segmentation and classification of range images the recognition of objects in three dimensional space is a desirable capability of a computer vision system range images which directly measure 3 d surface coordinates of a scene are well suited for this task in this paper we report a procedure to detect connected planar convex and concave surfaces of 3 d objects this is accomplished in three stages the first stage segments the range image into surface patches by a square error criterion clustering algorithm using surface points and associated surface normals the second stage classifies these patches as planar convex or concave based on a non parametric statistical test for trend curvature values and eigenvalue analysis in the final stage boundaries between adjacent surface patches are classified as crease or noncrease edges and this information is used to merge compatible patches to produce reasonable faces of the object s this procedure has been successfully applied to a large number of real and synthetic images four of which we present in this paper

planning graph as the basis for deriving heuristics for plan synthesis by state space and csp search most recent strides in scaling up planning have centered around two competing themesdisjunctive planners exemplified by graphplan and heuristic state search planners exemplified by unpop hsp and hsp r in this paper we present a novel approach for successfully harnessing the advantages of the two competing paradigms to develop planners that are significantly more powerful than either of the approaches specifically we show that the polynomial time planning graph structure that the graphplan builds provides a rich substrate for deriving a family of highly effective heuristics for guiding state space search as well as csp style search the main leverage provided by the planning graph structure is a systematic and graded way to take subgoal interactions into account in designing state space heuristics for state space search we develop several families of heuristics some aimed at search speed and others at optimality of solutions and analyze many approaches for improving the cost quality tradeoffs offered by these heuristics our normalized empirical comparisons show that our heuristics handily outperform the existing state space heuristics for csp style search we describe a novel way of using the planning graph structure to derive highly effective variable and value ordering heuristics we show that these heuristics can be used to improve graphplan s own backward search significantly to demonstrate the effectiveness of our approach vis a vis the state of the art in plan synthesis we present altalt a planner literally cobbled together from the implementations of graphplan and state search style planners using our theory we evaluate altalt on the suite of problems used in the recent aips 2000 planning competition the results place altalt in the top tier of the competition plannersoutperforming both graphplan based and heuristic search based planners

weighted a search unifying view and application the a algorithm is a well known heuristic best first search method several performance accelerated extensions of the exact a approach are known interesting examples are approximate algorithms where the heuristic function used is inflated by a weight often referred to as weighted a these methods guarantee a bounded suboptimality as a technical contribution this paper presents the previous results related to weighted a from authors like pohl pearl kim likhachev and others in a more condensed and unifying form with this unified view a novel general bound on suboptimality of the result is derived in the case of avoiding any reopening of expanded states for e 0 this bound is 1 e n 2 where n is an upper bound on an optimal solution length binary decision diagrams bdds are well known to ai e g from set based exploration of sparse memory and symbolic manipulation of state spaces the problem of exact or approximate bdd minimization is introduced as a possible new challenge for heuristic search like many classical ai domains this problem is motivated by real world applications several variants of weighted a search are applied to problems of bdd minimization and the more classical domains like blocksworld and sliding tile puzzles for bdd minimization the comparison of the evaluated methods also includes previous heuristic and simulation based methods such as rudell s hill climbing based sifting algorithm simulated annealing and evolutionary algorithms a discussion of the results obtained in the different problem domains gives our experiences with weighted a which is of value for the ai practitioner

subdimensional expansion for multirobot path planning abstract planning optimal paths for large numbers of robots is computationally expensive in this paper we introduce a new framework for multirobot path planning called subdimensional expansion which initially plans for each robot individually and then coordinates motion among the robots as needed more specifically subdimensional expansion initially creates a one dimensional search space embedded in the joint configuration space of the multirobot system when the search space is found to be blocked during planning by a robot robot collision the dimensionality of the search space is locally increased to ensure that an alternative path can be found as a result robots are only coordinated when necessary which reduces the computational cost of finding a path we present the m algorithm an implementation of subdimensional expansion that adapts the a planner to perform efficient multirobot planning m is proven to be complete and to find minimal cost paths simulation results are presented that show that m outperforms existing optimal multirobot path planning algorithms

