Clustering in Concept Association Networks

We view association of concepts as a complex network and present a heuristic for clustering concepts by taking into account the underlying network structure of their associations. Clusters generated from our approach are qualitatively better than clusters generated from the conventional spectral clustering mechanism used for graph partitioning.

Test of the Clustering Hypothesis in the Helsinki Exchanges

This paper investigates the clustering pattern in the Finnish stock market. Using trading volume and time as factors capturing the clustering pattern in the market, the Keim and Madhavan (1996) and the Engle and Russell (1998) model provide the framework for the analysis. The descriptive and the parametric analysis provide evidences that an important determinant of the famous U-shape pattern in the market is the rate of information arrivals as measured by large trading volumes and durations at the market open and close. Precisely, 1) the larger the trading volume, the greater the impact on prices both in the short and the long run, thus prices will differ across quantities. 2) Large trading volume is a non-linear function of price changes in the long run. 3) Arrival times are positively autocorrelated, indicating a clustering pattern and 4) Information arrivals as approximated by durations are negatively related to trading flow.

Scalable non-linear Support Vector Machine using hierarchical clustering

This paper discusses a method for scaling SVM with Gaussian kernel function to handle large data sets by using a selective sampling strategy for the training set. It employs a scalable hierarchical clustering algorithm to construct cluster indexing structures of the training data in the kernel induced feature space. These are then used for selective sampling of the training data for SVM to impart scalability to the training process. Empirical studies made on real world data sets show that the proposed strategy performs well on large data sets.

Agglomerative clustering using the concept of mutual nearest neighbourhood

A method for determining the mutual nearest neighbours (MNN) and mutual neighbourhood value (mnv) of a sample point, using the conventional nearest neighbours, is suggested. A nonparametric, hierarchical, agglomerative clustering algorithm is developed using the above concepts. The algorithm is simple, deterministic, noniterative, requires low storage and is able to discern spherical and nonspherical clusters. The method is applicable to a wide class of data of arbitrary shape, large size and high dimensionality. The algorithm can discern mutually homogenous clusters. Strong or weak patterns can be discerned by properly choosing the neighbourhood width.

Disaggregative Clustering Using the Concept of Mutual Nearest Neighborhood

A nonparametric, hierarchical, disaggregative clustering algorithm is developed using a novel similarity measure, called the mutual neighborhood value (MNV), which takes into account the conventional nearest neighbor ranks of two samples with respect to each other. The algorithm is simple, noniterative, requires low storage, and needs no specification of the expected number of clusters. The algorithm appears very versatile as it is capable of discerning spherical and nonspherical clusters, linearly nonseparable clusters, clusters with unequal populations, and clusters with lowdensity bridges. Changing of the neighborhood size enables discernment of strong or weak patterns.

Model-theoretic approach to clustering

The paper deals with a model-theoretic approach to clustering. The approach can be used to generate cluster description based on knowledge alone. Such a process of generating descriptions would be extremely useful in clustering partially specified objects. A natural byproduct of the proposed approach is that missing values of attributes of an object can be estimated with ease in a meaningful fashion. An important feature of the approach is that noisy objects can be detected effectively, leading to the formation of natural groups. The proposed algorithm is applied to a library database consisting of a collection of books.

A heuristic clustering algorithm using union of overlapping pattern-cells

Relative geometric arrangements of the sample points, with reference to the structure of the imbedding space, produce clusters. Hence, if each sample point is imagined to acquire a volume of a small M-cube (called pattern-cell), depending on the ranges of its (M) features and number (N) of samples; then overlapping pattern-cells would indicate naturally closer sample-points. A chain or blob of such overlapping cells would mean a cluster and separate clusters would not share a common pattern-cell between them. The conditions and an analytic method to find such an overlap are developed. A simple, intuitive, nonparametric clustering procedure, based on such overlapping pattern-cells is presented. It may be classified as an agglomerative, hierarchical, linkage-type clustering procedure. The algorithm is fast, requires low storage and can identify irregular clusters. Two extensions of the algorithm, to separate overlapping clusters and to estimate the nature of pattern distributions in the sample space, are also indicated.

A comparison between conceptual clustering and conventional clustering

Clustering is a process of partitioning a given set of patterns into meaningful groups. The clustering process can be viewed as consisting of the following three phases: (i) feature selection phase, (ii) classification phase, and (iii) description generation phase. Conventional clustering algorithms implicitly use knowledge about the clustering environment to a large extent in the feature selection phase. This reduces the need for the environmental knowledge in the remaining two phases, permitting the usage of simple numerical measure of similarity in the classification phase. Conceptual clustering algorithms proposed by Michalski and Stepp [IEEE Trans. PAMI, PAMI-5, 396–410 (1983)] and Stepp and Michalski [Artif. Intell., pp. 43–69 (1986)] make use of the knowledge about the clustering environment in the form of a set of predefined concepts to compute the conceptual cohesiveness during the classification phase. Michalski and Stepp [IEEE Trans. PAMI, PAMI-5, 396–410 (1983)] have argued that the results obtained with the conceptual clustering algorithms are superior to conventional methods of numerical classification. However, this claim was not supported by the experimental results obtained by Dale [IEEE Trans. PAMI, PAMI-7, 241–244 (1985)]. In this paper a theoretical framework, based on an intuitively appealing set of axioms, is developed to characterize the equivalence between the conceptual clustering and conventional clustering. In other words, it is shown that any classification obtained using conceptual clustering can also be obtained using conventional clustering and vice versa.

