scholarly journals Symmetry Based Automatic Evolution of Clusters: A New Approach to Data Clustering

2015 ◽  
Vol 2015 ◽  
pp. 1-21 ◽  
Author(s):  
Singh Vijendra ◽  
Sahoo Laxman
Keyword(s):  
Clustering Algorithm ◽  
Nearest Neighbor ◽  
A Priori ◽  
Clustering Algorithms ◽  
Real Data ◽  
Nearest Neighbor Search ◽  
Objective Functions ◽  
Neighbor Search ◽  
Genetic Clustering ◽  
Symmetric Points

We present a multiobjective genetic clustering approach, in which data points are assigned to clusters based on new line symmetry distance. The proposed algorithm is called multiobjective line symmetry based genetic clustering (MOLGC). Two objective functions, first the Davies-Bouldin (DB) index and second the line symmetry distance based objective functions, are used. The proposed algorithm evolves near-optimal clustering solutions using multiple clustering criteria, without a priori knowledge of the actual number of clusters. The multiple randomizedKdimensional (Kd) trees based nearest neighbor search is used to reduce the complexity of finding the closest symmetric points. Experimental results based on several artificial and real data sets show that proposed clustering algorithm can obtain optimal clustering solutions in terms of different cluster quality measures in comparison to existing SBKM and MOCK clustering algorithms.

NBC: An Efficient Hierarchical Clustering Algorithm for Large Datasets

2015 ◽  
Vol 09 (03) ◽  
pp. 307-331 ◽  
Author(s):  
Wei Zhang ◽  
Gongxuan Zhang ◽  
Yongli Wang ◽  
Zhaomeng Zhu ◽  
Tao Li
Keyword(s):  
Hierarchical Clustering ◽  
Time Complexity ◽  
Clustering Algorithm ◽  
Nearest Neighbor ◽  
Clustering Algorithms ◽  
Large Datasets ◽  
Nearest Neighbor Search ◽  
Large Dataset ◽  
Neighbor Search ◽  
Hierarchical Clustering Algorithm

Nearest neighbor search is a key technique used in hierarchical clustering and its computing complexity decides the performance of the hierarchical clustering algorithm. The time complexity of standard agglomerative hierarchical clustering is O(n3), while the time complexity of more advanced hierarchical clustering algorithms (such as nearest neighbor chain, SLINK and CLINK) is O(n2). This paper presents a new nearest neighbor search method called nearest neighbor boundary (NNB), which first divides a large dataset into independent subset and then finds nearest neighbor of each point in subset. When NNB is used, the time complexity of hierarchical clustering can be reduced to O(n log 2n). Based on NNB, we propose a fast hierarchical clustering algorithm called nearest-neighbor boundary clustering (NBC), and the proposed algorithm can be adapted to the parallel and distributed computing framework. The experimental results demonstrate that our algorithm is practical for large datasets.

scholarly journals Associative Memories to Accelerate Approximate Nearest Neighbor Search

2018 ◽  
Vol 8 (9) ◽  
pp. 1676 ◽  
Author(s):  
Vincent Gripon ◽  
Matthias Löwe ◽  
Franck Vermet
Keyword(s):  
Associative Memory ◽  
Nearest Neighbor ◽  
Synthetic Data ◽  
Random Variables ◽  
Real Data ◽  
Nearest Neighbor Search ◽  
Associative Memories ◽  
Neighbor Search ◽  
Trade Offs ◽  
Approximate Result

Nearest neighbor search is a very active field in machine learning. It appears in many application cases, including classification and object retrieval. In its naive implementation, the complexity of the search is linear in the product of the dimension and the cardinality of the collection of vectors into which the search is performed. Recently, many works have focused on reducing the dimension of vectors using quantization techniques or hashing, while providing an approximate result. In this paper, we focus instead on tackling the cardinality of the collection of vectors. Namely, we introduce a technique that partitions the collection of vectors and stores each part in its own associative memory. When a query vector is given to the system, associative memories are polled to identify which one contains the closest match. Then, an exhaustive search is conducted only on the part of vectors stored in the selected associative memory. We study the effectiveness of the system when messages to store are generated from i.i.d. uniform ±1 random variables or 0–1 sparse i.i.d. random variables. We also conduct experiments on both synthetic data and real data and show that it is possible to achieve interesting trade-offs between complexity and accuracy.

