a modified version of the k means algorithm with a distance based on cluster symmetry we propose a modified version of the k means algorithm to cluster data the proposed algorithm adopts a novel nonmetric distance measure based on the idea of point symmetry this kind of point symmetry distance can be applied in data clustering and human face detection several data sets are used to illustrate its effectiveness

a multi prototype clustering algorithm clustering is an important unsupervised learning technique widely used to discover the inherent structure of a given data set some existing clustering algorithms uses single prototype to represent each cluster which may not adequately model the clusters of arbitrary shape and size and hence limit the clustering performance on complex data structure this paper proposes a clustering algorithm to represent one cluster by multiple prototypes the squared error clustering is used to produce a number of prototypes to locate the regions of high density because of its low computational cost and yet good performance a separation measure is proposed to evaluate how well two prototypes are separated multiple prototypes with small separations are grouped into a given number of clusters in the agglomerative method new prototypes are iteratively added to improve the poor cluster separations as a result the proposed algorithm can discover the clusters of complex structure with robustness to initial settings experimental results on both synthetic and real data sets demonstrate the effectiveness of the proposed clustering algorithm

existence of minima for nonconvex functionals in spaces of functions depending on the distance from the boundary we prove that some nonconvex functionals admit a unique minimum in a functional space of functions which depend only on the distance from the boundary of the plane domain where they are defined the domains considered are disks and regular polygons we prove that the sequence of minima of the functional on the polygons converges to the unique minimum on the circumscribed disk as the number of sides tends to infinity our method also allows us to determine the explicit form of the minima

uniqueness theorems for positive radial solutions of quasilinear elliptic equations in a ball we establish a new pohozaev type identity and use it to prove a theorem on the uniqueness of positive radial solutions to the quasilinear elliptic problem div u m 2emsp14 u f u 0 inb andu 0 on b wherebis a finite ball in rn n 3 and 1 0 and 1 p q n 2 n 2 has a unique positive solution whenn 6 this gives a complete answer to an open problem raised by brezis and nirenberg in 1983 in the casen 6 we shall also derive some partial results to the open problem in the casesn 3 4 5

adaptive filtering using quantized output measurements a normalized stochastic gradient adaptive filtering algorithm based on a finite impulse response fir model is discussed the algorithm identifies the system exactly given only coarsely quantized output measurements a description of the quantizer is included in the overall input output model and the scheme exploits an approximation of the derivative of the quantizer using an associated differential equation global convergence is established to a zero output error except for possible colored measurement disturbances parameter setting or to the boundary of the model set

on the minimum problem for a class of noncoercive nonconvex functionals we are concerned with the problem of existence of solutions to the variational problem min left int 0 r g t v t dt v in ac 0 r v r 0 right with only one fixed endpoint prescribed the map g colon 0 r times mathbb r to overline mathbb r is a normal integrand for which neither convexity nor superlinear growth conditions are assumed as an application we give an existence result for the radially symmetric variational problem min u in wuu b r int b r f pt mod x mod nabla u x a x u x dx where b r is the ball of mathbb r n centered at the origin and with radius r 0 the map f colon 0 r times 0 infty to overline mathbb r is a normal integrand and a in l 0 r again neither convexity nor superlinear growth conditions are made on f these kinds of problems with nonconvex lagrangians with respect to nabla u arise in different fields of mathematical physics such as optimal design and nonlinear elasticity

anytime reliable transmission of real valued information through digital noisy channels the problem of reliably transmitting a real valued random vector through a digital noisy channel is relevant for the design of distributed estimation and control techniques over networked systems one important example consists in the remote state estimation under communication constraints in this case an anytime transmission scheme consists of an encoder which maps the real vector into a sequence of channel inputs and a decoder which sequentially updates its estimate of the vector as more and more channel outputs are observed the encoder performs both source and channel coding of the data assuming that no channel feedback is available at the transmitter this paper studies the rates of convergence to zero of the mean squared error two coding strategies are analyzed the first one has exponential convergence rate but is expensive in terms of its encoder decoder computational complexity while the second one has a convenient computational complexity but subexponential convergence rate general bounds are obtained describing the convergence properties of these classes of methods

