Graph neural networks (GNNs) gain significant interest in the domain of network representation learning. To obtain a graph level vector representation from individual node embeddings, hierarchical pooling algorithms are proposed in the recent literature which adhere the hierarchical structure of an input graph. A major limitation for most of the existing supervised GNNs is their dependency on large number of graph labels (often 80%-90%) to train the parameters of the neural architecture. But obtaining labels of a large number of graphs is expensive for real world applications. So in this work, we propose an unsupervised hierarchical neural network, referred as GraPHmax, for obtaining graph level representation. We propose the concept of periphery representation and show its effectiveness to obtain discriminative features of an input graph. Further, inspired by the concepts from self-supervised learning, we propose to maximize periphery and hierarchical information in the context of hierarchical GNN. Thorough experimentation on both synthetic and real-world graph datasets shows that GraPHmax is not only able to outperform unsupervised graph embedding techniques, it often achieves state-of-the-art performance even with respect to a set of popular supervised GNN algorithms.

Graph neural networks (GNNs) are able to achieve state-of-the-art performance for node representation and classification in a network. But, most of the existing GNNs can be applied to simple graphs, where an edge connects only a pair of nodes. Studies have shown that hypergraphs are effective to model real-world relationships which are of higher order in nature. Recently, graph neural networks are proposed for hypergraphs, but they implicitly use clique or star expansions to convert the hypergraph to a simple graph, or use computationally expensive hypergraph Laplacian.In this work, we propose a novel hypergraph neural network for semi-supervised hypernode classification, which operates directly on the hypergraphs with varying hyperedge sizes. Within each layer, it indirectly works on the line graph of the given hypergraph, without actually forming the line graph explicitly. Moreover, it also employs a self-attention mechanism to learn the weights of those edge relationships. Experimentally, HAIN is able to improve the state-of-the-art hypernode classification performance on all the datasets we use. We make the source code available to ease the reproducibility of the results.

Network (or graph) embedding is the task to map the nodes of a graph to a lower dimensional vector space, such that it preserves the graph properties and facilitates the downstream network mining tasks.Real world networks often come with (community) outlier nodes, which behave differently from the regular nodes of the community.These outlier nodes can affect the embedding of the regular nodes, if not handled carefully.In this paper, we propose a novel unsupervised graph embedding approach (called DMGD) which integrates outlier and community detection with node embedding.We extend the idea of deep support vector data description to the framework of graph embedding when there are multiple communities present in the given network, and an outlier is characterized relative to its community.We also show the theoretical bounds on the number of outliers detected by DMGD.Our formulation boils down to an interesting minimax game between the outliers, community assignments and the node embedding function.We also propose an efficient algorithm to solve this optimization framework.Experimental results on both synthetic and real world networks show the merit of our approach compared to state-of-the-arts.

Usual networks lossily (if not incorrectly) represent higher-order relations, i.e. those between multiple entities instead of a pair. This calls for complex structures such as hypergraphs to be used instead. Akin to the link prediction problem in graphs, we deal with hyperlink (higher-order link) prediction in hypergraphs. With a handful of solutions in the literature that seem to have merely scratched the surface, we provide improvements for the same. Motivated by observations in recent literature, we first formulate a "clique-closure" hypothesis (viz., hyperlinks are more likely to be formed from near-cliques rather than from non-cliques), test it on real hypergraphs, and then exploit it for our very problem. In the process, we generalize hyperlink prediction on two fronts: (1) from small-sized to arbitrary-sized hyperlinks, and (2) from a couple of domains to a handful. We perform experiments (both the hypothesis-test as well as the hyperlink prediction) on multiple real datasets, report results, and provide both quantitative and qualitative arguments favoring better performances w.r.t. the state-of-the-art.