breadth first heuristic search recent work shows that the memory requirements of a and related graph search algorithms can be reduced substantially by only storing nodes that are on or near the search frontier using special techniques to prevent node regeneration and recovering the solution path by a divide and conquer technique when this approach is used to solve graph search problems with unit edge costs we show that a breadth first search strategy can be more memory efficient than a best first strategy we also show that a breadth first strategy allows a technique for preventing node regeneration that is easier to implement and can be applied more widely the breadth first heuristic search algorithms introduced in this paper include a memory efficient implementation of breadth first branch and bound search and a breadth first iterative deepening a algorithm that is based on it computational results show that they outperform other systematic search algorithms in solving a range of challenging graph search problems

a validity measure for fuzzy clustering the authors present a fuzzy validity criterion based on a validity function which identifies compact and separate fuzzy c partitions without assumptions as to the number of substructures inherent in the data this function depends on the data set geometric distance measure distance between cluster centroids and more importantly on the fuzzy partition generated by any fuzzy algorithm used the function is mathematically justified via its relationship to a well defined hard clustering validity function the separation index for which the condition of uniqueness has already been established the performance of this validity function compares favorably to that of several others the application of this validity function to color image segmentation in a computer color vision system for recognition of ic wafer defects which are otherwise impossible to detect using gray scale image processing is discussed

unsupervised optimal fuzzy clustering this study reports on a method for carrying out fuzzy classification without a priori assumptions on the number of clusters in the data set assessment of cluster validity is based on performance measures using hypervolume and density criteria an algorithm is derived from a combination of the fuzzy k means algorithm and fuzzy maximum likelihood estimation the unsupervised fuzzy partition optimal number of classes algorithm performs well in situations of large variability of cluster shapes densities and number of data points in each cluster the algorithm was tested on different classes of simulated data and on a real data set derived from sleep eeg signal

bootstrap technique in cluster analysis abstract we define a method to estimate the number of clusters in a data set e using the bootstrap technique this approach involves the generation of several fake data sets by sampling patterns with replacement in e bootstrapping for each number k of clusters a measure of stability of the k cluster partitions over the bootstrap samples is used to characterize the significance of the k cluster partition for the original data set the value of k which provides the most stable partitions is the estimate of the number of clusters in e the performance of this new technique is demonstrated on both synthetic and real data and is applied to the segmentation of range images

real time heuristic search abstract we apply the two player game assumptions of limited search horizon and commitment to moves in constant time to single agent heuristic search problems we present a variation of minimax lookahead search and an analog to alpha beta pruning that significantly improves the efficiency of the algorithm paradoxically the search horizon reachable with this algorithm increases with increasing branching factor in addition we present a new algorithm called real time a for interleaving planning and execution we prove that the algorithm makes locally optimal decisions and is guaranteed to find a solution we also present a learning version of this algorithm that improves its performance over successive problem solving trials by learning more accurate heuristic values and prove that the learned values converge to their exact values along every optimal path these algorithms effectively solve significantly larger problems than have previously been solvable using heuristic evaluation functions

on a general concept of forgetting practice leads us to seek a simple method which would make parameter estimation and subsequent control or signal processing reliably adaptive unfortunately in most applications we lack sufficient information to specify a complete model of parameter variations in other words the problem is under determined which prevents us from employing standard equations of probability calculus in this paper we apply known principles of rational behaviour in such situations to propose a plausible and well justified solution the result we get is close to classical exponential forgetting but regularized by available prior information we demonstrate the practical implications of this feature

a clustering performance measure based on fuzzy set decomposition clustering is primarily used to uncover the true underlying structure of a given data set and for this purpose it is desirable to subject the same data to several different clustering algorithms this paper attempts to put an order on the various partitions of a data set obtained from different clustering algorithms the goodness of each partition is expressed by means of a performance measure based on a fuzzy set decomposition of the data set under consideration several experiments reported in here show that the proposed performance measure puts an order on different partitions of the same data which is consistent with the error rate of a classifier designed on the basis of the obtained cluster labelings