a modified k means algorithm for circular invariant clustering several important pattern recognition applications are based on feature vector extraction and vector clustering directional patterns are commonly represented by rotation variant vectors f sub d formed from features uniformly extracted in m directions it is often desirable that pattern recognition algorithms are invariant under pattern rotation this paper introduces a distance measure and a k means based algorithm namely circular k means ck means to cluster vectors containing directional information such as f sub d in a circular shift invariant manner a circular shift of f sub d corresponds to pattern rotation thus the algorithm is rotation invariant an efficient fourier domain representation of the proposed measure is presented to reduce computational complexity a split and merge approach smck means suited to the proposed ck means technique is proposed to reduce the possibility of converging at local minima and to estimate the correct number of clusters experiments performed for textural images illustrate the superior performance of the proposed algorithm for clustering directional vectors f sub d compared to the alternative approach that uses the original k means and rotation invariant feature vectors transformed from f sub d

asymptotically efficient parameter estimation using quantized output observations this paper studies identification of systems in which only quantized output observations are available an identification algorithm for system gains is introduced that employs empirical measures from multiple sensor thresholds and optimizes their convex combinations strong convergence of the algorithm is first derived the algorithm is then extended to a scenario of system identification with communication constraints in which the sensor output is transmitted through a noisy communication channel and observed after transmission the main results of this paper demonstrate that these algorithms achieve the cramer rao lower bounds asymptotically and hence are asymptotically efficient algorithms furthermore under some mild regularity conditions these optimal algorithms achieve error bounds that approach optimal error bounds of linear sensors when the number of thresholds becomes large these results are further extended to finite impulse response and rational transfer function models when the inputs are designed to be periodic and full rank

a new cluster isolation criterion based on dissimilarity increments this paper addresses the problem of cluster defining criteria by proposing a model based characterization of interpattern relationships taking a dissimilarity matrix between patterns as the basic measure for extracting group structure dissimilarity increments between neighboring patterns within a cluster are analyzed empirical evidence suggests modeling the statistical distribution of these increments by an exponential density we propose to use this statistical model which characterizes context to derive a new cluster isolation criterion the integration of this criterion in a hierarchical agglomerative clustering framework produces a partitioning of the data while exhibiting data interrelationships in terms of a dendrogram type graph the analysis of the criterion is undertaken through a set of examples showing the versatility of the method in identifying clusters with arbitrary shape and size the number of clusters is intrinsically found without requiring ad hoc specification of design parameters nor engaging in a computationally demanding optimization procedure

a novel clustering method based on hybrid k nearest neighbor graph abstract most of the existing clustering methods have difficulty in processing complex nonlinear data sets to remedy this deficiency in this paper a novel data model termed hybrid k nearest neighbor hknn graph which combines the advantages of mutual k nearest neighbor graph and k nearest neighbor graph is proposed to represent the nonlinear data sets moreover a clustering method based on the hknn graph chknn is proposed the chknn first generates several tight and small subclusters then merges these subclusters by exploiting the connectivity among them in order to select the optimal parameters for chknn we further propose an internal validity index termed k nearest neighbor index knni which can also be used to evaluate the validity of nonlinear clustering results by varying a control parameter experimental results on synthetic and real world data sets as well as that on the video clustering have demonstrated the significant improvement on performance over existing nonlinear clustering methods and internal validity indices

identification of arma models using intermittent and quantized output observations this paper studies system identification of arma models whose outputs are subject to finite level quantization and random packet dropouts using the maximum likelihood criterion we propose a recursive identification algorithm which we show to be strongly consistent and asymptotically normal we also propose a simple adaptive quantization scheme which asymptotically achieves the minimum parameter estimation error covariance the joint effect of finite level quantization and random packet dropouts on identification accuracy are exactly quantified the theoretical results are verified by simulations

unsupervised learning of finite mixture models this paper proposes an unsupervised algorithm for learning a finite mixture model from multivariate data the adjective unsupervised is justified by two properties of the algorithm 1 it is capable of selecting the number of components and 2 unlike the standard expectation maximization em algorithm it does not require careful initialization the proposed method also avoids another drawback of em for mixture fitting the possibility of convergence toward a singular estimate at the boundary of the parameter space the novelty of our approach is that we do not use a model selection criterion to choose one among a set of preestimated candidate models instead we seamlessly integrate estimation and model selection in a single algorithm our technique can be applied to any type of parametric mixture model for which it is possible to write an em algorithm in this paper we illustrate it with experiments involving gaussian mixtures these experiments testify for the good performance of our approach

