15790608
Clustering High-Dimensional Data with Low-Order Neighbors
Density-based and grid-based clustering are two main clustering approaches. The former is famous for its capability of discovering clusters of various shapes and eliminating noises, while the latter is well known for its high speed. Combination of the two approaches seems to provide better clustering results. To the best of our knowledge, however, all existing algorithms that combine density-based clustering and grid-based clustering take cells as atomic units, in the sense that either all objects in a cell belong to a cluster or no object in the cell belong to any cluster. This requires the cells to be small enough to ensure the fine resolution of results. In high-dimensional spaces, however, the number of cells can be very large when cells are small, which would make the clustering process extremely costly. On the other hand, the number of neighbors of a cell grows exponentially with the dimensionality of datasets, which makes the complexity increase further. In this paper, we present a new approach that takes objects (or points) as the atomic units, so that the restriction of cell size can be relaxed without degrading the resolution of clustering results. In addition, a concept of ith-order neighbors is introduced to avoid considering the exponential number of neighboring cells. By considering only low-order neighbors, our algorithm is very efficient while losing only a little bit of accuracy. Experiments on synthetic and public data show that our algorithm can cluster high-dimensional data effectively and efficiently.
15310670
A Recent-Biased Dimension Reduction Technique for Time Series Data
There are many techniques developed for tackling time series and most of them consider every part of a sequence equally. In many applications, however, recent data can often be much more interesting and significant than old data. This paper defines new recent-biased measures for distance and energy, and proposes a recent-biased technique based on DWT for time series in which more recent data are considered more significant. With such a recent-biased technique, the dimension of time series can be reduced while effectively preserving the recent-biased energy. Our experiments have demonstrated the effectiveness of the proposed approach for handling time series.
28734493
AGRID: An Efficient Algorithm for Clustering Large High-Dimensional Datasets
The clustering algorithm GDILC relies on density-based clustering with grid and is designed to discover clusters of arbitrary shapes and eliminate noises. However, it is not scalable to large high-dimensional datasets. In this paper, we improved this algorithm in five important directions. Through these improvements, AGRID is of high scalability and can process large high-dimensional datasets. It can discover clusters of various shapes and eliminate noises effectively. Besides, it is insensitive to the order of input and is a non-parametric algorithm. The high speed and accuracy of the AGRID clustering algorithm was shown in our experiments.
32435431
Regularized Semi-supervised Classification on Manifold
Semi-supervised learning gets estimated marginal distribution PX with a large number of unlabeled examples and then constrains the conditional probability p(y | x) with a few labeled examples. In this paper, we focus on a regularization approach for semi-supervised classification. The label information graph is first defined to keep the pairwise label relationship and can be incorporated with neighborhood graph which reflects the intrinsic geometry structure of PX. Then we propose a novel regularized semi-supervised classification algorithm, in which the regularization term is based on the modified Graph Laplacian. By redefining the Graph Laplacian, we can adjust and optimize the decision boundary using the labeled examples. The new algorithm combines the benefits of both unsupervised and supervised learning and can use unlabeled and labeled examples effectively. Encouraging experimental results are presented on both synthetic and real world datasets.
17699590
Adapting K-Means Algorithm for Discovering Clusters in Subspaces
Subspace clustering is a challenging task in the field of data mining. Traditional distance measures fail to differentiate the furthest point from the nearest point in very high dimensional data space. To tackle the problem, we design minimal subspace distance which measures the similarity between two points in the subspace where they are nearest to each other. It can discover subspace clusters implicitly when measuring the similarities between points. We use the new similarity measure to improve traditional k-means algorithm for discovering clusters in subspaces. By clustering with low-dimensional minimal subspace distance first, the clusters in low-dimensional subspaces are detected. Then by gradually increasing the dimension of minimal subspace distance, the clusters get refined in higher dimensional subspaces. Our experiments on both synthetic data and real data show the effectiveness of the proposed similarity measure and algorithm.
14675910
Generalized dimension-reduction framework for recent-biased time series analysis
Recent-biased approximations have received increased attention recently as a mechanism for learning trend patterns from time series or data streams. They have shown promise for clustering time series and incrementally pattern maintaining. In this paper, we design a generalized dimension-reduction framework for recent-biased approximations, aiming at making traditional dimension-reduction techniques actionable in recent-biased time series analysis. The framework is designed in two ways: equi-segmented scheme and vari-segmented scheme. In both schemes, time series data are first partitioned into segments and a dimension-reduction technique is applied to each segment. Then, more coefficients are kept for more recent data while fewer kept for older data. Thus, more details are preserved for recent data and fewer coefficients are kept for the whole time series, which improves the efficiency greatly. We experimentally evaluate the proposed approach, and demonstrate that traditional dimension-reduction techniques, such as SVD, DFT, DWT, PIP, PAA, and landmarks, can be embedded into our framework for recent-biased approximations over streaming time series.
