A Survey on Soft Subspace Clustering <s> Evolutionary Leaning <s> One of the main problems in cluster analysis is the weighting of attributes so as to discover structures that may be present. By using weighted dissimilarity measures for objects, a new approach is developed, which allows the use of the k-means-type paradigm to efficiently cluster large data sets. The optimization algorithm is presented and the effectiveness of the algorithm is demonstrated with both synthetic and real data sets. <s> BIB001 </s> A Survey on Soft Subspace Clustering <s> Evolutionary Leaning <s> Feature weighting is an aspect of increasing importance in clustering because data are becoming more and more complex nowadays. In this paper, we propose two new feature weighting methods based on coevolutive algorithms. The first one is inspired by the Lamarck theory (inheritance of acquired characteristics) and uses the distance-based cost function defined in the LKM algorithm as fitness function. The second method uses a fitness function based on a new partitioning quality measure. It does not need a distance-based measure. We compare classical hill-climbing optimization with these new genetic algorithms on three data sets from UCI. Results show that the proposed methods are better than the hill-climbing based algorithms. We also present a process of hyperspectral remotely sensed image classification. The experiments, corroborated by geographers, highlight the benefits of using coevolutionary feature weighting methods to improve knowledge discovery process. <s> BIB002 </s> A Survey on Soft Subspace Clustering <s> Evolutionary Leaning <s> In this paper, a multiobjective evolutionary algorithm based soft subspace clustering, MOSSC, is proposed to simultaneously optimize the weighting within-cluster compactness and weighting between-cluster separation incorporated within two different clustering validity criteria. The main advantage of MOSSC lies in the fact that it effectively integrates the merits of soft subspace clustering and the good properties of the multiobjective optimization-based approach for fuzzy clustering. This makes it possible to avoid trapping in local minima and thus obtain more stable clustering results. Substantial experimental results on both synthetic and real data sets demonstrate that MOSSC is generally effective in subspace clustering and can achieve superior performance over existing state-of-the-art soft subspace clustering algorithms. <s> BIB003
Most of the existing SSC algorithms make use of iterative learning strategy for optimizing the objective functions. However, these algorithms suffer from poor initialization sensitivity and local optimization of solutions. In order to overcome the deficiencies, evolutionary learning technique has been introduced to optimize the objective functions of SSC. Several representative XSSC algorithms developed based on evolutionary learning are reviewed below. (1) Coevolutionary SSC Gangrski et al. proposed two SSC algorithms based on coevolution learning BIB002 . The first algorithm was inspired by the Lamarck theory and used the distance-based cost function defined in the AWC algorithm BIB001 as the fitness function. The second algorithm employed a fitness function based on a new partitioning quality measure. The experimental results in BIB002 highlighted the benefits of using coevolutionary feature weighting methods to improve the knowledge discovery process.  By transforming the original constrained variable weighting problem into a problem with bound constraints, i.e., using a normalized representation of variable weights, the particle swarm BIB003 . Here, two objective functions are adopted for SSC, i.e., 