sequential estimation of hidden arma processes by particle filtering part ii this is part ii of a series of two papers where we address sequential estimation of wide sense stationary autoregressive moving average arma state processes by particle filtering in part i we considered a state space model where the state was an arma process of known order and where the parameters of the process could be known or unknown in this paper we extend our work from part i by considering the same type of models with the added complexity that the arma processes are now of unknown order instead of working on a scheme that first tracks the state by operating with different assumed models and then selects the best model by using a predefined criterion we present a method that directly estimates the state without the need of knowing the model order we derive the transition density of the state for unknown arma model order and propose a particle filter based on that density and the empirical bayesian methodology we demonstrate the performance of the proposed method with computer simulations and compare it with the methods from part i

marginalized particle filters for mixed linear nonlinear state space models the particle filter offers a general numerical tool to approximate the posterior density function for the state in nonlinear and non gaussian filtering problems while the particle filter is fairly easy to implement and tune its main drawback is that it is quite computer intensive with the computational complexity increasing quickly with the state dimension one remedy to this problem is to marginalize out the states appearing linearly in the dynamics the result is that one kalman filter is associated with each particle the main contribution in this paper is the derivation of the details for the marginalized particle filter for a general nonlinear state space model several important special cases occurring in typical signal processing applications will also be discussed the marginalized particle filter is applied to an integrated navigation system for aircraft it is demonstrated that the complete high dimensional system can be based on a particle filter using marginalization for all but three states excellent performance on real flight data is reported

bayesian multi object filtering for pairwise markov chains random finite sets rfs are recent tools for addressing the multi object filtering problem the probability hypothesis density phd filter is an approximation of the multi object bayesian filter which results from the rfs formulation of the problem and has been used in many applications in the rfs framework it is assumed that each target and associated observation follow a hidden markov chain hmc model hmcs conveniently describe some physical properties of practical interest for practitioners but they also implicitly imply restrictive independence properties which in practice may not be satisfied by data in this paper we show that these structural limitations of hmc models can somehow be relaxed by embedding them into the more general class of pairwise markov chain pmc models we thus focus on the computation of the phd filter in a pmc framework and we propose a practical implementation of the phd filter for a particular class of pmc models

the pn search algorithm application to tsume shogi abstract this paper proposes a new search algorithm denoted pn for and or tree search the algorithm is based on proof number pn search a best first search algorithm proposed by allis et al artificial intelligence 66 1 1994 91 124 and on korf s rbfs algorithm artificial intelligence 62 1 1993 41 78 pn combines several existing ideas it transforms a best first pn search algorithm into an iterative deepening depth first approach moreover it is enhanced by methods such as recursive iterative deepening dynamic evaluation efficient successor ordering and pruning by dependency relations the resulting algorithm turns out to be highly efficient as witnessed by the experimental results the pn algorithm is implemented in a tsume shogi japanese chess mating problem program and evaluated by testing it on 295 notoriously difficult tsume shogi problems one problem has a depth of search of over 1500 plies the experimental results are compared with those of other programs the pn program shows by far the best results solving all problems but one needless to say it outperforms the best human tsume shogi problem solvers by far

rational deployment of multiple heuristics in optimal state space search abstract the obvious way to use several admissible heuristics in searching for an optimal solution is to take their maximum in this paper we aim to reduce the time spent on computing heuristics within the context of a and i d a we discuss lazy a and lazy i d a variants of a and i d a respectively where heuristics are evaluated lazily only when they are essential to a decision to be made in the search process while these lazy algorithms outperform naive maximization we can do even better by intelligently deciding when to compute the more expensive heuristic we present a new rational metareasoning based scheme which decides whether to compute the more expensive heuristics at all based on a myopic regret estimate this scheme is used to create rational lazy a and rational lazy i d a we also present different methods for estimating the parameters necessary for making such decisions an empirical evaluation in several domains supports the theoretical results and shows that the rational variants rational lazy a and rational lazy i d a are better than their non rational counterparts

