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Fuzzy C-Means (FCM) is an effective and widely used clustering algorithm, but there are still some problems. considering the number of clusters must be determined manually, the local optimal solutions is easily influenced by the random selection of initial cluster centers, and the performance of Euclid distance in complex high-dimensional data is poor. To solve the above problems, the improved FCM clustering algorithm based on density Canopy and Manifold learning (DM-FCM) is proposed. First, a density Canopy algorithm based on improved local density is proposed to automatically deter-mine the number of clusters and initial cluster centers, which improves the self-adaptability and stability of the algorithm. Then, considering that high-dimensional data often present a nonlinear structure, the manifold learning method is applied to construct a manifold spatial structure, which preserves the global geometric properties of complex high-dimensional data and improves the clustering effect of the algorithm on complex high-dimensional datasets. Fowlkes-Mallows Index (FMI), the weighted average of homogeneity and completeness (V-measure), Adjusted Mutual Information (AMI), and Adjusted Rand Index (ARI) are used as performance measures of clustering algorithms. The experimental results show that the manifold learning method is the superior distance measure, and the algorithm improves the clustering accuracy and performs superiorly in the clustering of low-dimensional and complex high-dimensional data. [ABSTRACT FROM AUTHOR]

The operation of integrated energy systems (IESs) is confronted with great challenges for increasing penetration rate of renewable energy and growing complexity of energy forms. Scenario generation is one of ordinary methods to alleviate the system uncertainties by extracting several typical scenarios to represent the original high-dimensional data. This paper proposes a novel representative scenario generation method based on the feature extraction of panel data. The original high-dimensional data are represented by an aggregated indicator matrix using principal component analysis to preserve temporal variation. Then, the aggregated indicator matrix is clustered by an algorithm combining density canopy and K-medoids. Together with the proposed scenario generation method, an optimal operation model of IES is established, where the objective is to minimize the annual operation costs considering carbon trading cost. Finally, case studies based on the data of Aachen, Germany in 2019 are performed. The results indicate that the adjusted rand index (ARI) and silhouette coefficient (SC) of the proposed method are 0.6153 and 0.6770, respectively, both higher than the traditional methods, namely K-medoids, K-means++, and density-based spatial clustering of applications with noise (DBSCAN), which means the proposed method has better accuracy. The error between optimal operation results of the IES obtained by the proposed method and all-year time series benchmark value is 0.1%, while the calculation time is reduced from 11029 s to 188 s, which verifies that the proposed method can be used to optimize operation strategy of IES with high efficiency without loss of accuracy.

As the most widely used supervised classification algorithm, K nearest neighbor (KNN) algorithm is often inefficient in the processing of large-scale and multidimensional data. Therefore, an improved KNN algorithm for high dimensional large data processing is proposed. Firstly, deep neural networks (DNN) is used as feature extractor and dimension reduction is carried out to learn the most appropriate representation form of depth feature. Then, the appropriate number of clusters and the initial clustering center, obtained through the density Canopy algorithm become the input parameters of the subsequent K-means clustering. Finally, the learned data are clustered, and Hashing strategy in approximate similarity search (ASS) is used to cluster partitioning according to its approximate similarity, and the result is token as a new training sample of KNN classifier. In addition, considering that the nearest neighbor samples to be searched may fall in different clusters and the performance of KNN search is reduced, an additional clustering enhancement strategy is adopted in clustering, which effectively alleviates this situation. Five different data sets are used for comparison test. The results show that, compared with the experimental algorithms, this algorithm can not only greatly improve the accuracy of KNN classification, but also effectively improves the classification efficiency of the algorithm, reduces the distance required for searching, and has good robustness for noise data.

The carelessly selection of specialization course leaves some students with difficulty. Therefore, it is needed a recommendation system to solve it. Several approaches could be used to build the system, one of them was K-Means. K-Means required the number of initial centroid at random, so its result was not yet optimal. To determine the optimal initial centroid, Density Canopy (DC) algorithms had been proposed. In this research, DC and K-Means (DCKM) was implemented to build the recommendation system in the problem. The alpha criterion was also proposed to improve the performance of DCKM. The academic quality dataset in the 2018 informatics programs students of ITTP was used. There were three main stages in the system, namely determination of the weight of the course in dataset, implementation of DCKM, and determination of specialization recommendations. The results showed that the system by using DCKM has good quality based on the Silhouette results (at least 0.655). The system also used standar valuation scale in ITTP and silhouette index in the process of system. The results showed that 176 (65.91%) students were recommended in IT specialization, 25 (9.36%) students were recommended in MM specialization and 66 (24.7%) students were recommended in SC specialization.

