scholarly journals High-Order Co-Clustering via Strictly Orthogonal and Symmetric L1-Norm Nonnegative Matrix Tri-Factorization

2018 ◽  
Author(s):  
Kai Liu ◽  
Hua Wang
Keyword(s):  
Nonnegative Matrix ◽  
Factorization Method ◽  
High Order ◽  
Single Type ◽  
Objective Functions ◽  
Clustering Methods ◽  
Data Types ◽  
L1 Norm ◽  
Real World Data ◽  
Data Set

Different to traditional clustering methods that deal with one single type of data, High-Order Co- Clustering (HOCC) aims to cluster multiple types of data simultaneously by utilizing the inter- or/and intra-type relationships across different data types. In existing HOCC methods, data points routinely enter the objective functions with squared residual errors. As a result, outlying data samples can dominate the objective functions, which may lead to incorrect clustering results. Moreover, existing methods usually suffer from soft clustering, where the probabilities to different groups can be very close. In this paper, we propose an L1 -norm symmetric nonnegative matrix tri-factorization method to solve the HOCC problem. Due to the orthogonal constraints and the symmetric L1 -norm formulation in our new objective, conventional auxiliary function approach no longer works. Thus we derive the solution algorithm using the alternating direction method of multipliers. Extensive experiments have been conducted on a real world data set, in which promising empirical results, including less time consumption, strictly orthogonal membership matrix, lower local minima etc., have demonstrated the effectiveness of our proposed method.

Topology and Topic-Aware Service Clustering

2018 ◽  
Vol 15 (3) ◽  
pp. 18-37 ◽  
Author(s):  
Weifeng Pan ◽  
Jilei Dong ◽  
Kun Liu ◽  
Jing Wang
Keyword(s):  
Service Discovery ◽  
Clustering Algorithm ◽  
Latent Dirichlet Allocation ◽  
Empirical Evaluation ◽  
Single Type ◽  
Bipartite Network ◽  
Real World Data ◽  
Service Usage ◽  
Data Set ◽  
Service Clustering

This article describes how the number of services and their types being so numerous makes accurately discovering desired services become a problem. Service clustering is an effective way to facilitate service discovery. However, the existing approaches are usually designed for a single type of service documents, neglecting to fully use the topic and topological information in service profiles and usage histories. To avoid these limitations, this article presents a novel service clustering approach. It adopts a bipartite network to describe the topological structure of service usage histories and uses a SimRank algorithm to measure the topological similarity of services; It applies Latent Dirichlet Allocation to extract topics from service profiles and further quantifies the topic similarity of services; It quantifies the similarity of services by integrating topological and topic similarities; It uses the Chameleon clustering algorithm to cluster the services. The empirical evaluation on real-world data set highlights the benefits provided by the combination of topological and topic similarities.

Soft Subspace Clustering for High-Dimensional Data

2011 ◽  
pp. 1810-1814
Author(s):  
Liping Jing ◽  
Michael K. Ng ◽  
Joshua Zhexue Huang
Keyword(s):  
High Dimensional Data ◽  
Subspace Clustering ◽  
High Dimensional ◽  
Special Treatment ◽  
Clustering Methods ◽  
Real World Data ◽  
Text Data ◽  
Data Set ◽  
Dna Microarray Data ◽  
Text Document