Attributed network embedding is the task to learn a lower dimensional vector representation of the nodes of an attributed network, which can be used further for downstream network mining tasks. Nodes in a network exhibit community structure and most of the network embedding algorithms work well when the nodes, along with their attributes, adhere to the community structure of the network. But real life networks come with community outlier nodes, which deviate significantly in terms of their link structure or attribute similarities from the other nodes of the community they belong to. These outlier nodes, if not processed carefully, can even affect the embeddings of the other nodes in the network. Thus, a node embedding framework for dealing with both the link structure and attributes in the presence of outliers in an unsupervised setting is practically important. In this work, we propose a deep unsupervised autoencoders based solution which minimizes the effect of outlier nodes while generating the network embedding. We use both stochastic gradient descent and closed form updates for faster optimization of the network parameters. We further explore the role of adversarial learning for this task, and propose a second unsupervised deep model which learns by discriminating the structure and the attribute based embeddings of the network and minimizes the effect of outliers in a coupled way. Our experiments show the merit of these deep models to detect outliers and also the superiority of the generated network embeddings for different downstream mining tasks. To the best of our knowledge, these are the first unsupervised non linear approaches that reduce the effect of the outlier nodes while generating Network Embedding.

Attributed network embedding has received much interest from the research community as most of the networks come with some content in each node, which is also known as node attributes. Existing attributed network approaches work well when the network is consistent in structure and attributes, and nodes behave as expected. But real world networks often have anomalous nodes. Typically these outliers, being relatively unexplainable, affect the embeddings of other nodes in the network. Thus all the downstream network mining tasks fail miserably in the presence of such outliers. Hence an integrated approach to detect anomalies and reduce their overall effect on the network embedding is required.Towards this end, we propose an unsupervised outlier aware network embedding algorithm (ONE) for attributed networks, which minimizes the effect of the outlier nodes, and hence generates robust network embeddings. We align and jointly optimize the loss functions coming from structure and attributes of the network. To the best of our knowledge, this is the first generic network embedding approach which incorporates the effect of outliers for an attributed network without any supervision. We experimented on publicly available real networks and manually planted different types of outliers to check the performance of the proposed algorithm. Results demonstrate the superiority of our approach to detect the network outliers compared to the state-of-the-art approaches. We also consider different downstream machine learning applications on networks to show the efficiency of ONE as a generic network embedding technique. The source code is made available at https://github.com/sambaranban/ONE.

Similarity based grouping of patterns has been explored profusely under the well celebrated clustering paradigm in pattern recognition and machine learning. In clustering, objects in the same cluster are similar to each other and objects belonging to different clusters are dissimilar in a corresponding sense. However, it is not rare to come across situations where instead of a similarity based grouping, forming groups of diverse objects is needed. Resource allocation across different parts of an organization, performing cross-validation splits of dataset with class imbalance, heterogeneous or mixed ability partitioning of students, etc. are the applications of grouping which require each group to contain diverse set of patterns. Moreover, these applications also demand different groups to be similar to each other in some sense. In this work, we propose a generic framework for partitioning a collection of patterns into a set of groups such that the above two criteria are fulfilled. To the best of our knowledge, this is the first work to propose such a framework irrespective of any particular application. Towards this end, it turns out that finding an optimal solution to the problem that we developed is NP Hard. So we Propose an approximate solution for the same. We conduct experiments on both synthetic and real world datasets to evaluate the performance of the proposed algorithm. We show the merit of the algorithm by comparing the results with some related state-of-the-art baseline methods.

Measuring influence, through centrality measures, has been a center-piece of research in the analysis of complex social networks, such as finding coherent communities (clusters) and locating trend setters (prototypes) in viral marketing. Even though there exists a few axiomatic frameworks associated with some specific forms of influence measures in the literature, these formal frameworks are not generic in nature in terms of characterizing the space of influence measures for complex social networks. To address this research gap, we propose a generic axiomatic framework, in this paper, to capture most of the key intrinsic properties of any influence measure in networks. We further analyze certain popular centrality measures using this framework. Interestingly, our analysis reveals that none of the centrality measures considered satisfies all the desirable axioms. We finally conclude this paper by stating an appealing conjecture on a potential impossibility theorem associated with the proposed axiomatic framework.