particle filtering with dependent noise processes modeling physical systems often leads to discrete time state space models with dependent process and measurement noises for linear gaussian models the kalman filter handles this case as is well described in literature however for nonlinear or non gaussian models the particle filter as described in literature provides a general solution only for the case of independent noise here we present an extended theory of the particle filter for dependent noises with the following key contributions i the optimal proposal distribution is derived ii the special case of gaussian noise in nonlinear models is treated in detail leading to a concrete algorithm that is as easy to implement as the corresponding kalman filter iii the marginalized rao blackwellized particle filter handling linear gaussian substructures in the model in an efficient way is extended to dependent noise and finally iv the parameters of a joint gaussian distribution of the noise processes are estimated jointly with the state in a recursive way

heuristic allocation based on a dynamic programming state space representation in this paper we focus on the lower level allocation problem of a hierarchical time constrained product development situation commonly found in the industrial practice the type of product development process we consider is the radical experiential model of product development of eisenhardt and tabrizi administr sci q 40 1995 84 the description of the main characteristics of the process follows the line of the recent research of bowers et al in m t brannick e salas c prince eds team performance assessment and measurement theory research and applications lawrence erlbaum associates inc publishers new jersey 1997 pp 85 108 and oorschot analysing radical npd projects from an operational control perspective ph d thesis eindhoven university of technology the netherlands 2001 starting from the dynamic programming techniques we propose a solution to this optimization problem by employing an a monotonic heuristic evaluation function for best search algorithms this function is based on aggregate information on the design task set we discuss the efficiency of the general best first search algorithm using an a evaluation function and of an rbfs variant of it which also searches in best first order using the same a evaluation function we prove that the algorithms find an optimal feasible allocation provided that there exists a feasible allocation we conclude by commenting upon some experimental results

clustering irregular shapes using high order neurons this article introduces a method for clustering irregularly shaped data arrangements using high order neurons complex analytical shapes are modeled by replacing the classic synaptic weight of the neuron by high order tensors in homogeneous coordinates in the first and second order cases this neuron corresponds to a classic neuron and to an ellipsoidalmetric neuron we show how high order shapes can be formulated to follow the maximum correlation activation principle and permit simple local hebbian learning we also demonstrate decomposition of spatial arrangements of data clusters including very close and partially overlapping clusters which are difficult to distinguish using classic neurons superior results are obtained for the iris data

best first minimax search we describe a very simple selective search algorithm for two player games called best first minimax it always expands next the node at the end of the expected line of play which determines the minimax value of the root it uses the same information as alpha beta minimax and takes roughly the same time per node generation we present an implementation of the algorithm that reduces its space complexity from exponential to linear in the search depth but at significant time cost our actual implementation saves the subtree generated for one move that is still relevant after the player and opponent move pruning subtrees below moves not chosen by either player we also show how to efficiently generate a class of incremental random game trees on uniform random game trees best first minimax outperforms alpha beta when both algorithms are given the same amount of computation on random trees with random branching factors best first outperforms alpha beta for shallow depths but eventually loses at greater depths we obtain similar results in the game of othello finally we present a hybrid best first extension algorithm that combines alpha beta with best first minimax and performs significantly better than alpha beta in both domains even at greater depths in othello it beats alpha beta in two out of three games

the effect of cluster size dimensionality and the number of clusters on recovery of true cluster structure an evaluation of four clustering methods and four external criterion measures was conducted with respect to the effect of the number of clusters dimensionality and relative cluster sizes on the recovery of true cluster structure the four methods were the single link complete link group average upgma and ward s minimum variance algorithms the results indicated that the four criterion measures were generally consistent with each other of which two highly similar pairs were identified the tirst pair consisted of the rand and corrected rand statistics and the second pair was the jaccard and the fowlkes and mallows indexes with respect to the methods recovery was found to improve as the number of clusters increased and as the number of dimensions increased the relative cluster size factor produced differential performance effects with ward s procedure providing the best recovery when the clusters were of equal size the group average method gave equivalent or better recovery when the clusters were of unequal size