High dimensional data is a phenomenon in real-world data mining applications. Text data is a typical example. In text mining, a text document is viewed as a vector of terms whose dimension is equal to the total number of unique terms in a data set, which is usually in thousands. High dimensional data occurs in business as well. In retails, for example, to effectively manage supplier relationship, suppliers are often categorized according to their business behaviors (Zhang, Huang, Qian, Xu, & Jing, 2006). The supplier’s behavior data is high dimensional, which contains thousands of attributes to describe the supplier’s behaviors, including product items, ordered amounts, order frequencies, product quality and so forth. One more example is DNA microarray data. Clustering high-dimensional data requires special treatment (Swanson, 1990; Jain, Murty, & Flynn, 1999; Cai, He, & Han, 2005; Kontaki, Papadopoulos & Manolopoulos., 2007), although various methods for clustering are available (Jain & Dubes, 1988). One type of clustering methods for high dimensional data is referred to as subspace clustering, aiming at finding clusters from subspaces instead of the entire data space. In a subspace clustering, each cluster is a set of objects identified by a subset of dimensions and different clusters are represented in different subsets of dimensions. Soft subspace clustering considers that different dimensions make different contributions to the identification of objects in a cluster. It represents the importance of a dimension as a weight that can be treated as the degree of the dimension in contribution to the cluster. Soft subspace clustering can find the cluster memberships of objects and identify the subspace of each cluster in the same clustering process.

scholarly journals Graph Sparse Nonnegative Matrix Factorization Algorithm Based on the Inertial Projection Neural Network

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Xiangguang Dai ◽  
Chuandong Li ◽  
Biqun Xiang
Keyword(s):  
Neural Network ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Optimal Solution ◽  
Factorization Method ◽  
Real World Data ◽  
Factorization Problem ◽  
Sparse Nonnegative Matrix Factorization ◽  
And Performance

We present a novel method, called graph sparse nonnegative matrix factorization, for dimensionality reduction. The affinity graph and sparse constraint are further taken into consideration in nonnegative matrix factorization and it is shown that the proposed matrix factorization method can respect the intrinsic graph structure and provide the sparse representation. Different from some existing traditional methods, the inertial neural network was developed, which can be used to optimize our proposed matrix factorization problem. By adopting one parameter in the neural network, the global optimal solution can be searched. Finally, simulations on numerical examples and clustering in real-world data illustrate the effectiveness and performance of the proposed method.

scholarly journals Comparison of Fuzzy Clustering Methods and Their Applications to Geophysics Data

2009 ◽  
Vol 2009 ◽  
pp. 1-16 ◽  
Author(s):  
David J. Miller ◽  
Carl A. Nelson ◽  
Molly Boeka Cannon ◽  
Kenneth P. Cannon
Keyword(s):  
Fuzzy Clustering ◽  
Real World ◽  
Clustering Algorithm ◽  
Clustering Algorithms ◽  
Optimal Number ◽  
Optimum Number ◽  
Clustering Methods ◽  
Real World Data ◽  
Data Set ◽  
World Data

Fuzzy clustering algorithms are helpful when there exists a dataset with subgroupings of points having indistinct boundaries and overlap between the clusters. Traditional methods have been extensively studied and used on real-world data, but require users to have some knowledge of the outcome a priori in order to determine how many clusters to look for. Additionally, iterative algorithms choose the optimal number of clusters based on one of several performance measures. In this study, the authors compare the performance of three algorithms (fuzzy c-means, Gustafson-Kessel, and an iterative version of Gustafson-Kessel) when clustering a traditional data set as well as real-world geophysics data that were collected from an archaeological site in Wyoming. Areas of interest in the were identified using a crisp cutoff value as well as a fuzzyα-cut to determine which provided better elimination of noise and non-relevant points. Results indicate that theα-cut method eliminates more noise than the crisp cutoff values and that the iterative version of the fuzzy clustering algorithm is able to select an optimum number of subclusters within a point set (in both the traditional and real-world data), leading to proper indication of regions of interest for further expert analysis

scholarly journals A unified framework for the integration of multiple hierarchical clusterings or networks from multi-source data

2021 ◽  
Vol 22 (1) ◽  
Author(s):  
Audrey Hulot ◽  
Denis Laloë ◽  
Florence Jaffrézic
Keyword(s):  
Breast Cancer ◽  
Simple Procedure ◽  
Data Sets ◽  
Integration Step ◽  
Visual Interpretation ◽  
Data Types ◽  
Unified Framework ◽  
Real World Data ◽  
Multiple Factor Analysis ◽  
Data Set

