Model order selection for approximate Boolean matrix factorization problem

Trnečka, Martin; Trnečková, Markéta

doi:10.1016/j.knosys.2021.107184

Cited by 3 publications

(2 citation statements)

References 8 publications

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“…In logistic regression function, one of the methods to judge the binary prediction accuracy of the model is to use confusion matrix. The confusion matrix includes four parameters [4,5]: TP (True Positive) represents the number of benign people in this study who were correctly predicted by the model compared to the real data FP (False Positive) represents the number of benign people in this study who were incorrectly predicted by the model compared to the real data TN (True Negative) represents the number of malignant people in this study who were correctly predicted by the model compared to the real data FN (False Negative) represents the number of benign people in this study who were incorrectly predicted by the model compared to the real data precision = TP TP + FP recall = TP TP+FN (5) Because the value predicted by the model is the possibility of malignancy, this paper classifies the value of prediction result greater than 0.5 as 1 (malignant), and the value of prediction result less than 0.5 as 0 (benign). After the prediction by AIC, the confusion matrix was obtained as follows: According to the above results, AIC has higher accuracy than BIC, so AIC model is better than BIC model in this data set.…”

Section: Methodsmentioning

confidence: 99%

Using Stepwise Method to Find the Most Influencing Feature to the Cell Nuclei of a Breast Mass

Huang¹

2022

HSET

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In real life, the influencing factors that lead to an outcome are varied and complex. However, how to organize the complex variable relationship into a concise and effective model for prediction is critical. Therefore, the Stepwise method was used in this study to organize the relationship between malignant and benign detection of breast cancer tumors and changes in cell characteristics into a model. In this paper, the diagnosis data of breast cancer of patients in the hospital were quoted. The benign and malignant characteristics of breast cancer were taken as independent variables, and the characteristic changes of cells were taken as dependent variables to conduct data analysis with R language, so as to obtain the most effective model. The results show that the prediction accuracy of the model obtained by AIC method is the highest. AIC selected seven dependent variables and reached 79.8 percent. The model prediction accuracy of BIC was 77.2 percent. Compared with AIC method, BIC only selected four dependent variables and obtained a more concise model. However, BIC is too concise and loses the accuracy of model prediction in some aspects.

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Section: Methodsmentioning

confidence: 99%

Using Stepwise Method to Find the Most Influencing Feature to the Cell Nuclei of a Breast Mass

Huang¹

2022

HSET

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“…For higher rank matrices and decompositions, the average of the scores of all rank one factors is taken, after the decompositions are permuted to maximize the scores. For reference, we also report results of other Boolean model selection strategies: (1) Minimum Description Length (MDL) [32] and (2) Covarge Quality (CQ) [37]. While BMFk focuses on the solution stability, MDL minimizes the description of the data using the BMF model and CQ measures the change of the angle in the coverage (or reconstruction) curve.…”

Section: Experimental Evaluationmentioning

confidence: 99%

Factorization of Binary Matrices: Rank Relations, Uniqueness and Model Selection of Boolean Decomposition

DeSantis

Skau

Truong

et al. 2022

ACM Trans. Knowl. Discov. Data

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The application of binary matrices are numerous. Representing a matrix as a mixture of a small collection of latent vectors via low-rank decomposition is often seen as an advantageous method to interpret and analyze data. In this work, we examine the factorizations of binary matrices using standard arithmetic (real and nonnegative) and logical operations (Boolean and \(\mathbb {Z}_2 \) ). We examine the relationships between the different ranks, and discuss when factorization is unique. In particular, we characterize when a Boolean factorization X = W ∧ H has a unique W , a unique H (for a fixed W ), and when both W and H are unique, given a rank constraint. We introduce a method for robust Boolean model selection, called BMF k , and show on numerical examples that BMF k not only accurately determines the correct number of Boolean latent features but reconstruct the pre-determined factors accurately.

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Boolean matrix factorization for symmetric binary variables

Konecny,

Trnecka

2023

Knowledge-Based Systems

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Model order selection for approximate Boolean matrix factorization problem

Cited by 3 publications

References 8 publications

Using Stepwise Method to Find the Most Influencing Feature to the Cell Nuclei of a Breast Mass

Using Stepwise Method to Find the Most Influencing Feature to the Cell Nuclei of a Breast Mass

Factorization of Binary Matrices: Rank Relations, Uniqueness and Model Selection of Boolean Decomposition

Boolean matrix factorization for symmetric binary variables

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