Sliding window aggregation, which extracts summaries from data streams, is a core operation in streaming analysis. Though existing sliding window algorithms that perform single eviction and insertion operations can achieve a worst-case time complexity of O(1) for in-order streams, real-world data streams often involve out-of-order data and exhibit burst data characteristics, which pose performance challenges to these sliding window algorithms. To address this challenging issue, we propose Gecko - a novel sliding window aggregation algorithm that supports bulk eviction. Gecko leverages a granular-based eviction strategy for various bulk sizes, enabling efficient bulk eviction while maintaining the performance close to that of in-order stream algorithms for single evictions. For large data bulks, Gecko performs coarse-grained eviction at the chunk level, followed by fine-grained eviction using leftward binary tree aggregation (LTA) as a complementary method. Moreover, Gecko partitions data based on chunks to prevent the impacts of out-of-order data on other chunks, thereby enabling efficient handling of out-of-order data streams. We conduct extensive experiments to evaluate the performance of Gecko. Experimental results demonstrate that Gecko exhibits superior performance over other solutions, which is consistent with theoretical expectations. In real-world data scenarios, Gecko improves the average throughput of the state-of-the-art algorithm b_FiBA by 1.7 times, with a maximum improvement of up to 3.5 times. Gecko also demonstrates the best latency performance among all compared schemes.

Gradient descent method is the preferred method to optimize neural networks and many other machine learning algorithms. Especially with the wide use of deep learning in recent years, gradient descent algorithm has become more and more important. In gradient descent algorithm, learning rate is a very important parameter. The setting of learning rate directly affects the performance of the final model. The existing learning rate optimization algorithms adjusts learning rate based on the idea of step-by-step reduction. Different from this idea, this paper based on human walking law proposes a new optimization algorithm, the consolidate step-by-step algorithm (CSBS), which determines the learning rate according to the gradient of each iteration. In this paper, MNIST data set is used to verify the performance of the algorithm. The experimental results show that the CSBS algorithm accelerates the convergence speed of the model and reduces the sensitivity to the initial parameters.

Fuzzy C-means clustering (FCM) has been a commonly used algorithm in fuzzy clustering for decades. However, it still faces two problems: how to determine the initial cluster center and how to determine the number of clusters. The recently proposed robust learning fuzzy C-means (RL-FCM) can automatically obtain the optimal number of clusters. However, it assumes that the initial cluster center is the entire dataset, which incurs a significant time cost and involves parameters that are also difficult to determine. Additionally, RL-FCM is unable to handle imbalanced datasets and datasets with a large span of sample attributes. Therefore, we propose a robust learning membership scaling fuzzy C-means algorithm based on new belief peaks (RL-MFCM). Within the framework of the confidence function, the neighbors of the sample points provide evidence for the sample points being cluster centers. Consequently, according to Jiang's combination rule, we consider the new belief peak as the initial cluster center. To avoid excessive interference of the mixing ratio of the cluster to the calculation of membership degree, we employ triangle inequality to improve the influence of the samples in the cluster in the clustering process. We analyze the time complexity of the proposed algorithm and conduct comparative experiments with existing fuzzy clustering algorithms on artificial and real datasets in the article. Experiments demonstrate that our proposed algorithm accurately estimates the number of clusters and exhibits superior clustering performance without needing initialization.

Cluster analysis is a crucial data mining technology widely used in image segmentation, language processing, and pattern recognition. Most existing clustering algorithms cannot identify complex shapes in manifold data sets and data sets with varying-density distribution, especially when clusters with significant differences in density are close to each other. Hierarchical clustering algorithms can identify data sets of arbitrary shapes. However, hierarchical clustering algorithms not only cannot cluster datasets with significant density variations but also have a high time cost. So in this paper, we propose a novel hierarchical clustering algorithm based on density-distance cores, called HCDC. It first selects the density-distance representative points for each point from the set of candidate representative points. Then it selects density-distance cores from all density-distance representatives. And it replaces the whole data set with density-distance cores and uses a new distance between them to apply hierarchical clustering. To avoid the influence of noise points in the dataset when finding density-distance cores, we also propose the noise point detection method and verify the feasibility of this method. In this paper, we compare our proposed algorithm with existing classical and novel algorithms on synthetic and real datasets. Experiments show that our algorithm clusters better than existing algorithms on complex-shaped datasets and datasets with different densities. On datasets with sparse and dense clusters close to each other, the ARI score of HCDC is more than 0.1 higher than that of LDP-MST. In particular, on the grid dataset, HCDC’s ARI score is 0.997 higher than LDP-MST. On DS3 and DS8, HCDC’s ARI score is more than 0.14 higher than the second-best algorithm, RNN-DBSCAN. Moreover, on the zoo dataset, HCDC’s ARI score is 0.15 and 0.6 higher than RNN-DBSCAN and LDP-MST, respectively. On the olivetti face dataset, HCDC is the only algorithm with an NMI score above 0.9 on photo1 and photo2 datasets.

Spectral clustering algorithm has become more popular in data clustering problems in recent years, due to the idea of optimally dividing the graph to solve the data clustering problems. However, the performance of the spectral clustering algorithm is affected by the quality of the similarity matrix. In addition, the traditional spectral clustering algorithm is unstable because it uses the K-means algorithm in the final clustering stage. Therefore, we propose a spectral clustering algorithm based on fast diffusion search for natural neighbor and affinity propagation (FDAP-SC). The algorithm obtains neighbor information more efficiently by changing the way of determining the number of neighbors. And it uses the shared nearest neighbors and the shared reverse neighbors between two points to construct the similarity matrix. Moreover, the algorithm regards all data points as nodes in the network and then calculates the clustering center of each sample through message passing between nodes. In this paper, we first experimentally on real datasets to verify that our proposed method for determining the number of neighbors outperforms the traditional natural nearest neighbor algorithm. We then demonstrate on synthetic datasets that FDAP-SC can handle complex shape datasets well. Finally, we compare FDAP-SC with several existing classical and novel algorithms on real datasets and Olivetti face datasets, proving the superiority and stability of FDAP-SC algorithm performance. Among the seven real datasets, FDAP-SC has the best performance on five datasets, and in the Olivetti face datasets, FDAP-SC achieves more than 87.5% accuracy.