Abstract Background Integrating data from different sources is a recurring question in computational biology. Much effort has been devoted to the integration of data sets of the same type, typically multiple numerical data tables. However, data types are generally heterogeneous: it is a common place to gather data in the form of trees, networks or factorial maps, as these representations all have an appealing visual interpretation that helps to study grouping patterns and interactions between entities. The question we aim to answer in this paper is that of the integration of such representations. Results To this end, we provide a simple procedure to compare data with various types, in particular trees or networks, that relies essentially on two steps: the first step projects the representations into a common coordinate system; the second step then uses a multi-table integration approach to compare the projected data. We rely on efficient and well-known methodologies for each step: the projection step is achieved by retrieving a distance matrix for each representation form and then applying multidimensional scaling to provide a new set of coordinates from all the pairwise distances. The integration step is then achieved by applying a multiple factor analysis to the multiple tables of the new coordinates. This procedure provides tools to integrate and compare data available, for instance, as tree or network structures. Our approach is complementary to kernel methods, traditionally used to answer the same question. Conclusion Our approach is evaluated on simulation and used to analyze two real-world data sets: first, we compare several clusterings for different cell-types obtained from a transcriptomics single-cell data set in mouse embryos; second, we use our procedure to aggregate a multi-table data set from the TCGA breast cancer database, in order to compare several protein networks inferred for different breast cancer subtypes.

Auto-sharing parameters for transfer learning based on multi-objective optimization

2021 ◽  
pp. 1-13
Author(s):  
Hailin Liu ◽  
Fangqing Gu ◽  
Zixian Lin
Keyword(s):  
Transfer Learning ◽  
Optimization Problem ◽  
Data Sets ◽  
Multi Objective Optimization ◽  
Particle Swarm Optimizer ◽  
Real World Data ◽  
Data Set ◽  
Target Task ◽  
Main Research ◽  
Multi Objective

Transfer learning methods exploit similarities between different datasets to improve the performance of the target task by transferring knowledge from source tasks to the target task. “What to transfer” is a main research issue in transfer learning. The existing transfer learning method generally needs to acquire the shared parameters by integrating human knowledge. However, in many real applications, an understanding of which parameters can be shared is unknown beforehand. Transfer learning model is essentially a special multi-objective optimization problem. Consequently, this paper proposes a novel auto-sharing parameter technique for transfer learning based on multi-objective optimization and solves the optimization problem by using a multi-swarm particle swarm optimizer. Each task objective is simultaneously optimized by a sub-swarm. The current best particle from the sub-swarm of the target task is used to guide the search of particles of the source tasks and vice versa. The target task and source task are jointly solved by sharing the information of the best particle, which works as an inductive bias. Experiments are carried out to evaluate the proposed algorithm on several synthetic data sets and two real-world data sets of a school data set and a landmine data set, which show that the proposed algorithm is effective.

Adaptive sampling of potential-field data: A direct approach to compressive inversion

Geophysics ◽  
2014 ◽  
Vol 79 (1) ◽  
pp. IM1-IM9 ◽  
Author(s):  
Nathan Leon Foks ◽  
Richard Krahenbuhl ◽  
Yaoguo Li
Keyword(s):  
Potential Field ◽  
Adaptive Sampling ◽  
Field Data ◽  
Computational Cost ◽  
Large Field ◽  
Magnetic Data ◽  
Data Sampling ◽  
Data Types ◽  
Data Set ◽  
Potential Field Data

