A fuzzy clustering algorithm for the mode-seeking framework

Abstract

In this paper, we propose a new fuzzy clustering algorithm based on the modeseeking framework. Given a dataset in R d , we define regions of high density that we call cluster cores. We then consider a random walk on a neighborhood graph built on top of our data points which is designed to be attracted by high density regions. The strength of this attraction is controlled by a temperature parameter β > 0. The membership of a point to a given cluster is then the probability for the random walk to hit the corresponding cluster core before any other. While many properties of random walks (such as hitting times, commute distances, etc. . . ) have been shown to enventually encode purely local information when the number of data points grows, we show that the regularization introduced by the use of cluster cores solves this issue. Empirically, we show how the choice of β influences the behavior of our algorithm: for small values of β the result is close to hard modeseeking whereas when β is close to 1 the result is similar to the output of a (fuzzy) spectral clustering. Finally, we demonstrate the scalability of our approach by providing the fuzzy clustering of a protein configuration dataset containing a million data points in 30 dimensions.

Fuzzy clustering and Whale-based neural network to food recognition and calorie estimation for daily dietary assessment

“…Step 1: Initialization Clustering [30][31][32] of the data matrix M f ij allows the segmentation of the image I f . The initial step of CSW-WLIFC algorithm is the initialization of the required number of clusters to perform the clustering.…”

“…The total number of the input layers in the NN is equal to the total feature size of the feature database (i.e., y). The size of the feature vector is expressed in the equation (30). The input layer of the NN is expressed by the equation (28).…”

“…The input layer is multiplied with the weight to form the hidden layer. The equation (30) expresses the weight value of each hidden layer. The equation (31) expresses the weight of the hidden layers in the NN.…”

Safety Warning Model of Coal Face Based on FCM Fuzzy Clustering and GA-BP Neural Network

“…However, when BP neural network is trained by gradient descent method, it may produce local minimum problem, and there is also the sensitivity problem of the initial weight of the network, that is, any slight change in the initial weight will affect the convergence speed and precision of the network, and even the network vibration [38][39][40]. A genetic algorithm (GA) has strong global search ability, which can quickly and effectively find the global optimal solution in the complex, multi-peak and non-differentiable large vector space, and has the characteristics of efficient, parallel and global search [41]. A genetic algorithm is used to overcome the above defects of BP neural network.…”

“…Fuzzy C-means (FCM) is an algorithm that uses membership degree to determine that each data point belongs to a certain degree of clustering [41]. It converges the target clustering function through multiple iterations.…”