a distance based clustering method for arbitrary shaped clusters in large datasets clustering has been widely used in different fields of science technology social science etc naturally clusters are in arbitrary non convex shapes in a dataset one important class of clustering is distance based method however distance based clustering methods usually find clusters of convex shapes classical single link is a distance based clustering method which can find arbitrary shaped clusters it scans dataset multiple times and has time requirement of o n 2 where n is the size of the dataset this is potentially a severe problem for a large dataset in this paper we propose a distance based clustering method l sl to find arbitrary shaped clusters in a large dataset in this method first leaders clustering method is applied to a dataset to derive a set of leaders subsequently single link method with distance stopping criteria is applied to the leaders set to obtain final clustering the l sl method produces a flat clustering it is considerably faster than the single link method applied to dataset directly clustering result of the l sl may deviate nominally from final clustering of the single link method distance stopping criteria applied to dataset directly to compensate deviation of the l sl an improvement method is also proposed experiments are conducted with standard real world and synthetic datasets experimental results show the effectiveness of the proposed clustering methods for large datasets

input design in worst case system identification using binary sensors this technical note addresses system identification using binary valued sensors in a worst case set membership setting the main contribution is the solution of the optimal input design problem for identification of scalar gains which is instrumental to the construction of suboptimal input signals for identification of fir models of arbitrary order two different cost functions are considered for input design the maximum parametric identification error and the relative uncertainty reduction with respect to the minimum achievable error it is shown that in the latter case the solution enjoys the property of being independent of the length of the identification experiment and as such it can be implemented as an optimal recursive procedure over a time interval of arbitrary length

on the capacity of the gaussian channel with a finite number of input levels an analytic confirmation of an observation made by g ungerboeck 1965 that approximately optimal performance on a gaussian channel with capacity c can be obtained with about 2 sup c 1 levels is given in particular the results imply that by using about 2 sup c 1 levels a rate of nearly c 1 bit can be achieved and that by using 2 sup c 1 levels a rate of about c 0 4 bits can be achieved

almost sure convergence rates for system identification using binary quantized and regular sensors abstract this paper presents almost sure convergence rates for system identification under binary quantized and regular sensors to accommodate practical model complexity constraints the system under consideration is represented by a modeled part together with an unknown but bounded unmodeled dynamics under uncorrelated noise sequences identification errors with different sensor types are studied and tight error bounds are obtained without information or constraints on noise moment conditions the results are then extended to correlated noise sequences whose remote past and distant future are asymptotically independent in both cases almost sure error bounds of the laws of iterated logarithms type are derived

support vector clustering we present a novel clustering method using the approach of support vector machines data points are mapped by means of a gaussian kernel to a high dimensional feature space where we search for the minimal enclosing sphere this sphere when mapped back to data space can separate into several components each enclosing a separate cluster of points we present a simple algorithm for identifying these clusters the width of the gaussian kernel controls the scale at which the data is probed while the soft margin constant helps coping with outliers and overlapping clusters the structure of a dataset is explored by varying the two parameters maintaining a minimal number of support vectors to assure smooth cluster boundaries we demonstrate the performance of our algorithm on several datasets

a maximum variance cluster algorithm we present a partitional cluster algorithm that minimizes the sum of squared error criterion while imposing a hard constraint on the cluster variance conceptually hypothesized clusters act in parallel and cooperate with their neighboring clusters in order to minimize the criterion and to satisfy the variance constraint in order to enable the demarcation of the cluster neighborhood without crucial parameters we introduce the notion of foreign cluster samples finally we demonstrate a new method for cluster tendency assessment based on varying the variance constraint parameter

on minima of radially symmetric functionals of the gradient where b is the unit ball of ir and the map u g r v is lower semicontinuous but not necessarily convex problems of this kind arise in domains as different as nonlinear elasticity fluid dynamics and shape optimization and either for the problem of the existence of solutions or for the properties of the relaxed problem are considered in l 7 in particular the very same problem is considered in 7 our results present the following features a no smoothness on g or h is required g is either a normal integrand or a lower semicontinuous function b the case h 0 is allowed in this case the assumption on g reduces for the existence of solutions to g being lower semicontinuous and growing at infinity as is to be expected for the uniqueness in addition to g being strictly increasing as is also to be expected c the case h au is allowed for a 0 our theorems yield at once existence and uniqueness of solutions with no further assumptions on g besides lower semicontinuity and growth at infinity

