16662300
A comparative investigation on subspace dimension determination
It is well-known that constrained Hebbian self-organization on multiple linear neural units leads to the same k-dimensional subspace spanned by the first k principal components. Not only the batch PCA algorithm has been widely applied in various fields since 1930s, but also a variety of adaptive algorithms have been proposed in the past two decades. However, most studies assume a known dimension k or determine it heuristically, though there exist a number of model selection criteria in the literature of statistics. Recently, criteria have also been obtained under the framework of Bayesian Ying-Yang (BYY) harmony learning. This paper further investigates the BYY criteria in comparison with existing typical criteria, including Akaike's information criterion (AIC), the consistent Akaike's information criterion (CAIC), the Bayesian inference criterion (BIC), and the cross-validation (CV) criterion. This comparative study is made via experiments not only on simulated data sets of different sample sizes, noise variances, data space dimensions, and subspace dimensions, but also on two real data sets from air pollution problem and sport track records, respectively. Experiments have shown that BIC outperforms AIC, CAIC, and CV while the BYY criteria are either comparable with or better than BIC. Therefore, BYY harmony learning is a more preferred tool for subspace dimension determination by further considering that the appropriate subspace dimension k can be automatically determined during implementing BYY harmony learning for the principal subspace while the selection of subspace dimension k by BIC, AIC, CAIC, and CV has to be made at the second stage based on a set of candidate subspaces with different dimensions which have to be obtained at the first stage of learning.
26341684
Automatic Cluster Number Determination via BYY Harmony Learning
Selection of the number of clusters is a crucial problem in clustering. Conventionally, it was effected via cost function based criteria such as AIC and MDL. In this paper we empirically investigate automatic selection of the number of clusters via BYY harmony empirical learning. Results of experiments show that the true number of clusters can be automatically obtained during BYY harmony empirical learning. It is superior to conventional methods in that it needs much less computational cost.
38024133
A Comparative Study on Selection of Cluster Number and Local Subspace Dimension in the Mixture PCA Models
How to determine the number of clusters and the dimensions of local principal subspaces is an important and challenging problem in various applications. Based on a probabilistic model of local PCA, this problem can be solved by one of existing statistical model selection criteria in a two-phase procedure. However, such a two-phase procedure is too time-consuming especially when there is no prior knowledge. The BYY harmony learning has provided a promising mechanism to make automatic model selection in parallel with parameter learning. This paper investigates the BYY harmony learning with automatic model selection on a mixture PCA model in comparison with three typical model selection criteria: AIC, CAIC, and MDL. This comparative study is made by experiments for different model selection tasks on simulated data sets under different conditions. Experiments have shown that automatic model selection by the BYY harmony learning are not only as good as or even better than conventional methods in terms of performances, but also considerably supervisory in terms of much less computational cost.
30531140
A Comparative Study of Several Cluster Number Selection Criteria
The selection of the number of clusters is an important and challenging issue in cluster analysis. In this paper we perform an experimental comparison of several criteria for determining the number of clusters based on Gaussian mixture model. The criteria that we consider include Akaike’s information criterion (AIC), the consistent Akaike’s information criterion (CAIC), the minimum description length (MDL) criterion which formally coincides with the Bayesian inference criterion (BIC), and two model selection methods driven from Bayesian Ying-Yang (BYY) harmony learning: harmony empirical learning criterion (BYY-HEC) and harmony data smoothing criterion (BYY-HDS). We investigate these methods on synthetic data sets of different sample size and the iris data set. The results of experiments illustrate that BYY-HDS has the best overall success rate and obviously outperforms other methods for small sample size. CAIC and MDL tend to underestimate the number of clusters, while AIC and BYY-HEC tend to overestimate the number of clusters especially in the case of small sample size.
30664092
Mining Candidate Viruses as Potential Bio-terrorism Weapons from Biomedical Literature
In this paper we present a semantic-based data mining approach to identify candidate viruses as potential bio-terrorism weapons from biomedical literature. We first identify all the possible properties of viruses as search key words based on Geissler’s 13 criteria; the identified properties are then defined using MeSH terms. Then, we assign each property an importance weight based on domain experts’ judgment. After generating all the possible valid combinations of the properties, we search the biomedical literature, retrieving all the relevant documents. Next our method extracts virus names from the downloaded documents for each search keyword and identifies the novel connection of the virus according to these 4 properties. If a virus is found in the different document sets obtained by several search keywords, the virus should be considered as suspicious and treated as candidate viruses for bio-terrorism. Our findings are intended as a guide to the virus literature to support further studies that might then lead to appropriate defense and public health measures.
