Improved Fuzzy Cognitive Maps for Gene Regulatory Networks Inference Based on Time Series Data

Abstract

Recently with the advancement of high-throughput sequencing, gene regulatory network inference has turned into an interesting subject in bioinformatics and system biology. But there are many challenges in the field such as noisy data, uncertainty, time-series data with numerous gene numbers and low data, time complexity and so on. In recent years, many research works have been conducted to tackle these challenges, resulting in different methods in gene regulatory networks inference. A number of models have been used in modeling of the gene regulatory networks including Boolean networks, Bayesian networks, Markov model, relational networks, state space model, differential equations model, artificial neural networks and so on. In this paper, the fuzzy cognitive maps are used to model gene regulatory networks because of their dynamic nature and learning capabilities for handling non-linearity and inherent uncertainty. Fuzzy cognitive maps belong to the family of recurrent networks and are well-suited for gene regulatory networks. In this research study, the Kalman filtered compressed sensing is used to infer the fuzzy cognitive map for the gene regulatory networks. This approach, using the advantages of compressed sensing and Kalman filters, allows robustness to noise and learning of sparse gene regulatory networks from data with high gene number and low samples. In the proposed method, stream data and previous knowledge can be used in the inference process. Furthermore, compressed sensing finds likely edges and Kalman filter estimates their weights. The proposed approach uses a novel method to decrease the noise of data. The proposed method is compared to CSFCM, LASSOFCM, KFRegular, ABC, RCGA, ICLA, and CMI2NI. The results show that the proposed approach is superior to the other approaches in fuzzy cognitive maps learning. This behavior is related to the stability against noise and offers a proper balance between data error and network structure.

MICFuzzy: A maximal information content based fuzzy approach for reconstructing genetic networks

“…Therefore, in this research, we used F-score, Structural Accuracy, and MCC as performance evaluation measurements. In addition, SS_mean, a sensitivity specificity-based measure, was also used, since the results of most of the fuzzy concepts-based models for GRN inference are reported in terms of SS_mean [33][34][35]49].…”

“…The time complexity of CS-FCM is O(n 3 MI) as reported in [34], where n is the number of nodes (genes) in FCM, M is the number of iterations for data sequences, and I is the number of iterations required for CS-FCM for optimal results. Based on the design of LAS-SO-FCM, and KFCSFCM, each method requires approximately the same computational time as CS-FCM, as demonstrated in experiments [33][34][35]. Thus, the required time complexity of these considered FCM-based methods can be simplified as O(n 3 MI).…”

“…Due to their ability to deal with uncertain and imprecise information fuzzy concept-based models for GRN inference [31][32][33][34][35][36] have been extensively investigated in the last decade [36]. Fuzzy logic, a knowledge-based problem-solving approach, consists of three main stages: fuzzification, inference, and defuzzification.…”

“…In addition to classical fuzzy models, fuzzy logic-based tools have been introduced, such as fuzzy cognitive maps (FCM), a powerful intelligent tool for GRN inference. LASSO-FCM, a least absolute shrinkage and selection operator-based FCM [33], compressed sensing-based FCM (CF-FCM) [34], and Kalman filter and compressed sensing-based FCM (KFCSFCM) [35] are recently developed accurate methods. However, these methods have known limitations in model learning [36].…”