recursive identification of fir systems with binary valued outputs and communication channels this paper investigates the recursive identification of the finite impulse response systems whose outputs are subject to both the binary valued quantization and the communication unreliability the discrete memoryless channel with packet losses and the additive white gaussian noise channel with time delay are considered a stochastic gradient type algorithm and a stochastic approximation type algorithm are respectively proposed to estimate the unknown system parameters under some mild conditions the algorithms can be proved to be convergent in the almost sure and mean square senses also the convergence rates are given numerical examples are included to illustrate the performance of the algorithms

consensus conditions of multi agent systems with time varying topologies and stochastic communication noises this paper investigates the average consensus problem of first order discrete time multi agent networks in uncertain communication environments each agent can only use its own and neighbors information to design its control input to attenuate the communication noises a distributed stochastic approximation type protocol is used by using probability limit theory and algebraic graph theory consensus conditions for this kind of protocols are obtained a for the case of fixed topologies a necessary and sufficient condition for mean square average consensus is given which is also sufficient for almost sure consensus b for the case of time varying topologies sufficient conditions for mean square average consensus and almost sure consensus are given respectively especially if the network switches between jointly containing spanning tree instantaneously balanced graphs then the designed protocol can guarantee that each individual state converges both almost surely and in mean square to a common random variable whose expectation is right the average of the initial states of the whole system and whose variance describes the static maximum mean square error between each individual state and the average of the initial states of the whole system

coordination and consensus of networked agents with noisy measurements stochastic algorithms and asymptotic behavior this paper considers the coordination and consensus of networked agents where each agent has noisy measurements of its neighbors states for consensus seeking we propose stochastic approximation type algorithms with a decreasing step size and introduce the notions of mean square and strong consensus although the decreasing step size reduces the detrimental effect of the noise it also reduces the ability of the algorithm to drive the individual states towards each other the key technique is to ensure a trade off for the decreasing rate of the step size by following this strategy we first develop a stochastic double array analysis in a two agent model which leads to both mean square and strong consensus and extend the analysis to a class of well studied symmetric models subsequently we consider a general network topology and introduce stochastic lyapunov functions together with the so called direction of invariance to establish mean square consensus finally we apply the stochastic lyapunov analysis to a leader following scenario

quantized identification with dependent noise and fisher information ratio of communication channels system identification is studied in which the system output is quantized transmitted through a digital communication channel and observed afterwards this paper explores strong convergence efficiency and complexity of identification algorithms under colored noise and dependent communication channels it first presents algorithms for certain core identification problems using quantized observations on the basis of empirical measures and nonlinear mappings strong consistency with probability one convergence is established under mixing noises furthermore with pre quantization signal processing it is shown that certain modified algorithms can achieve asymptotic efficiency under correlated noises to improve convergence speeds quantization threshold adaptation algorithms are introduced these results are then used to study the impact of communication channels on system identification under dependent channels the concept of fisher information ratio is introduced to characterize such impact it is shown that the fisher information ratio can be calculated from certain channel characteristic matrices the relationship between the fisher information ratio and shannon s channel capacity is discussed from the angle of time and space information the methods of identification input designs that link general system parameters to core identification problems are reviewed

ecmdd evidential c medoids clustering with multiple prototypes in this work a new prototype based clustering method named evidential c medoids ecmdd which belongs to the family of medoid based clustering for proximity data is proposed as an extension of fuzzy c medoids fcmdd on the theoretical framework of belief functions in the application of fcmdd and original ecmdd a single medoid prototype which is supposed to belong to the object set is utilized to represent one class for the sake of clarity this kind of ecmdd using a single medoid is denoted by secmdd in real clustering applications using only one pattern to capture or interpret a class may not adequately model different types of group structure and hence limits the clustering performance in order to address this problem a variation of ecmdd using multiple weighted medoids denoted by wecmdd is presented unlike secmdd in wecmdd objects in each cluster carry various weights describing their degree of representativeness for that class this mechanism enables each class to be represented by more than one object experimental results in synthetic and real data sets clearly demonstrate the superiority of secmdd and wecmdd moreover the clustering results by wecmdd can provide richer information for the inner structure of the detected classes with the help of prototype weights