In the past, hybrid recommender systems have shown the power of exploiting relationships amongst objects which directly or indirectly effect the recommendation task. However, the effect of all relations is not equal, and choosing their right balance for a recommendation problem at hand is non-trivial. We model these interactions using a Heterogeneous Information Network, and propose a systematic framework for learning their influence weights for a given recommendation task. Further, we address the issue of redundant results, which is very much prevalent in recommender systems. To alleviate redundancy in recommendations we use Vertex Reinforced Random Walk (a non-Markovian random walk) over a heterogeneous graph. It works by boosting the transitions to the influential nodes, while simultaneously shrinking the weights of others. This helps in discouraging recommendation of multiple influential nodes which lie in close proximity of each other, thus ensuring diversity. Finally, we demonstrate the effectiveness of our approach by experimenting on real world datasets. We find that, with the weights of relations learned using the proposed non-Markovian random walk based framework, the results consistently improve over the baselines.

Although clustering is one of the central tasks in machine learning for the last few decades, analysis of clustering irrespective of any particular algorithm was not undertaken for a long time. In the recent literature, axiomatic frameworks have been proposed for clustering and its quality. But none of the proposed frameworks has concentrated on the computational aspects of clustering, which is essential in current big data analytics. In this paper, we propose an axiomatic framework for clustering which considers both the quality and the computational complexity of clustering algorithms. The axioms proposed by us necessarily associate the problem of clustering with the important concept of incremental learning and divide and conquer learning. We also propose an order independent incremental clustering algorithm which satisfies all of these axioms in some constrained manner.

Classification of entities based on the underlying network structure is an important problem. Networks encountered in practice are sparse and have many missing and noisy links. Statistical learning techniques have been used in intra-network classification; however, they typically exploit only the local neighborhood, so may not perform well. In this paper, we propose a novel structural neighborhood-based classifier learning using a random walk. For classifying a node, we take a random walk from the node and make a decision based on how nodes in the respective k^th-level neighborhood are labeled. We observe that random walks of short length are helpful in classification. Emphasizing role of longer random walks may cause the underlying Markov chain to converge to a stationary distribution. Considering this, we take a lazy random walk based approach with variable termination probability for each node, based on the node's structural properties including its degree. Our experimental study on real world datasets demonstrates the superiority of the proposed approach over the existing state-of-the-art approaches.

Clustering techniques which can handle incomplete data have become increasingly important due to varied applications in marketing research, medical diagnosis and survey data analysis. Existing techniques cope up with missing values either by using data modification/imputation or by partial distance computation, often unreliable depending on the number of features available. In this paper, we propose a novel approach for clustering data with missing values, which performs the task by Symmetric Non-Negative Matrix Factorization (SNMF) of a complete pair-wise similarity matrix, computed from the given incomplete data. To accomplish this, we define a novel similarity measure based on Average Overlap similarity metric which can effectively handle missing values without modification of data. Further, the similarity measure is more reliable than partial distances and inherently possesses the properties required to perform SNMF. The experimental evaluation on real world datasets demonstrates that the proposed approach is efficient, scalable and shows significantly better performance compared to the existing techniques.

F-measure is a popular performance metric used in classification when the dataset is unbalanced. Optimizing this measure directly is often challenging since no closed form solution exists. Current algorithms use approximations to the F-measure and design classifiers using maximum margin or logistic regression framework. These algorithms are not scalable and the classifiers designed are not robust to outliers. In this work, we propose a general framework for approximate F-measure maximization. We also propose a non-convex loss function which is robust to outliers. Use of elastic net regularizer in the problem formulation enables us to do simultaneous classifier design and feature selection. We present an efficient algorithm to solve the proposed problem formulation. The proposed algorithm is simple and is easy to implement. Numerical experiments on real-world benchmark datasets demonstrate that the proposed algorithm is fast and gives better generalization performance compared to some existing approaches. Thus, it is a powerful alternative for optimizing F-measure and designing a sparse classifier.

