scholarly journals OPTIMAL CONSTRUCTION OF THE PATTERN MATRIX FOR PROBABILISTIC NEURAL NETWORKS IN TECHNICAL DIAGNOSTICS BASED ON EXPERT ESTIMATIONS

2021 ◽  
Author(s):  
Vadim Romanuke
Keyword(s):  
Neural Network ◽  
Error Rate ◽  
Probabilistic Neural Network ◽  
Optimal Number ◽  
Technical Diagnostics ◽  
Probabilistic Neural Networks ◽  
Number Of Clusters ◽  
Operation Speed ◽  
Pattern Matrix ◽  
Optimal Number Of Clusters

In the field of technical diagnostics, many tasks are solved by using automated classification. For this, such classifiers like probabilistic neural networks fit best owing to their simplicity. To obtain a probabilistic neural network pattern matrix for technical diagnostics, expert estimations or measurements are commonly involved. The pattern matrix can be deduced straightforwardly by just averaging over those estimations. However, averages are not always the best way to process expert estimations. The goal is to suggest a method of optimally deducing the pattern matrix for technical diagnostics based on expert estimations. The main criterion of the optimality is maximization of the performance, in which the subcriterion of maximization of the operation speed is included. First of all, the maximal width of the pattern matrix is determined. The width does not exceed the number of experts. Then, for every state of an object, the expert estimations are clustered. The clustering can be done by using the k-means method or similar. The centroids of these clusters successively form the pattern matrix. The optimal number of clusters determines the probabilistic neural network optimality by its performance maximization. In general, most results of the error rate percentage of probabilistic neural networks appear to be near-exponentially decreasing as the number of clustered expert estimations is increased. Therefore, if the optimal number of clusters defines a too “wide” pattern matrix whose operation speed is intolerably slow, the performance maximization implies a tradeoff between the error rate percentage minimum and maximally tolerable slowness in the probabilistic neural network operation speed. The optimal number of clusters is found at an asymptotically minimal error rate percentage, or at an acceptable error rate percentage which corresponds to maximally tolerable slowness in operation speed. The optimality is practically referred to the simultaneous acceptability of error rate and operation speed.

Determining the Optimal Number of Clusters by an Extended RPCL Algorithm

1999 ◽  
Vol 3 (6) ◽  
pp. 467-473 ◽  
Author(s):  
Xin Li ◽  
◽  
Man Wai Mak ◽  
Chi Kwong Li
Keyword(s):  
Gaussian Distribution ◽  
Error Rate ◽  
Basis Function ◽  
Recognition Accuracy ◽  
Speaker Verification ◽  
Optimal Number ◽  
Covariance Matrices ◽  
Training Data ◽  
Number Of Clusters ◽  
Optimal Number Of Clusters

Determining an appropriate number of clusters is a difficult yet important problem that the rival penalized competitive learning (RPCL) algorithm was designed to solve, but its performance is not satifactory with overlapping clusters or cases where input vectors contain dependent components. We address this problem by incorporating full covariance matrices into the original RPCL algorithm. The resulting extended RPCL algorithm progressively eliminates units whose clusters contain only a small amount of training data. The algorithm is used to determine the number of clusters in a Gaussian distribution. It is also used to optimize the architecture of elliptical basis function networks for speaker verification and vowel classification. We found that covariance matrices obtained by the extended RPCL algorithm have a better representation of clusters than those obtained by the original RPCL algorithm, resulting in a lower verification error rate in speaker verification and a higher recognition accuracy in vowel classification.

Clustering Count-based RNA Methylation Data Using a Nonparametric Generative Model

2018 ◽  
Vol 14 (1) ◽  
pp. 11-23 ◽  
Author(s):  
Lin Zhang ◽  
Yanling He ◽  
Huaizhi Wang ◽  
Hui Liu ◽  
Yufei Huang ◽  
...  
Keyword(s):  
Clustering Analysis ◽  
Methylation Level ◽  
Optimal Number ◽  
Generative Model ◽  
Methylation Data ◽  
Sequencing Data ◽  
Number Of Clusters ◽  
Rna Methylation ◽  
Clustering Effect ◽  
Optimal Number Of Clusters

