Density peaks clustering algorithm (DP) has difficulty in clustering large-scale data, because it requires the distance matrix to compute the density and $\delta$ -distance for each object, which has $O(n^2)$ time complexity. Granular ball (GB) is a coarse-grained representation of data. It is based on the fact that an object and its local neighbors have similar distribution and they have high possibility of belonging to the same class. It has been introduced into supervised learning by Xia et al. to improve the efficiency of supervised learning, such as support vector machine, $k$ -nearest neighbor classification, rough set, etc. Inspired by the idea of GB, we introduce it into unsupervised learning for the first time and propose a GB-based DP algorithm, called GB-DP. First, it generates GBs from the original data with an unsupervised partitioning method. Then, it defines the density of GBs, instead of the density of objects, according to the centers, radius, and distances between its members and centers, without setting any parameters. After that, it computes the distance between the centers of GBs as the distance between GBs and defines the $\delta$ -distance of GBs. Finally, it uses GBs’ density and $\delta$ -distance to plot the decision graph, employs DP algorithm to cluster them, and expands the clustering result to the original data. Since there is no need to calculate the distance between any two objects and the number of GBs is far less than the scale of a data, it greatly reduces the running time of DP algorithm. By comparing with $k$ -means, ball $k$ -means, DP, DPC-KNN-PCA, FastDPeak, and DLORE-DP, GB-DP can get similar or even better clustering results in much less running time without setting any parameters. The source code is available at https://github.com/DongdongCheng/GB-DP.

Due to simplicity, K-means has become a widely used clustering method. However, its clustering result is seriously affected by the initial centers and the allocation strategy makes it hard to identify manifold clusters. Many improved K-means are proposed to accelerate it and improve the quality of initialize cluster centers, but few researchers pay attention to the shortcoming of K-means in discovering arbitrary-shaped clusters. Using graph distance (GD) to measure the dissimilarity between objects is a good way to solve this problem, but computing the GD is time-consuming. Inspired by the idea that granular ball uses a ball to represent the local data, we select representatives from a local neighborhood, called natural density peaks (NDPs). On the basis of NDPs, we propose a novel K-means algorithm for identifying arbitrary-shaped clusters, called NDP-Kmeans. It defines neighbor-based distance between NDPs and takes advantage of the neighbor-based distance to compute the GD between NDPs. Afterward, an improved K-means with high-quality initial centers and GD is used to cluster NDPs. Finally, each remaining object is assigned according to its representative. The experimental results show that our algorithms can not only recognize spherical clusters but also manifold clusters. Therefore, NDP-Kmeans has more advantages in detecting arbitrary-shaped clusters than other excellent algorithms.

Spectral clustering is becoming more and more popular because it has good performance in discovering clusters with varying characteristics. However, it suffers from high computational cost, unstable clustering results and noises. This work presents a novel approximate spectral clustering based on dense cores and density peaks, called DCDP-ASC. It first finds a reduced data set by introducing the concept of dense cores; then defines a new distance based on the common neighborhood of dense cores and calculates geodesic distances between dense cores according to the new defined distance; after that constructs a decision graph with a parameter-free local density and geodesic distance for obtaining initial centers; finally calculates the similarity between dense cores with their new defined geodesic distance, employs normalized spectral clustering method to divide dense cores, and expands the result on dense cores to the whole data set by assigning each point to its representative. The results on some challenging data sets and the comparison of our algorithm with some other excellent methods demonstrate that the proposed method DCDP-ASC is more advantageous in identifying complex structured clusters containing a lot of noises.

Pine wilt disease (PWD), caused by the pine wood nematode (Bursaphelenchus xylophilus), is a global destructive threat to forests and has led to serious economic losses all over the world. Therefore, it is necessary to establish a feasible and effective method to accurately monitor and estimate PWD infection. In this study, we used hyperspectral imagery (HI) collected by an unmanned airship with a hyperspectral imaging spectrometer to detect PWD in healthy, early, middle and serious infection stages. To avoid massive calculations on the full spectral dimensions of the HI, 16 spectral features were extracted from the HI, and a genetic algorithm (GA) was implemented to identify the optimal ones with the least fitness. Simultaneously, a support vector machine (SVM) classifier was established to predict the PWD infection stage for an individual pine tree. The following results were obtained: (1) the spectral characteristics for pine trees in different PWD infection stages were distinctive in the green region (510–580 nm), red edge (680–760 nm) and near-infrared (780–1000 nm) spectra; (2) the six optimal spectral features (D_green, SD_green, D_red, D_RE, D_NIR, SD_NIR) selected with the GA effectively distinguished the PWD infection stages of pine trees with a lower calculation cost; (3) compared with the traditional classifiers, such as k-nearest neighbor (KNN), random forest (RF) and single SVM, the proposed GA and SVM classifier achieved the highest overall accuracy (95.24%) and Kappa coefficient (0.9234). The approach could also be employed for monitoring and detecting other forest pests.