We propose a new approach to clustering. Our idea is to map cluster formation to coalition formation in cooperative games, and to use the Shapley value of the patterns to identify clusters and cluster representatives. We show that the underlying game is convex and this leads to an efficient biobjective clustering algorithm that we call BiGC. The algorithm yields high-quality clustering with respect to average point-to-center distance (potential) as well as average intracluster point-to-point distance (scatter). We demonstrate the superiority of BiGC over state-of-the-art clustering algorithms (including the center based and the multiobjective techniques) through a detailed experimentation using standard cluster validity criteria on several benchmark data sets. We also show that BiGC satisfies key clustering properties such as order independence, scale invariance, and richness.

The rapid growth in the field of data mining has lead to the development of various methods for outlier detection. Though detection of outliers has been well explored in the context of numerical data, dealing with categorical data is still evolving. In this paper, we propose a two-phase algorithm for detecting outliers in categorical data based on a novel definition of outliers. In the first phase, this algorithm explores a clustering of the given data, followed by the ranking phase for determining the set of most likely outliers. The proposed algorithm is expected to perform better as it can identify different types of outliers, employing two independent ranking schemes based on the attribute value frequencies and the inherent clustering structure in the given data. Unlike some existing methods, the computational complexity of this algorithm is not affected by the number of outliers to be detected. The efficacy of this algorithm is demonstrated through experiments on various public domain categorical data sets.

Outlier detection in high dimensional categorical data has been a problem of much interest due to the extensive use of qualitative features for describing the data across various application areas. Though there exist various established methods for dealing with the dimensionality aspect through feature selection on numerical data, the categorical domain is actively being explored. As outlier detection is generally considered as an unsupervised learning problem due to lack of knowledge about the nature of various types of outliers, the related feature selection task also needs to be handled in a similar manner. This motivates the need to develop an unsupervised feature selection algorithm for efficient detection of outliers in categorical data. Addressing this aspect, we propose a novel feature selection algorithm based on the mutual information measure and the entropy computation. The redundancy among the features is characterized using the mutual information measure for identifying a suitable feature subset with less redundancy. The performance of the proposed algorithm in comparison with the information gain based feature selection shows its effectiveness for outlier detection. The efficacy of the proposed algorithm is demonstrated on various high-dimensional benchmark data sets employing two existing outlier detection methods.

In this paper, we propose a classification algorithm based on the maximum entropy principle. This algorithm finds the most appropriate class-conditional maximum entropy distributions for classification. No prior knowledge about the form of density function for estimating the class conditional density is assumed except that the information is given in the form of expected valued of features. This algorithm also incorporates a method to select relevant features for classification. The proposed algorithm is suitable for large data-sets and is demonstrated by simulation results on some real world benchmark data-sets.

Most enterprise data is distributed in multiple relational databases with expert-designed schema. Using traditional single-table machine learning techniques over such data not only incur a computational penalty for converting to a ”flat” form (mega-join), even the human-specified semantic information present in the relations is lost. In this paper, we present a two-phase hierarchical meta-classification algorithm for relational databases with a semantic divide and conquer approach. We propose a recursive, prediction aggregation technique over heterogeneous classifiers applied on individual database tables. A preliminary evaluation on TPCH and UCI benchmarks shows reduced training time without any loss of prediction accuracy.

Even though several techniques have been proposed in the literature for achieving multiclass classification using Support Vector Machine(SVM), the scalability aspect of these approaches to handle large data sets still needs much of exploration. Core Vector Machine(CVM) is a technique for scaling up a two class SVM to handle large data sets. In this paper we propose a Multiclass Core Vector Machine(MCVM). Here we formulate the multiclass SVM problem as a Quadratic Programming(QP) problem defining an SVM with vector valued output. This QP problem is then solved using the CVM technique to achieve scalability to handle large data sets. Experiments done with several large synthetic and real world data sets show that the proposed MCVM technique gives good generalization performance as that of SVM at a much lesser computational expense. Further, it is observed that MCVM scales well with the size of the data set.