Background: RNA methylome has been discovered as an important layer of gene regulation and can be profiled directly with count-based measurements from high-throughput sequencing data. Although the detailed regulatory circuit of the epitranscriptome remains uncharted, clustering effect in methylation status among different RNA methylation sites can be identified from transcriptome-wide RNA methylation profiles and may reflect the epitranscriptomic regulation. Count-based RNA methylation sequencing data has unique features, such as low reads coverage, which calls for novel clustering approaches. <P><P> Objective: Besides the low reads coverage, it is also necessary to keep the integer property to approach clustering analysis of count-based RNA methylation sequencing data. <P><P> Method: We proposed a nonparametric generative model together with its Gibbs sampling solution for clustering analysis. The proposed approach implements a beta-binomial mixture model to capture the clustering effect in methylation level with the original count-based measurements rather than an estimated continuous methylation level. Besides, it adopts a nonparametric Dirichlet process to automatically determine an optimal number of clusters so as to avoid the common model selection problem in clustering analysis. <P><P> Results: When tested on the simulated system, the method demonstrated improved clustering performance over hierarchical clustering, K-means, MClust, NMF and EMclust. It also revealed on real dataset two novel RNA N6-methyladenosine (m6A) co-methylation patterns that may be induced directly by METTL14 and WTAP, which are two known regulatory components of the RNA m6A methyltransferase complex. <P><P> Conclusion: Our proposed DPBBM method not only properly handles the count-based measurements of RNA methylation data from sites of very low reads coverage, but also learns an optimal number of clusters adaptively from the data analyzed. <P><P> Availability: The source code and documents of DPBBM R package are freely available through the Comprehensive R Archive Network (CRAN): https://cran.r-project.org/web/packages/DPBBM/.

scholarly journals Computing Discrete Adriatic Indices of Probabilistic Neural Network

2020 ◽  
Vol 13 (5) ◽  
pp. 1149-1161
Author(s):  
T Deepika ◽  
V. Lokesha
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Topological Index ◽  
Probabilistic Neural Network ◽  
Topological Indices ◽  
Probabilistic Neural Networks ◽  
Mathematical Chemistry ◽  
International Academy

A Topological index is a numeric quantity which characterizes the whole structure of a graph. Adriatic indices are also part of topological indices, mainly it is classified into two namely extended variables and discrete adriatic indices, especially, discrete adriatic indices are analyzed on the testing sets provided by the International Academy of Mathematical Chemistry (IAMC) and it has been shown that they have good presaging substances in many compacts. This contrived attention to compute some discrete adriatic indices of probabilistic neural networks.

Investigating cluster validation metrics for optimal number of clusters determination

2021 ◽  
pp. 1-16
Author(s):  
Aikaterini Karanikola ◽  
Charalampos M. Liapis ◽  
Sotiris Kotsiantis
Keyword(s):  
Real World ◽  
Optimal Number ◽  
Cluster Validation ◽  
Clustering Methods ◽  
Number Of Clusters ◽  
Validity Indices ◽  
Selection Of ◽  
Specific Distance ◽  
Optimal Number Of Clusters

In short, clustering is the process of partitioning a given set of objects into groups containing highly related instances. This relation is determined by a specific distance metric with which the intra-cluster similarity is estimated. Finding an optimal number of such partitions is usually the key step in the entire process, yet a rather difficult one. Selecting an unsuitable number of clusters might lead to incorrect conclusions and, consequently, to wrong decisions: the term “optimal” is quite ambiguous. Furthermore, various inherent characteristics of the datasets, such as clusters that overlap or clusters containing subclusters, will most often increase the level of difficulty of the task. Thus, the methods used to detect similarities and the parameter selection of the partition algorithm have a major impact on the quality of the groups and the identification of their optimal number. Given that each dataset constitutes a rather distinct case, validity indices are indicators introduced to address the problem of selecting such an optimal number of clusters. In this work, an extensive set of well-known validity indices, based on the approach of the so-called relative criteria, are examined comparatively. A total of 26 cluster validation measures were investigated in two distinct case studies: one in real-world and one in artificially generated data. To ensure a certain degree of difficulty, both real-world and generated data were selected to exhibit variations and inhomogeneity. Each of the indices is being deployed under the schemes of 9 different clustering methods, which incorporate 5 different distance metrics. All results are presented in various explanatory forms.

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