optimal design and relaxation of variational problems iii abstract this paper has attempted a synthesis of three subjects that have developed separately optimal design homogenization and relaxation in the calculus of variations the underlying theme is that of oscillations they occur with certain definite patterns in minimizing sequences for the variational problem the same patterns recur in nearly optimal designs and in the coefficients of the equation being homogenized each problem is resolved by determining the structure of those oscillations and above all their macroscopic averages it is those averages that solve the relaxed problem they also determine the optimal design and the solution of the homogenized equation we emphasize also the role of optimization the homogenized equations and composite materials of interest here come not from arbitrary mixtures but from those that are extremal since they correspond to minimizing sequences for the variational problem the effective properties of these composites attain the optimal bounds for given materials in fixed proportions

an examination of procedures for determining the number of clusters in a data set a monte carlo evaluation of 30 procedures for determining the number of clusters was conducted on artificial data sets which contained either 2 3 4 or 5 distinct nonoverlapping clusters to provide a variety of clustering solutions the data sets were analyzed by four hierarchical clustering methods external criterion measures indicated excellent recovery of the true cluster structure by the methods at the correct hierarchy level thus the clustering present in the data was quite strong the simulation results for the stopping rules revealed a wide range in their ability to determine the correct number of clusters in the data several procedures worked fairly well whereas others performed rather poorly thus the latter group of rules would appear to have little validity particularly for data sets containing distinct clusters applied researchers are urged to select one or more of the better criteria however users are cautioned that the performance of some of the criteria may be data dependent

recursive algorithms for parameter estimation with adaptive quantizer this paper studies a parameter estimation problem of networked linear systems with fixed rate quantization under the minimum mean square error criterion we propose a recursive estimator of stochastic approximation type and derive a necessary and sufficient condition for its asymptotic unbiasedness this motivates to design an adaptive quantizer for the estimator whose strong consistency asymptotic unbiasedness and asymptotic normality are rigorously proved using the newton based and averaging techniques we obtain two accelerated recursive estimators with the fastest convergence speed of o 1 k and exactly evaluate the quantization effect on the estimation accuracy if the observation noise is gaussian an optimal quantizer and the accelerated estimators are co designed to asymptotically approach the minimum cramer rao lower bound all the estimators share almost the same computational complexity as the gradient algorithms with un quantized observations and can be easily implemented finally the theoretical results are validated by simulations

towards identification of wiener systems with the least amount of a priori information on the nonlinearity in this paper we investigate what constitutes the least amount of a priori information on the nonlinearity so that the fir linear part is identifiable in the non gaussian input case three types of a priori information are considered including quadrant information point information and locally monotonous information in all three cases identifiability has been established and corresponding identification algorithms are developed with their convergence proofs

recursive projection algorithm on fir system identification with binary valued observations this paper studies the identification of finite impulse response fir systems with binary valued observations combining with the stochastic gradient algorithm and statistical property of the system noise a recursive projection algorithm is proposed to estimate the unknown system parameters under some mild conditions on the a priori knowledge of the unknown parameters and inputs the algorithm is proved to be convergent in the almost sure and mean square sense furthermore the almost sure and mean square convergence rates of estimation errors are also obtained a numerical example is given to demonstrate the effectiveness of the algorithm and the main results obtained

on radially symmetric minima of nonconvex functionals abstract we study a minimization problem in the space w1 10 br where br is the ball of radius r with center at the origin the functional considered is not necessarily convex under suitable assumptions we prove the existence of a radially symmetric decreasing solution by strengthening the assumptions we obtain uniqueness results finally we study under which assumptions and in which sense the solutions found solve the corresponding euler equation the proofs are very direct and simple they only make use of the functions t n introduced by the author arch rational mech anal 1999

the k means type algorithms versus imbalanced data distributions k means is a partitional clustering technique that is well known and widely used for its low computational cost the representative algorithms include the hard k means and the fuzzy k means however the performance of these algorithms tends to be affected by skewed data distributions i e imbalanced data they often produce clusters of relatively uniform sizes even if input data have varied cluster sizes which is called the uniform effect in this paper we analyze the causes of this effect and illustrate that it probably occurs more in the fuzzy k means clustering process than the hard k means clustering process as the fuzzy index m increases the uniform effect becomes evident to prevent the effect of the uniform effect we propose a multicenter clustering algorithm in which multicenters are used to represent each cluster instead of one single center the proposed algorithm consists of the three subalgorithms the fast global fuzzy k means best m plot and grouping multicenter algorithms they will be respectively used to address the three important problems 1 how are the reliable cluster centers from a dataset obtained 2 how are the number of clusters which these obtained cluster centers represent determined 3 how is it judged as to which cluster centers represent the same clusters the experimental studies on both synthetic and real datasets illustrate the effectiveness of the proposed clustering algorithm in clustering balanced and imbalanced data