16630001
Model-based Runtime Verification Framework for Self-optimizing Systems
This paper describes a novel on-line model checking approach offered as service of a real-time operating system (RTOS). The verification system is intended especially for self-optimizing component-based real-time systems where self-optimization is performed by dynamically exchanging components. The verification is performed at the level of (RT-UML) models. The properties to be checked are expressed by RT-OCL terms where the underlying temporal logic is restricted to either time-annotated ACTL or LTL formulae. The on-line model checking runs interleaved with the execution of the component to be checked in a pipelined manner. The technique applied is based on on-the-fly model checking. More specifically for ACTL formulae this means on-the-fly solution of the NHORNSAT problem while in the case of LTL the emptiness checking method is applied.
1706033
Hierarchical Clustering Algorithms for Document Datasets
Fast and high-quality document clustering algorithms play an important role in providing intuitive navigation and browsing mechanisms by organizing large amounts of information into a small number of meaningful clusters. In particular, clustering algorithms that build meaningful hierarchies out of large document collections are ideal tools for their interactive visualization and exploration as they provide data-views that are consistent, predictable, and at different levels of granularity. This paper focuses on document clustering algorithms that build such hierarchical solutions and (i) presents a comprehensive study of partitional and agglomerative algorithms that use different criterion functions and merging schemes, and (ii) presents a new class of clustering algorithms called constrained agglomerative algorithms, which combine features from both partitional and agglomerative approaches that allows them to reduce the early-stage errors made by agglomerative methods and hence improve the quality of clustering solutions. The experimental evaluation shows that, contrary to the common belief, partitional algorithms always lead to better solutions than agglomerative algorithms; making them ideal for clustering large document collections due to not only their relatively low computational requirements, but also higher clustering quality. Furthermore, the constrained agglomerative methods consistently lead to better solutions than agglomerative methods alone and for many cases they outperform partitional methods, as well.
1405072
Effective document clustering for large heterogeneous law firm collections
Computational resources for research in legal environments have historically implied remote access to large databases of legal documents such as case law, statutes, law reviews and administrative materials. Today, by contrast, there exists enormous growth in lawyers' electronic work product within these environments, specifically within law firms. Along with this growth has come the need for accelerated knowledge management---automated assistance in organizing, analyzing, retrieving and presenting this content in a useful and distributed manner.In cases where a relevant legal taxonomy is available, together with representative labeled data, automated text classification tools can be applied. In the absence of these resources, document clustering offers an alternative approach to organizing collections, and an adjunct to search.To explore this approach further, we have conducted sets of successively more complex clustering experiments using primary and secondary law documents as well as actual law firm data. Tests were run to determine the efficiency and effectiveness of a number of essential clustering functions. After examining the performance of traditional or hard clustering applications, we investigate soft clustering (multiple cluster assignments) as well as hierarchical clustering. We show how these latter clustering approaches are effective, in terms of both internal and external quality measures, and useful to legal researchers. Moreover, such techniques can ultimately assist in the automatic or semi-automatic generation of taxonomies for subsequent use by classification programs.
2480088
Melting and flowing in multiphase environment
Abstract This paper presents a method to simulate the melting and flowing phenomena with different materials in multiple phases. In such a multiphase environment, solid objects are melted because of heating and the melted liquid flows while interacting with the ambient air flow. Our simulation is based on a modified lattice Boltzmann method (LBM), where the fluid dynamics of the air flow and the melted liquid is modeled within a common lattice framework. Therefore, no particular front tracking methods are required for the liquid–air interface. The liquid–solid and air–solid interfaces are implemented as curved boundaries in the LBM, which can accommodate arbitrarily shaped solid objects. Heat transfer is incorporated with a finite difference discretization of a standard diffusion–advection equation simulating the temperature evolution. The temperature and body forces (gravity and surface tension) are easily applied by adopting a new version of the LBM: multiple-relaxation-time LBM (MRTLBM). The melting and flowing behavior is controlled by the heat source, the viscosity and the body forces. All the numerical computations in our method are local and parallelizable, therefore, interactive speed is achieved by hardware acceleration on the contemporary graphics hardware (GPU).
210649
Combining Statistical Language Models via the Latent Maximum Entropy Principle
We present a unified probabilistic framework for statistical language modeling which can simultaneously incorporate various aspects of natural language, such as local word interaction, syntactic structure and semantic document information. Our approach is based on a recent statistical inference principle we have proposed—the latent maximum entropy principle—which allows relationships over hidden features to be effectively captured in a unified model. Our work extends previous research on maximum entropy methods for language modeling, which only allow observed features to be modeled. The ability to conveniently incorporate hidden variables allows us to extend the expressiveness of language models while alleviating the necessity of pre-processing the data to obtain explicitly observed features. We describe efficient algorithms for marginalization, inference and normalization in our extended models. We then use these techniques to combine two standard forms of language models: local lexical models (Markov N-gram models) and global document-level semantic models (probabilistic latent semantic analysis). Our experimental results on the Wall Street Journal corpus show that we obtain a 18.5% reduction in perplexity compared to the baseline tri-gram model with Good-Turing smoothing.