In this paper we propose a novel, scalable, clustering based Ordinal Regression formulation, which is an instance of a Second Order Cone Program (SOCP) with one Second Order Cone (SOC) constraint. The main contribution of the paper is a fast algorithm, CB-OR, which solves the proposed formulation more eficiently than general purpose solvers. Another main contribution of the paper is to pose the problem of focused crawling as a large scale Ordinal Regression problem and solve using the proposed CB-OR. Focused crawling is an efficient mechanism for discovering resources of interest on the web. Posing the problem of focused crawling as an Ordinal Regression problem avoids the need for a negative class and topic hierarchy, which are the main drawbacks of the existing focused crawling methods. Experiments on large synthetic and benchmark datasets show the scalability of CB-OR. Experiments also show that the proposed focused crawler outperforms the state-of-the-art.

A geometric and non parametric procedure for testing if two finite set of points are linearly separable is proposed. The Linear Separability Test is equivalent to a test that determines if a strictly positive point h > 0 exists in the range of a matrix A (related to the points in the two finite sets). The algorithm proposed in the paper iteratively checks if a strictly positive point exists in a subspace by projecting a strictly positive vector with equal co-ordinates (p), on the subspace. At the end of each iteration, the subspace is reduced to a lower dimensional subspace. The test is completed within r ≤ min(n, d + 1) steps, for both linearly separable and non separable problems (r is the rank of A, n is the number of points and d is the dimension of the space containing the points). The worst case time complexity of the algorithm is O(nr3) and space complexity of the algorithm is O(nd). A small review of some of the prominent algorithms and their time complexities is included. The worst case computational complexity of our algorithm is lower than the worst case computational complexity of Simplex, Perceptron, Support Vector Machine and Convex Hull Algorithms, if d

Core vector machine(CVM) is suitable for efficient large-scale pattern classification. In this paper, a method for improving the performance of CVM with Gaussian kernel function irrespective of the orderings of patterns belonging to different classes within the data set is proposed. This method employs a selective sampling based training of CVM using a novel kernel based scalable hierarchical clustering algorithm. Empirical studies made on synthetic and real world data sets show that the proposed strategy performs well on large data sets.

Classification tasks involving high dimensional vectors are affected by the curse of dimensionality requiring large amount of training data. This is because a high-dimensional space with a modest number of samples is mostly empty. To overcome this we employ the principle of Projection Pursuit. The principle is motivated by the aim to search for clusters in high-dimensional space. Data points are projected onto an appropriate projection direction. Search for clusters is in this single dimensional projection space. As a result inherent sparsity of the high-dimensional space is avoided. Classical discriminant analysis methods also seek clusters but require class labels to be specified. One such technique, the Fisher's Linear Discriminant (FLD) method, has been used to arrive at an unsupervised algorithm that seeks bimodal projection directions.

This paper presents a novel Second Order Cone Programming (SOCP) formulation for large scale binary classification tasks. Assuming that the class conditional densities are mixture distributions, where each component of the mixture has a spherical covariance, the second order statistics of the components can be estimated efficiently using clustering algorithms like BIRCH. For each cluster, the second order moments are used to derive a second order cone constraint via a Chebyshev-Cantelli inequality. This constraint ensures that any data point in the cluster is classified correctly with a high probability. This leads to a large margin SOCP formulation whose size depends on the number of clusters rather than the number of training data points. Hence, the proposed formulation scales well for large datasets when compared to the state-of-the-art classifiers, Support Vector Machines (SVMs). Experiments on real world and synthetic datasets show that the proposed algorithm outperforms SVM solvers in terms of training time and achieves similar accuracies.

A generalized evolutionary algorithm based on Tsallis statistics is proposed. The algorithm uses Tsallis generalized canonical distribution, which is one parameter generalization of Boltzmann distribution, to weigh the configurations in the selection mechanism. This generalization is motivated by the recently proposed generalized simulated annealing algorithm based on Tsallis statistics. We also present an information theoretic justification to use Boltzmann distribution in the selection mechanism, since these 'canonical' distributions have deep roots in information theory. Our simulation results show that for an appropriate choice of non-extensive index that is offered by Tsallis statistics, evolutionary algorithms based on this generalization outperform algorithms based on Boltzmann distribution.