Compressive inversion uses computational algorithms that decrease the time and storage needs of a traditional inverse problem. Most compression approaches focus on the model domain, and very few, other than traditional downsampling focus on the data domain for potential-field applications. To further the compression in the data domain, a direct and practical approach to the adaptive downsampling of potential-field data for large inversion problems has been developed. The approach is formulated to significantly reduce the quantity of data in relatively smooth or quiet regions of the data set, while preserving the signal anomalies that contain the relevant target information. Two major benefits arise from this form of compressive inversion. First, because the approach compresses the problem in the data domain, it can be applied immediately without the addition of, or modification to, existing inversion software. Second, as most industry software use some form of model or sensitivity compression, the addition of this adaptive data sampling creates a complete compressive inversion methodology whereby the reduction of computational cost is achieved simultaneously in the model and data domains. We applied the method to a synthetic magnetic data set and two large field magnetic data sets; however, the method is also applicable to other data types. Our results showed that the relevant model information is maintained after inversion despite using 1%–5% of the data.

SEMIPARAMETRIC CLUSTERING METHOD FOR MICROARRAY DATA ANALYSIS

2008 ◽  
Vol 06 (02) ◽  
pp. 261-282 ◽  
Author(s):  
AO YUAN ◽  
WENQING HE
Keyword(s):  
Data Analysis ◽  
Microarray Data ◽  
Mixture Distribution ◽  
Information Criterion ◽  
Optimal Number ◽  
Microarray Data Analysis ◽  
Parametric Methods ◽  
Clustering Methods ◽  
Microarray Gene Expression ◽  
Data Set

Clustering is a major tool for microarray gene expression data analysis. The existing clustering methods fall mainly into two categories: parametric and nonparametric. The parametric methods generally assume a mixture of parametric subdistributions. When the mixture distribution approximately fits the true data generating mechanism, the parametric methods perform well, but not so when there is nonnegligible deviation between them. On the other hand, the nonparametric methods, which usually do not make distributional assumptions, are robust but pay the price for efficiency loss. In an attempt to utilize the known mixture form to increase efficiency, and to free assumptions about the unknown subdistributions to enhance robustness, we propose a semiparametric method for clustering. The proposed approach possesses the form of parametric mixture, with no assumptions to the subdistributions. The subdistributions are estimated nonparametrically, with constraints just being imposed on the modes. An expectation-maximization (EM) algorithm along with a classification step is invoked to cluster the data, and a modified Bayesian information criterion (BIC) is employed to guide the determination of the optimal number of clusters. Simulation studies are conducted to assess the performance and the robustness of the proposed method. The results show that the proposed method yields reasonable partition of the data. As an illustration, the proposed method is applied to a real microarray data set to cluster genes.

scholarly journals A simple clustering technique to extract subsets of data for function approximation

2015 ◽  
Vol 17 (5) ◽  
pp. 719-732
Author(s):  
Dulakshi Santhusitha Kumari Karunasingha ◽  
Shie-Yui Liong
Keyword(s):  
Function Approximation ◽  
Prediction Models ◽  
Data Extraction ◽  
Single Parameter ◽  
Subtractive Clustering ◽  
Data Sets ◽  
Clustering Methods ◽  
Clustering Method ◽  
Data Set ◽  
Functional Relationships

A simple clustering method is proposed for extracting representative subsets from lengthy data sets. The main purpose of the extracted subset of data is to use it to build prediction models (of the form of approximating functional relationships) instead of using the entire large data set. Such smaller subsets of data are often required in exploratory analysis stages of studies that involve resource consuming investigations. A few recent studies have used a subtractive clustering method (SCM) for such data extraction, in the absence of clustering methods for function approximation. SCM, however, requires several parameters to be specified. This study proposes a clustering method, which requires only a single parameter to be specified, yet it is shown to be as effective as the SCM. A method to find suitable values for the parameter is also proposed. Due to having only a single parameter, using the proposed clustering method is shown to be orders of magnitudes more efficient than using SCM. The effectiveness of the proposed method is demonstrated on phase space prediction of three univariate time series and prediction of two multivariate data sets. Some drawbacks of SCM when applied for data extraction are identified, and the proposed method is shown to be a solution for them.

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