For solving the incomplete data problem of missing feature values in prototype data, various strategies were proposed. In this paper, two improved approaches are proposed to estimate the missing values of incomplete data. The two approaches are based on combining the adaptive volume GustafsonKessel algorithm (GKA) and the nearest vector features under the distance norm evaluated by complete data. The GKA with adaptive volume is applied for clustering and classifying the results. At last, compared the result with other strategies, and the computer simulations show that the improved strategies provide superior effects.
A fuzzy classifier using multiple ellipsoids to approximate decision regions for classification is designed in this paper. To learn the sizes and orientations of ellipsoids, an algorithm called evolutionary ellipsoidal classification algorithm (EECA) that integrates the genetic algorithm (GA) with the Gustafson-Kessel algorithm (GKA) is proposed. Within EECA the GA is employed to learn the size of every ellipsoid. With the size of every ellipsoid encoded and intelligently estimated in the GA chromosome, GKA is utilized to learn the corresponding ellipsoid. GKA is able to adapt the distance norm to the underlying distribution of the prototype data points for an assigned ellipsoid size. A process called directed initialization is proposed to improve EECA's learning efficiency. Because EECA learns the data point distribution in every cluster by adjusting an ellipsoid with suitable size and orientation, the information contained in the ellipsoid is further utilized to improve the cluster validity. A cluster validity measure based on the ratio of summation for each intra-cluster scatter with respect to the inter-cluster separation is defined in this paper. The proposed cluster validity measure takes advantage of EECA's learning capability and serves as an effective index for determining the adequate number of ellipsoids required for classification.
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