwhile a uniform design for experiments with mixtures is also introduced for model selection second in the new rkhs kernel cca is further improved by performing principal component analysis pca followed by cca for effective dimensionality reduction we prove that mkcca can actually be decomposed into two separate components i e pca and cca which can be used to better remove noises and tackle the issue of trivial learning existing in cca or traditional kernel cca after this the proposed mkcca can be implemented in multiple types of learning such as multi view learning supervised learning semi supervised learning and transfer learning with the reduced data we show its superiority over existing methods in different types of learning by extensive experimental results