Perturbative growth of cosmological clustering. I: Formalism

Here we rederive the hierarchy of equations for the evolution of distribution functions of various orders using a convenient parameterization. We use this to obtain equations for two- and three-point correlation functions in powers of a small parameter, viz., the initial density contrast. The correspondence of the lowest order solutions of these equations to the results from the linear theory of density perturbations is shown for an OMEGA = 1 universe. These equations are then used to calculate, to the lowest order, the induced three-point correlation function that arises from Gaussian initial conditions in an OMEGA = 1 universe. We obtain an expression which explicitly exhibits the spatial structure of the induced three-point correlation function. It is seen that the spatial structure of this quantity is independent of the value of OMEGA. We also calculate the triplet momentum. We find that the induced three-point correlation function does not have the ''hierarchical'' form often assumed. We discuss possibilities of using the induced three-point correlation to interpret observational data. The formalism developed here can also be used to test a validity of different schemes to close the

Knowledge-based clustering

In the knowledge-based clustering approaches reported in the literature, explicit know ledge, typically in the form of a set of concepts, is used in computing similarity or conceptual cohesiveness between objects and in grouping them. We propose a knowledge-based clustering approach in which the domain knowledge is also used in the pattern representation phase of clustering. We argue that such a knowledge-based pattern representation scheme reduces the complexity of similarity computation and grouping phases. We present a knowledge-based clustering algorithm for grouping hooks in a library.

Perturbative growth of cosmological clustering .2. The two-point correlation

We use the BBGKY hierarchy equations to calculate, perturbatively, the lowest order nonlinear correction to the two-point correlation and the pair velocity for Gaussian initial conditions in a critical density matter-dominated cosmological model. We compare our results with the results obtained using the hydrodynamic equations that neglect pressure and find that the two match, indicating that there are no effects of multistreaming at this order of perturbation. We analytically study the effect of small scales on the large scales by calculating the nonlinear correction for a Dirac delta function initial two-point correlation. We find that the induced two-point correlation has a x(-6) behavior at large separations. We have considered a class of initial conditions where the initial power spectrum at small k has the form k(n) with 0 < n less than or equal to 3 and have numerically calculated the nonlinear correction to the two-point correlation, its average over a sphere and the pair velocity over a large dynamical range. We find that at small separations the effect of the nonlinear term is to enhance the clustering, whereas at intermediate scales it can act to either increase or decrease the clustering. At large scales we find a simple formula that gives a very good fit for the nonlinear correction in terms of the initial function. This formula explicitly exhibits the influence of small scales on large scales and because of this coupling the perturbative treatment breaks down at large scales much before one would expect it to if the nonlinearity were local in real space. We physically interpret this formula in terms of a simple diffusion process. We have also investigated the case n = 0, and we find that it differs from the other cases in certain respects. We investigate a recently proposed scaling property of gravitational clustering, and we find that the lowest order nonlinear terms cause deviations from the scaling relations that are strictly valid in the linear regime. The approximate validity of these relations in the nonlinear regime in l(T)-body simulations cannot be understood at this order of evolution.

Quantum clustering and network analysis of MD simulation trajectories to probe the conformational ensembles of protein-ligand interactions

In this article, we present a novel application of a quantum clustering (QC) technique to objectively cluster the conformations, sampled by molecular dynamics simulations performed on different ligand bound structures of the protein. We further portray each conformational population in terms of dynamically stable network parameters which beautifully capture the ligand induced variations in the ensemble in atomistic detail. The conformational populations thus identified by the QC method and verified by network parameters are evaluated for different ligand bound states of the protein pyrrolysyl-tRNA synthetase (DhPylRS) from D. hafniense. The ligand/environment induced re-distribution of protein conformational ensembles forms the basis for understanding several important biological phenomena such as allostery and enzyme catalysis. The atomistic level characterization of each population in the conformational ensemble in terms of the re-orchestrated networks of amino acids is a challenging problem, especially when the changes are minimal at the backbone level. Here we demonstrate that the QC method is sensitive to such subtle changes and is able to cluster MD snapshots which are similar at the side-chain interaction level. Although we have applied these methods on simulation trajectories of a modest time scale (20 ns each), we emphasize that our methodology provides a general approach towards an objective clustering of large-scale MD simulation data and may be applied to probe multistate equilibria at higher time scales, and to problems related to protein folding for any protein or protein-protein/RNA/DNA complex of interest with a known structure.

Dynamic subspace clustering for very large high-dimensional databases

Emerging high-dimensional data mining applications needs to find interesting clusters embeded in arbitrarily aligned subspaces of lower dimensionality. It is difficult to cluster high-dimensional data objects, when they are sparse and skewed. Updations are quite common in dynamic databases and they are usually processed in batch mode. In very large dynamic databases, it is necessary to perform incremental cluster analysis only to the updations. We present a incremental clustering algorithm for subspace clustering in very high dimensions, which handles both insertion and deletions of datapoints to the backend databases.