40136335
On Rearrangeability of Multirate Clos Networks
Chung and Ross [SIAM J. Comput., 20 (1991), pp. 726--736] conjectured that the multirate three-stage Clos network C(n,2n-1,r) is rearrangeable in the general discrete bandwidth case; i.e., each connection has a weight chosen from a given finite set {p1, p2,. . .,pk} where $1 \geq p_1 > p_2 > \cdots > p_k > 0$ and pi is an integer multiple of pi, denoted by $p_k \mid p_i$, for $1 \leq i \leq k-1$. In this paper, we prove that multirate three-stage Clos network C(n,2n-1,r) is rearrangeable when each connection has a weight chosen from a given finite set {p1, p2,. . .,pk} where $1 \geq p_1 > p_2 > \cdots > p_{h} > 1/2 \geq p_{h+1} > \cdots > p_k > 0$ and ph+2 | ph+1,ph+3 |ph+2,. . . ,pk | ph+1. We also prove that C(n,2n-1,r) is two-rate rearrangeable and $C(n, \lceil \frac{7n}{3} \rceil, r)$ is three-rate rearrangeable.
2425436
Cluster Ensemble and Its Applications in Gene Expression Analysis
Huge amount of gene expression data have been generated as a result of the human genomic project. Clustering has been used extensively in mining these gene expression data to find important genetic and biological information. Obtaining high quality clustering results is very challenging because of the inconsistency of the results of different clustering algorithms and noise in the gene expression data. Many clustering algorithms are available and different clustering algorithms may generate different clustering results due to their bias and assumptions. It is a challenging and daunting task for the genomic researchers to choose the best clustering algorithm and generate the best clustering results for their data sets. In this paper, we present a cluster ensemble framework for gene expression analysis to generate high quality and robust clustering results. In our framework, the clustering results of individual clustering algorithm are converted into a distance matrix, these distance matrices are combined and a weighted graph is constructed according to the combined matrix. Then a graph partitioning approach is used to cluster the graph to generate the final clusters. The experiment results indicate that cluster ensemble approach yields better clustering results than the single best clustering algorithm on both synthetic data set and yeast gene expression data set.
6260724
Finding an optimal path without growing the tree
For problems on computing an optimal path as well as its length in a certain setting, the "standard" approach for finding an actual optimal path is by building (or "growing") a single-source optimal path tree. In this paper, we study a class of optimal path problems with the following phenomenon: The space complexity of the algorithms for reporting the lengths of single-source optimal paths for these problems is asymptotically smaller than the space complexity of the "standard" tree-growing algorithms for finding actual optimal paths. We present a general and efficient algorithmic paradigm for finding an actual optimal path for such problems without having to grow a single-source optimal path tree. Our paradigm is based on the "marriage-before-conquer" strategy, the prune-and-search technique, and a new data structure called clipped trees. The paradigm enables us to compute an actual path for a number of optimal path problems and dynamic programming problems in computational geometry, graph theory, and combinatorial optimization. Our algorithmic solutions improve the space bounds (in certain cases, the time bounds as well) of the previously best known algorithms, and settle some open problems. Our techniques are likely to be applicable to other problems.
110727
Classification Comparison of Prediction of Solvent Accessibility From Protein Sequences
The prediction of residue solvent accessibility from protein sequences has been studied by various methods. The direct comparison of these methods is impossible due to the variety of datasets used and the difference in structure definition. In this paper we choose 5 classification approaches (decision tree (DT), Support Vector Machine (SVM), Bayesian Statistics (BS), Neural Network (NN) and Multiple Linear Regression (MLR)) for predicting solvent accessibility based on the same dataset and using the same structure definition so that we can directly compare different methods. We evaluate these methods in a cross-validation test on 2148 unique proteins using single sequences and multiple sequences approaches with a cutoff of 20% for two-state definition of solvent accessibility. According to the experiment results, SVM and NN are both the best predictors with accuracy 79%, correlation coefficient 0.59, 2~4% superior to other three methods on multiple sequences prediction. A further test result on a blind test set from Critical Assessment of Techniques for Protein Structure Prediction experiment (CASP5) is consistent with this result. On single sequence prediction, DT, BS and MLR perform about the same at 71~72% with correlation coefficient 0.43. The improvement over the baseline model that use only the identity of target residue is small. Local sequence seems embed very little information on accessibility. Separate training according to protein size improves the prediction when there are sufficiently large dataset available. The consensus prediction combining the 5 approaches is not significantly better than the best single method.