memory intensive and or search for combinatorial optimization in graphical models in this paper we explore the impact of caching during search in the context of the recent framework of and or search in graphical models specifically we extend the depth first and or branch and bound tree search algorithm to explore an and or search graph by equipping it with an adaptive caching scheme similar to good and no good recording furthermore we present best first search algorithms for traversing the same underlying and or search graph and compare both algorithms empirically we focus on two common optimization problems in graphical models finding the most probable explanation mpe in belief networks and solving weighted csps wcsp in an extensive empirical evaluation we demonstrate conclusively the superiority of the memory intensive and or search algorithms on a variety of benchmarks

performance of linear space search algorithms abstract search algorithms that use space linear in the search depth are widely employed in practice to solve difficult problems optimally such as planning and scheduling in this paper we study the average case performance of linear space search algorithms including depth first branch and bound dfbnb iterative deepening id and recursive best first search rbfs to facilitate our analyses we use a random tree t b d that has mean branching factor b depth d and node costs that are the sum of the costs of the edges from the root to the nodes we prove that the expected number of nodes expanded by dfbnb on a random tree is no more than bd times the expected number of nodes expanded by best first search bfs on the same tree which usually requires space that is exponential in depth d we also show that dfbnb is asymptotically optimal when bfs runs in exponential time and id and rbfs are asymptotically optimal when the edge costs of t b d are integers if bp 0 is the expected number of children of a node whose costs are the same as that of their parent then the expected number of nodes expanded by these three linear space algorithms is exponential when bp o d 4 when bp 0 1 and at most quadratic when bp 0 1 in addition we study the heuristic branching factor of t b d and the effective branching factor of bfs dfbnb id and rbfs on t b d furthermore we use our analytic results to explain a surprising anomaly in the performance of these algorithms and to predict the existence of a complexity transition in the asymmetric traveling salesman problem

reducing reexpansions in iterative deepening search by controlling cutoff bounds abstract it is known that a best first search algorithm like a 5 6 requires too much space which often renders it unusable and a depth first search strategy does not guarantee an optimal cost solution the iterative deepening algorithm ida 4 achieves both space and cost optimality for a class of tree searching problems however for many other problems it takes too much of computation time due to excessive reexpansion of nodes this paper presents a modification of ida to an admissible iterative depth first branch and bound algorithm ida cr for trees which overcomes this drawback of ida and operates much faster using the same amount of storage algorithm ida cra a bounded suboptimal cost variation of ida cr is also presented in order to reduce the execution time still further results with the 0 1 knapsack problem traveling salesman problem and the flow shop scheduling problem are shown

a survey of convergence results on particle filtering methods for practitioners optimal filtering problems are ubiquitous in signal processing and related fields except for a restricted class of models the optimal filter does not admit a closed form expression particle filtering methods are a set of flexible and powerful sequential monte carlo methods designed to solve the optimal filtering problem numerically the posterior distribution of the state is approximated by a large set of dirac delta masses samples particles that evolve randomly in time according to the dynamics of the model and the observations the particles are interacting thus classical limit theorems relying on statistically independent samples do not apply in this paper our aim is to present a survey of convergence results on this class of methods to make them accessible to practitioners

a meta learning approach for determining the number of clusters with consideration of nearest neighbors an important and challenging problem in data clustering is the determination of the best number of clusters a variety of estimation methods has been proposed over the years to address this problem most of these methods depend on several nontrivial assumptions about the data structure and such methods may thus fail to discover the true clusters in a dataset that does not satisfy those assumptions we develop a new approach that takes as a starting point the simple and intuitive observation that close objects should fall within the same cluster whereas distant ones should not based on this simple notion we utilize a new measurement of good clustering called disconnectivity as well as existing goodness measurements and we embed these measures into a meta learning approach for estimating the number of clusters a simulation experiment based on 13 representative models and an application to real world datasets are conducted to show the effectiveness of the proposed method