Kullback-Leibler cross-entropy has unique properties in cases involving distributions resulting from cross-entropy minimization. Nonextensive entropy (Tsallis entropy), which is a one-parameter generalization of Shannon entropy, is proposed to study certain class of physical systems. Thermostatistics based on Tsallis entropy is termed as nonextensive statistics or Tsallis statistics. Previously, Kullback-Leibler cross-entropy has been generalized and studied in this framework. In this paper we study properties of generalized cross-entropy minimization and present some differences with the classical case. In the representation of such a minimum cross-entropy distribution, we highlight the use of the q-product, an operator that has been recently introduced, to derive the mathematical structure behind the Tsallis statistics. One of our main results is the generalization of the triangle equality of cross-entropy minimization, in nonextensive framework

Boltzmann selection is an important selection mechanism in evolutionary algorithms as it has theoretical properties which help in theoretical analysis. However, Boltzmann selection is not used in practice because a good annealing schedule for the inverse temperature parameter is lacking. In this paper, we propose a Cauchy annealing schedule for Boltzmann selection scheme based on a hypothesis that selection-strength should increase as evolutionary process goes on and distance between two selection strengths should decrease for the process to converge. To formalize these aspects, we develop formalism for selection mechanisms using fitness distributions and give an appropriate measure for selection strength. In this paper, we prove an important result, by which we derive an annealing schedule called Cauchy annealing schedule. We demonstrate the novelty of proposed annealing schedule using simulations in the framework of genetic algorithms.

Classification of large datasets is a challenging task in data mining. In the current work, we propose a novel method that compresses the data and classifies the test data directly in its compressed form. The work forms a hybrid learning approach integrating the activities of data abstraction, frequent item generation, compression, classification and use of rough sets.

Boosting is a general method for improving the accuracy of a learning algorithm. AdaBoost, short form for adaptive boosting method, consists of repeated use of a weak or a base learning algorithm to find corresponding weak hypothesis by adapting to the error rates of the individual weak hypotheses. A large, complex handwritten data is under study. A repeated use of weak learner on the huge data results in large amount of processing time. In view of this, instead of using the entire training data for learning, we propose to use only prototypes. Further, in the current work, the base learner consists of a nearest neighbour classifier that employs prototypes generated using "leader" clustering algorithm. The leader algorithm is a single pass algorithm and is linear in terms of time as well as computation complexity. The prototype set alone is used as training data. In the process of developing an algorithm, domain knowledge of the Handwritten data, which is under study, is made use of. With the fusion of clustering, prototype selection, AdaBoost and Nearest Neighbour classifier, a very high classification accuracy, which is better than reported earlier on the considered data, is obtained in less number of iterations. The procedure integrates clustering outcome in terms of prototypes with boosting.

Darwinian evolution, which is characterized in terms of particular macroscopic behavior that emerges from microscopic organismic interaction, considers populations as units of evolutionary change. We formalize these concepts in evolutionary computation by developing notion of quotient evolutionary space (QES). We map set of all finite populations to a set of macroscopic properties of population those are chosen a priori; and we call this mapping as evolutionary criteria. On the 'quotient set of populations' that is induced by evolutionary criteria, we define mathematical structures to define evolutionary change with respect to chosen macroscopic parameters at populational level. This allows us to transform the objective defined on the search space that is imposed by the fitness function to an objective on the population space. We call quotient set of populations along with the mathematical structures the quotient evolutionary space. To demonstrate the abstraction we consider fitness distribution of population as evolutionary criteria and give a detailed analysis of resulting spaces and basic convergence results.

