Protein–protein interactions (PPIs) are the basis for understanding most cellular events in biological systems. Several experimental methods, e.g., biochemical, molecular, and genetic methods, have been used to identify protein–protein associations. However, some of them, such as mass spectrometry, are time-consuming and expensive. Machine learning (ML) techniques have been widely used to characterize PPIs, increasing the number of proteins analyzed simultaneously and optimizing time and resources for identifying and predicting protein–protein functional linkages. Previous ML approaches have focused on well-known networks or specific targets but not on identifying relevant proteins with partial or null knowledge of the interaction networks. The proposed approach aims to generate a relevant protein sequence based on bidirectional Long-Short Term Memory (LSTM) with partial knowledge of interactions. The general framework comprises conducting a scale-free and fractal complex network analysis. The outcome of these analyses is then used to fine-tune the fractal method for the vital protein extraction of PPI networks. The results show that several PPI networks are self-similar or fractal, but that both features cannot coexist. The generated protein sequences (by the bidirectional LSTM) also contain an average of 39.5% of proteins in the original sequence. The average length of the generated sequences was 17% of the original one. Finally, 95% of the generated sequences were true.

Decision trees are decision support data mining tools that create, as the name suggests, a tree-like model. The classical C4.5 decision tree, based on the Shannon entropy, is a simple algorithm to calculate the gain ratio and then split the attributes based on this entropy measure. Tsallis and Renyi entropies (instead of Shannon) can be employed to generate a decision tree with better results. In practice, the entropic index parameter of these entropies is tuned to outperform the classical decision trees. However, this process is carried out by testing a range of values for a given database, which is time-consuming and unfeasible for massive data. This paper introduces a decision tree based on a two-parameter fractional Tsallis entropy. We propose a constructionist approach to the representation of databases as complex networks that enable us an efficient computation of the parameters of this entropy using the box-covering algorithm and renormalization of the complex network. The experimental results support the conclusion that the two-parameter fractional Tsallis entropy is a more sensitive measure than parametric Renyi, Tsallis, and Gini index precedents for a decision tree classifier.

This article introduces a new fractional approach to the concept of information dimensions in complex networks based on the ($q,q^{\prime }$)-entropy proposed in the literature. The q parameter measures how far the number of sub-systems (for a given size $\epsilon$) is from the mean number of overall sizes, whereas $q^{\prime }$ (the interaction index) measures when the interactions between sub-systems are greater ($q^{\prime }>1$), lesser ($q^{\prime }<1$), or equal to the interactions into these sub-systems. Computation of the proposed information dimension is carried out on several real-world and synthetic complex networks. The results for the proposed information dimension are compared with those from the classic information dimension based on Shannon entropy. The obtained results support the conjecture that the fractional ($q,q^{\prime }$)-information dimension captures the complexity of the topology of the network better than the information dimension.

A novel definition of volume dimension for a mass function based on a sigmoid asymptote is proposed; in particular, we extend the volume dimension of a mass function to define the volume dimensions for nodes and edges in complex networks. Furthermore, the relationship between the proposed volume dimension and the non-specificity term of the Deng entropy is shown, and the traditional volume dimension and volume dimension based on the node degree in complex networks are revisited. Our experiments show that in both real and synthetic complex networks, the volume dimension tends to follow a sigmoidal asymptote rather than the previously utilized power law asymptote.

This article introduces a new fractional approach to the concept of information dimension of complex networks, based on a (q,q′)-entropy proposed in the literature. The q parameter measures how far is the number of subsystems (for a given size ε) from the mean number of overall sizes. The q′ (interaction index) measures when the interactions between subsystems are greater (q′>1), lesser (q′<1) or equal to the interactions into these subsystems. The computations of the proposed information dimension are carried out on several real-world and synthetic complex networks. The results from the proposed information dimension are compared with those from the information dimension based on the Shannon entropy.