frontier search the critical resource that limits the application of best first search is memory we present a new class of best first search algorithms that reduce the space complexity the key idea is to store only the open list of generated nodes but not the closed list of expanded nodes the solution path can be recovered by a divide and conquer technique either as a bidirectional or unidirectional search for many problems frontier search dramatically reduces the memory required by best first search we apply frontier search to breadth first search of sliding tile puzzles and the 4 peg towers of hanoi problem dijkstra s algorithm on a grid with random edge costs and the a algorithm on the fifteen puzzle the four peg towers of hanoi problem and optimal sequence alignment in computational biology

a tutorial on particle filters for online nonlinear non gaussian bayesian tracking increasingly for many application areas it is becoming important to include elements of nonlinearity and non gaussianity in order to model accurately the underlying dynamics of a physical system moreover it is typically crucial to process data on line as it arrives both from the point of view of storage costs as well as for rapid adaptation to changing signal characteristics in this paper we review both optimal and suboptimal bayesian algorithms for nonlinear non gaussian tracking problems with a focus on particle filters particle filters are sequential monte carlo methods based on point mass or particle representations of probability densities which can be applied to any state space model and which generalize the traditional kalman filtering methods several variants of the particle filter such as sir asir and rpf are introduced within a generic framework of the sequential importance sampling sis algorithm these are discussed and compared with the standard ekf through an illustrative example

clustering of the self organizing map using a clustering validity index based on inter cluster and intra cluster density the self organizing map som has been widely used in many industrial applications classical clustering methods based on the som often fail to deliver satisfactory results specially when clusters have arbitrary shapes in this paper through some preprocessing techniques for filtering out noises and outliers we propose a new two level som based clustering algorithm using a clustering validity index based on inter cluster and intra cluster density experimental results on synthetic and real data sets demonstrate that the proposed clustering algorithm is able to cluster data better than the classical clustering algorithms based on the som and find an optimal number of clusters

cabob a fast optimal algorithm for winner determination in combinatorial auctions combinatorial auctions where bidders can bid on bundles of items can lead to more economically efficient allocations but determining the winners is complete and inapproximable we present cabob a sophisticated optimal search algorithm for the problem it uses decomposition techniques upper and lower bounding also across components elaborate and dynamically chosen bid ordering heuristics and a host of structural observations cabob attempts to capture structure in any instance without making assumptions about the instance distribution experiments against the fastest prior algorithm cplex 8 0 show that cabob is often faster seldom drastically slower and in many cases drastically faster especially in cases with structure cabob s search runs in linear space and has significantly better anytime performance than cplex we also uncover interesting aspects of the problem itself first problems with short bids which were hard for the first generation of specialized algorithms are easy second almost all of the cats distributions are easy and the run time is virtually unaffected by the number of goods third we test several random restart strategies showing that they do not help on this problem the run time distribution does not have a heavy tail

controlling the learning process of real time heuristic search real time search provides an attractive framework for intelligent autonomous agents as it allows us to model an agent s ability to improve its performance through experience however the behavior of real time search agents is far from rational during the learning convergence process in that they fail to balance the efforts to achieve a short term goal i e to safely arrive at a goal state in the present problem solving trial and a long term goal to find better solutions through repeated trials as a remedy we introduce two techniques for controlling the amount of exploration both overall and per trial the weighted real time search reduces the overall amount of exploration and accelerates convergence it sacrifices admissibility but provides a nontrivial bound on the converged solution cost the real time search with upper bounds insures solution quality in each trial when the state space is undirected these techniques result in a convergence process more stable compared with that of the learning real time a algorithm

depth first iterative deepening an optimal admissible tree search abstract the complexities of various search algorithms are considered in terms of time space and cost of solution path it is known that breadth first search requires too much space and depth first search can use too much time and doesn t always find a cheapest path a depth first iterative deepening algorithm is shown to be asymptotically optimal along all three dimensions for exponential tree searches the algorithm has been used successfully in chess programs has been effectively combined with bi directional search and has been applied to best first heuristic search as well this heuristic depth first iterative deepening algorithm is the only known algorithm that is capable of finding optimal solutions to randomly generated instances of the fifteen puzzle within practical resource limits