Naive models of evolution define natural selection as a process which brings in differential reproductive capabilities in organisms of a population, and hence, evolutionary algorithms implement selection by differential reproduction: the fittest members of the population are reproduced preferentially at the expense of the less fit members of the population. Formal models in evolutionary biology often subdivide selection into components, called 'episodes of selection', to capture the different complex mechanisms of nature by which Darwinian evolution can occur. In this paper we introduce the concept of 'episodes of selection' in evolutionary computation by means of a conceptual evolutionary model (ACE-model). This model captures selection in two episodes and in two phases of the evolutionary cycle. Here we give a formal description of the ACE-model, in which one can mechanize the two phases in different possible ways. We propose evolutionary algorithms based on the ACE-model, by giving simple mechanisms for implementation of two phases. Finally, we discuss the importance of introducing episodes of selection in evolutionary algorithms by simulations of the proposed evolutionary algorithms for function optimization.

In this paper, a stochastic connectionist approach is proposed for solving function optimization problems with real-valued parameters. With the assumption of increased processing capability of a node in the connectionist network, we show how a broader class of problems can be solved. As the proposed approach is a stochastic search technique, it avoids getting stuck in local optima. Robustness of the approach is demonstrated on several multi-modal functions with different numbers of variables. Optimization of a well-known partitional clustering criterion, the squared-error criterion (SEC), is formulated as a function optimization problem and is solved using the proposed approach. This approach is used to cluster selected data sets and the results obtained are compared with that of the K-means algorithm and a simulated annealing (SA) approach. The amenability of the connectionist approach to parallelization enables effective use of parallel hardware.

In this paper, we propose a novel hybrid genetic algorithm (GA) that finds a globally optimal partition of a given data into a specified number of clusters. GA's used earlier in clustering employ either an expensive crossover operator to generate valid child chromosomes from parent chromosomes or a costly fitness function or both. To circumvent these expensive operations, we hybridize GA with a classical gradient descent algorithm used in clustering, viz. K-means algorithm. Hence, the name genetic K-means algorithm (GKA). We define K-means operator, one-step of K-means algorithm, and use it in GKA as a search operator instead of crossover. We also define a biased mutation operator specific to clustering called distance-based-mutation. Using finite Markov chain theory, we prove that the GKA converges to the global optimum. It is observed in the simulations that GKA converges to the best known optimum corresponding to the given data in concurrence with the convergence result. It is also observed that GKA searches faster than some of the other evolutionary algorithms used for clustering.

In statistical pattern recognition, the decision of which features to use is usually left to human judgment. If possible, automatic methods are desirable. Like multilayer perceptrons, learning subspace methods (LSMs) have the potential to integrate feature extraction and classification. In this paper, we propose two new algorithms, along with their neural-network implementations, to overcome certain limitations of the earlier LSMs. By introducing one cluster at a time and adapting it if necessary, we eliminate one limitation of deciding how many clusters to have in each class by trial-and-error. By using the principal component analysis neural networks along with this strategy, we propose neural-network models which are better in overcoming another limitation, scalability. Our results indicate that the proposed classifiers are comparable to classifiers like the multilayer perceptrons and the nearest-neighbor classifier in terms of classification accuracy. In terms of classification speed and scalability in design, they appear to be better for large-dimensional problems.

Clustering is concerned with grouping a collection of input objects. Conventional clustering algorithms cluster unlabelled objects. We argue that there are useful applications that involve clustering of labelled objects. We propose an approach for clustering of labelled objects. The proposed approach makes use of the domain knowledge represented in the form of a directed acyclic graph for clustering. We also propose a set of proper axioms in logic as a basis for the proposed algorithm. We study some of the properties of the approach such as order-independence and describe in detail an application of the proposed algorithm in the context of document retrieval.

The general form of a decision-making model raises hypotheses about the dynamics of stimulus, conception, and response. One might suppose that the decision progress begins with the perception of some sort of stimulus. The amount of information available for decision-making is often incomplete and hence any logic that attempts to model decision-making must be nonmonotonic in nature. The existing logics can handle defeasible nonmonotonic inferences. The authors propose a modified first-order logic so that defeasible beliefs can also be handled. The modification is in the form of a set of proper axioms to handle belief revision, and a modified modus ponens to capture nonmonotonic reasoning. The proposed logic is extended to model decision-making activity.>