Mapping the quality of education units is needed by stakeholders in education. To do this, clustering is considered as one of the methods that can be applied. K-means is a popular algorithm in the clustering method. In its process, K-means requires initial centroids randomly. Some scientists have proposed algorithms to determine the number of initial centroids and their location, one of which is density canopy (DC) algorithm. In the process, DC forms centroids based on the number of neighbors. This study proposes additional Silhouette criteria for DC algorithm. The development of DC is called Silhouette Density Canopy (SDC). SDC K-means (SDCKM) is applied to map the quality of education units and is compared with DC K-means (DCKM) and K-means (KM). The data used in this study originated from the 2019 senior high school national examination dataset of natural science, social science, and language programs in the Banyumas Regency. The results of the study revealed that clustering through SDKCM was better than DCKM and KM, but it took more time in the process. Mapping the quality of education with SDKCM formed three clusters for social science and natural science datasets and two clusters for language program dataset. Schools included in cluster 2 had a better quality of education compared to other schools.

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As a generalization algorithm of spectral clustering, p-spectral clustering has gradually attracted extensive attention of researchers. Gaussian kernel function is generally used in traditional p-spectral clustering to construct the similarity matrix of data. However, the Gaussian kernel function based on Euclidean distance is not effective when the data-set is complex with multiple density peaks or the density distribution is uniform. In order to solve this problem, an improved Density-based adaptive p-spectral clustering algorithm (DAPSC) is proposed, the prior information is considering to adjust the similarity between sample points and strengthen the local correlation between data points. In addition, by combining the density canopy method to update the initial clustering center and the number of clusters, the algorithm sensitivity of the original p-spectral clustering caused by the two is weakened. By experiments on four artificial data-sets and 8F UCI data-sets, we show that the proposed DAPSC has strong adaptability and more accurate compared with the four baseline methods. [ABSTRACT FROM AUTHOR]

In order to improve the accuracy and stability of K-means algorithm and solve the problem of determining the most appropriate number K of clusters and best initial seeds, an improved K-means algorithm based on density Canopy is proposed. Firstly, the density of sample data sets, the average sample distance in clusters and the distance between clusters are calculated, choosing the density maximum sampling point as the first cluster center and removing the density cluster from the data sets. Defining the product of sample density, the reciprocal of the average distance between the samples in the cluster, and the distance between the clusters as weight product, the other initial seeds is determined by the maximum weight product in the remaining data sets until the data sets is empty. The density Canopy is used as the preprocessing procedure of K-means and its result is used as the cluster number and initial clustering center of K-means algorithm. Finally, the new algorithm is tested on some well-known data sets from UCI machine learning repository and on some simulated data sets with different proportions of noise samples. The simulation results show that the improved K-means algorithm based on density Canopy achieves better clustering results and is insensitive to noisy data compared to the traditional K-means algorithm, the Canopy-based K-means algorithm, Semi-supervised K-means++ algorithm and K-means-u* algorithm. The clustering accuracy of the proposed K-means algorithm based on density Canopy is improved by 30.7%, 6.1%, 5.3% and 3.7% on average on UCI data sets, and improved by 44.3%, 3.6%, 9.6% and 8.9% on the simulated data sets with noise signal respectively. With the increase of the noise ratio, the noise immunity of the new algorithm is more obvious, when the noise ratio reached 30%, the accuracy rate is improved 50% and 6% compared to the traditional K-means algorithm and the Canopy-based K-means algorithm. [ABSTRACT FROM AUTHOR]

The aim of this study was to analyze the population structure, regeneration and spatial distribution of Araucaria angustifolia (Bertol.) Kuntz. within a natural forest and in forest edge with agricultural monoculture. All araucaria individuals from 10 cm high were recorded in 200 plots of 10 x 10 m. 479 individuals were sampled (416 at the edge and 63 inside). Of these, 33 were females, 37 males, 49 juveniles and 360 regenerating individuals. The population structure performance was similar to standard inverted-J. Regenerating individuals had mainly the aggregate distribution pattern, while juveniles, males and females had a uniform pattern. Density of the canopy affected frequency of the individuals, where higher frequencies at higher densities were observed, indicating that regeneration of this species is more effective in shadowed environments. Due to the large number of individuals sampled in different size classes, the Iguaçu National Park is an important conservation remaining of A. angustifolia. [ABSTRACT FROM AUTHOR]