agent searching in a tree and the optimality of iterative deepening the agent searching framework models the effort of a search strategy in terms of the distance traversed by an agent while exploring the search space the framework has been found to be useful in modeling search problems where the cost of backtracking and retracing search paths is important in determining search complexity in this paper we show that depth first iterative deepening dfid strategies are optimal for an agent searching in a line in m concurrent rays and in uniform b ary trees in the conventional search model it is known that dfid is asymptotically optimal for uninformed search of uniform b ary trees in this paper we prove the stronger result that for agent searching in uniform b ary trees iterative deepening is optimal up to lower order terms we also discuss the problems involved in optimally performing agent search in a graph

cluster validity for fuzzy clustering algorithms abstract the proportion exponent is introduced as a measure of the validity of the clustering obtained for a data set using a fuzzy clustering algorithm it is assumed that the output of an algorithm includes a fuzzy nembership function for each data point we show how to compute the proportion of possible memberships whose maximum entry exceeds the maximum entry of a given membership function and use these proportions to define the proportion exponent its use as a validity functional is illustrated with four numerical examples and its effectiveness compared to other validity functionals namely classification entropy and partition coefficient

cluster validity for the fuzzy c means clustering algorithrm the uniform data function is a function which assigns to the output of the fuzzy c means fc m or fuzzy isodata algorithm a number which measures the quality or validity of the clustering produced by the algorithm for the preselected number of cluster c the fc m algorithm produces c vectors in the space in which the data lie called cluster centers which represent points about which the data are concentrated it also produces for each data point c membership values numbers between zero and one which measure the similarity of the data points to each of the cluster centers it is these membership values which indicate how the point is classified they also indicate how well the point has been classified in that values close to one indicate that the point is close to a particular center but uniformly low memberships indicate that the point has not been classified clearly the uniform data functional udf combines the memberships in such a way as to indicate how well the data have been classified and is computed as follows for each data point compute the ratio of its smallest membership to its largest and then compute the probability that one could obtain a smaller ratio indicating better classification from a clustering of a standard data set in which there is no cluster structure these probabilities are then averaged over the data set to obtain the values of the udf

linear space best first search abstract best first search is a general heuristic search algorithm that always expands next a frontier node of lowest cost it includes as special cases breadth first search dijkstra s single source shortest path algorithm and the a algorithm its applicability however is limited by its exponential memory requirement previous approaches to this problem such as iterative deepening do not expand nodes in best first order if the cost function can decrease along a path we present a linear space best first search algorithm rbfs that always explores new nodes in best first order regardless of the cost function and expands fewer nodes than iterative deepening with a nondecreasing cost function on the sliding tile puzzles rbfs with a nonmonotonic weighted evaluation function dramatically reduces computation time with only a small penalty in solution cost in general rbfs reduces the space complexity of best first search from exponential to linear at the cost of only a constant factor in time complexity in our experiments

a new separation measure for improving the effectiveness of validity indices many validity indices have been proposed for quantitatively assessing the performance of clustering algorithms one limitation of existing indices is their lack of generalizability due to their dependence on the specific algorithms and structures of the data space to handle large scale datasets with arbitrary structures this research study proposes a new cluster separation measure for improving the effectiveness of existing validity indices this is achieved by partitioning the original data space into a grid based structure which allows the introduction of a new measurement for assessing the true data distribution between any two clusters instead of the distance between the two cluster prototypes to validate the effectiveness of the proposed separation measure we adopt two commonly used validity indices the davies bouldin s function db and tibshirani s gap statistic gs these indices are denoted as r db 1 and r gs 1 for clusters with sphere shaped structures and r db 2 and r gs 2 for irregular shaped structures this integration enables the indices to evaluate both partitional algorithms and hierarchical algorithms partitional algorithms including c means cm fuzzy c means fcm and hierarchical algorithms including dbscan and clique are used to test the performance of the new indices two synthetic datasets with spherical structures and four synthetic datasets with irregular shapes are first compared five real datasets from the uci machine learning repository are then used to further test the measure s performance the experimental results provide evidence that the new indices outperform the original indices

