## 2 Related Work  
In this section, the existing work of stability computation is summarized.  
The concept lattice theory is hampered by the overwhelming size of the extracted knowledge induced by formal concepts [19]. In addition, the noise contained in the dataset may generate a large number of similar but completely distinct concepts, which seriously affects knowledge quality. Stability measure is more prominent than other interestingness measures for assessing the concept quality and improving the readability of concept lattices. Computing the stability comes down to explore all the power set of the extent of the considered concept and check whether it is a generator [18].  
To overcome such an NP-complete problem computation task, the dedicated literature could be roughly divided into two categories: computing approximate or exact values of stability. In the category of calculating approximate values, [PERSON] et al. [21] used sufficient conditions to select formal concepts with low stability values. Later, [PERSON] and [PERSON] [15] proposed an approximate calculation algorithm using random Monte Carlo Sampling. Subsequently, [PERSON] et al. [22] provided the lower and upper bounds of stability values which rely on the existence of the concept lattice. Recently, [PERSON] et al. [17] explored and proposed a new set of approximation methods for estimating stability, which are variance reduction techniques that leverage stratification, low-discrepancy and hybridization approaches. In the category of calculating accurate values, [PERSON] et al. [16] presented that computing the concept stability requires browsing all its subconcepts. Later, [PERSON] [20] studied the inclusion-exclusion principle of the minimal generator to calculate concept stability. It is worth noting that [PERSON] et al. [18] pioneered an algorithm called DFSP that handles straightforwardly concepts stability computation by showing that most of this search space could be smartly ignored thanks to the saturation of generators.  
Compared with the approximate algorithm, the accurate calculation algorithm can obtain the accurate value of the stability. [PERSON]'s algorithm considers the existing knowledge in the concept lattice, but because it needs to traverse all sub-concepts, its scalability is not well. In contrast, although [PERSON]'s algorithm does not need to traverse the concept lattice, the process of directly calculating the minimal generator is very complicated, which is also reflected in the experiment section. Although the DFSP algorithm optimizes the process of calculating the minimal generator, it can only calculate one concept at a time, and does not make full use of the potential knowledge in the concept lattice to speed up the algorithm. On the contrary to the previous algorithm, we propose an algorithm called MNG-SC that fully considers the existing knowledge in the concept lattice to reduce computational complexity. The novelty of the MNG-SC algorithm is the proved equivalence between the maximal non-generator and lower neighbor concept, which makes it possible that only exploring its lower neighbor concept is sufficient to compute its stability. It means that our algorithm does not have to traverse all concepts such as [PERSON]'s algorithm, thus ensuring that our algorithm is more scalable. Because the existing knowledge in the concept lattice is fully considered, there is no need to separately design the method of calculating the minimal generator or maximal non-generator (such as Zhi and DFSP), which reduces computational complexity and speeds up the algorithm.