clustering ensembles models of consensus and weak partitions clustering ensembles have emerged as a powerful method for improving both the robustness as well as the stability of unsupervised classification solutions however finding a consensus clustering from multiple partitions is a difficult problem that can be approached from graph based combinatorial or statistical perspectives this study extends previous research on clustering ensembles in several respects first we introduce a unified representation for multiple clusterings and formulate the corresponding categorical clustering problem second we propose a probabilistic model of consensus using a finite mixture of multinomial distributions in a space of clusterings a combined partition is found as a solution to the corresponding maximum likelihood problem using the em algorithm third we define a new consensus function that is related to the classical intraclass variance criterion using the generalized mutual information definition finally we demonstrate the efficacy of combining partitions generated by weak clustering algorithms that use data projections and random data splits a simple explanatory model is offered for the behavior of combinations of such weak clustering components combination accuracy is analyzed as a function of several parameters that control the power and resolution of component partitions as well as the number of partitions we also analyze clustering ensembles with incomplete information and the effect of missing cluster labels on the quality of overall consensus experimental results demonstrate the effectiveness of the proposed methods on several real world data sets

a weighted least squares approach to parameter estimation problems based on binary measurements we present a new approach to parameter estimation problems based on binary measurements motivated by the need to add integrated low cost self test features to microfabricated devices this approach is based on the use of original weighted least squares criteria as opposed to other existing methods it requires no dithering signal and it does not rely on an approximation of the quantizer in this technical note we focus on a simple choice for the weights and establish some asymptotical properties of the corresponding criterion to achieve this the assumption that the quantizer s input is gaussian and centered is made in this context we prove that the proposed criterion is locally convex and that it is possible to use a simple gradient descent to find a consistent estimate of the unknown system parameters regardless of the presence of measurement noise at the quantizer s input

minimum spanning tree based split and merge a hierarchical clustering method most clustering algorithms become ineffective when provided with unsuitable parameters or applied to datasets which are composed of clusters with diverse shapes sizes and densities to alleviate these deficiencies we propose a novel split and merge hierarchical clustering method in which a minimum spanning tree mst and an mst based graph are employed to guide the splitting and merging process in the splitting process vertices with high degrees in the mst based graph are selected as initial prototypes and k means is used to split the dataset in the merging process subgroup pairs are filtered and only neighboring pairs are considered for merge the proposed method requires no parameter except the number of clusters experimental results demonstrate its effectiveness both on synthetic and real datasets

existence uniqueness and qualitative properties of minima to radially symmetric non coercive non convex variational problems we are concerned with the problem of existence uniqueness and qualitative properties of solutions to the radially symmetric variational problem min u in wuu b r int b r pq f pt mod x mod nabla u x h x u x dx where b r is the ball of mathbb r n centered at the origin and with radius r 0 the map f colon 0 r times 0 infty to overline mathbb r is a normal integrand and h colon 0 r times r to r is a convex function of the second variable this kind of problems with non convex lagrangians with respect to nabla u arise in various fields of applied sciences such as optimal design and nonlinear elasticity

effects of sampling and quantization on single tone frequency estimation the effects of sampling and quantization on frequency estimation for a single sinusoid are investigated the cramer rao bound for 1 bit quantization is derived and compared with the limit of infinite quantization it is found that 1 bit quantization gives a slightly worse performance however with a dramatic increase of variance at certain frequencies this can be avoided by using four times oversampling the effect of sampling when using nonideal antialiasing lowpass filters is therefore investigated through derivation of the cramer rao lower bounds finally fast estimators for 1 bit quantization in particular correlation based estimators are derived and their performance is investigated the paper is concluded with simulation results for four times oversampled 1 bit quantization

sep cop an efficient method to find the best partition in hierarchical clustering based on a new cluster validity index hierarchical clustering algorithms provide a set of nested partitions called a cluster hierarchy since the hierarchy is usually too complex it is reduced to a single partition by using cluster validity indices we show that the classical method is often not useful and we propose sep a new method that efficiently searches in an extended partition set furthermore we propose a new cluster validity index cop since many of the commonly used indices cannot be used with sep experiments performed with 80 synthetic and 7 real datasets confirm that sep cop is superior to the method currently used and furthermore it is less sensitive to noise