heuristic search in restricted memory research note abstract this paper presents heuristic search algorithms which work within memory constraints these algorithms ma for ordinary graphs and mao for and or graphs guarantee admissible solutions within specified memory limitations above the minimum required the memory versus node expansions tradeoff is analyzed for the worst case in the case of ordinary graphs some experiments using the fifteen puzzle problem are carried out under various pruning conditions these parameterized algorithms are found to encompass a wide class of best first search algorithms

duality in permutation state spaces and the dual search algorithm geometrical symmetries are commonly exploited to improve the efficiency of search algorithms a new type of symmetry in permutation state spaces duality is introduced each state has a dual state both states share important attributes such as their distance to the goal given a state s it is shown that an admissible heuristic of the dual state of s is an admissible heuristic for s this provides opportunities for additional heuristic evaluations an exact definition of the class of problems where duality exists is provided a new search algorithm dual search is presented which switches between the original state and the dual state when it seems likely that the switch will improve the chance of reaching the goal faster the decision of when to switch is very important and several policies for doing this are investigated experimental results show significant improvements for a number of applications for using the dual state s heuristic evaluation and or dual search

generalized best first search strategies and the optimality of a this paper reports several properties of heuristic best first search strategies whose scoring functions depend on all the information available from each candidate path not merely on the current cost g and the estimated completion cost h it is shown that several known properties of a retain their form with the minmax of f playing the role of the optimal cost which helps establish general tests of admissibility and general conditions for node expansion for these strategies on the basis of this framework the computational optimality of a in the sense of never expanding a node that can be skipped by some other algorithm having access to the same heuristic information that a uses is examined a hierarchy of four optimality types is defined and three classes of algorithms and four domains of problem instances are considered computational performances relative to these algorithms and domains are appraised for each class domain combination we then identify the strongest type of optimality that exists and the algorithm for achieving it the main results of this paper relate to the class of algorithms that like a return optimal solutions i e admissible when all cost estimates are optimistic i e h h on this class a is shown to be not optimal and it is also shown that no optimal algorithm exists but if the performance tests are confirmed to cases in which the estimates are also consistent then a is indeed optimal additionally a is also shown to be optimal over a subset of the latter class containing all best first algorithms that are guided by path dependent evaluation functions

robust estimation in non linear state space models with state dependent noise in this paper we present a robust estimation algorithm for non linear state space models driven by state dependent noise the algorithm is robust to outliers in the data we derive the algorithm step by step from first principles from theory to implementation the implementation is straightforward and consists mainly of two components 1 a slightly modified version of the rauch tung striebel recursions and 2 a backtracking line search strategy since it preserves the underlying chain structure of the problem its computational complexity grows linearly with the number of data the algorithm is iterative and is guaranteed to converge under mild assumptions to a local optimum from any starting point we validate our approach via experiments on synthetic data from a multi variate stochastic volatility model

bida an improved perimeter search algorithm abstract in this paper we present a new bidirectional heuristic search algorithm our algorithm can be viewed as a perimeter search algorithm and it uses a new technique for reducing the number of heuristic evaluations we also prove some general results on the behavior of iterative deepening perimeter search algorithms and we discuss some new lazy evaluation techniques for improving their performance the theoretical and experimental results show that perimeter search algorithms outperform the other bidirectional algorithms and we believe it is worthwhile to give them a deep look in subsequent research

mixture kalman filters in treating dynamic systems sequential monte carlo methods use discrete samples to represent a complicated probability distribution and use rejection sampling importance sampling and weighted resampling to complete the on line filtering task we propose a special sequential monte carlo method the mixture kalman filter which uses a random mixture of the gaussian distributions to approximate a target distribution it is designed for on line estimation and prediction of conditional and partial conditional dynamic linear models which are themselves a class of widely used non linear systems and also serve to approximate many others compared with a few available filtering methods including monte carlo methods the gain in efficiency that is provided by the mixture kalman filter can be very substantial another contribution of the paper is the formulation of many non linear systems into conditional or partial conditional linear form to which the mixture kalman filter can be applied examples in target tracking and digital communications are given to demonstrate the procedures proposed