Fast algorithm for anchor graph hashing

2021 ◽  
Vol 14 (6) ◽  
pp. 916-928
Author(s):  
Yasuhiro Fujiwara ◽  
Sekitoshi Kanai ◽  
Yasutoshi Ida ◽  
Atsutoshi Kumagai ◽  
Naonori Ueda
Keyword(s):  
Clustering Algorithm ◽  
Nearest Neighbor ◽  
Nearest Neighbor Search ◽  
Computation Cost ◽  
Neighbor Search ◽  
The Matrix ◽  
Data Points ◽  
Anchor Points ◽  
Data Point ◽  
Hash Codes

Anchor graph hashing is used in many applications such as cancer detection, web page classification, and drug discovery. It computes the hash codes from the eigenvectors of the matrix representing the similarities between data points and anchor points; anchors refer to the points representing the data distribution. In performing an approximate nearest neighbor search, the hash codes of a query data point are determined by identifying its closest anchor points. Anchor graph hashing, however, incurs high computation cost since (1) the computation cost of obtaining the eigenvectors is quadratic to the number of anchor points, and (2) the similarities of the query data point to all the anchor points must be computed. Our proposal, Tridiagonal hashing , increases the efficiency of anchor graph hashing because of its two advances: (1) we apply a graph clustering algorithm to compute the eigenvectors from the tridiagonal matrix obtained from the similarities between data points and anchor points, and (2) we detect anchor points closest to the query data point by using a dimensionality reduction approach. Experiments show that our approach is several orders of magnitude faster than the previous approaches. Besides, it yields high search accuracy than the original anchor graph hashing approach.

scholarly journals A Novel Local Density Hierarchical Clustering Algorithm Based on Reverse Nearest Neighbors

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Yaohui Liu ◽  
Dong Liu ◽  
Fang Yu ◽  
Zhengming Ma
Keyword(s):  
Hierarchical Clustering ◽  
Clustering Algorithm ◽  
Nearest Neighbor ◽  
Local Density ◽  
Clustering Algorithms ◽  
Real Data ◽  
Nearest Neighbors ◽  
Clustering Methods ◽  
Density Peak ◽  
Hierarchical Clustering Algorithm

Clustering is widely used in data analysis, and density-based methods are developed rapidly in the recent 10 years. Although the state-of-art density peak clustering algorithms are efficient and can detect arbitrary shape clusters, they are nonsphere type of centroid-based methods essentially. In this paper, a novel local density hierarchical clustering algorithm based on reverse nearest neighbors, RNN-LDH, is proposed. By constructing and using a reverse nearest neighbor graph, the extended core regions are found out as initial clusters. Then, a new local density metric is defined to calculate the density of each object; meanwhile, the density hierarchical relationships among the objects are built according to their densities and neighbor relations. Finally, each unclustered object is classified to one of the initial clusters or noise. Results of experiments on synthetic and real data sets show that RNN-LDH outperforms the current clustering methods based on density peak or reverse nearest neighbors.

scholarly journals A K-means algorithm based on characteristics of density applied to network intrusion detection

2020 ◽  
Vol 17 (2) ◽  
pp. 665-687
Author(s):  
Jing Xu ◽  
Dezhi Han ◽  
Kuan-Ching Li ◽  
Hai Jiang
Keyword(s):  
Intrusion Detection ◽  
Nearest Neighbor ◽  
Clustering Algorithms ◽  
Search Space ◽  
Nearest Neighbor Search ◽  
Network Intrusion Detection ◽  
Neighbor Search ◽  
Network Intrusion ◽  
Initial Seed ◽  
Unsupervised Algorithms

K-means algorithms are a group of popular unsupervised algorithms widely used for cluster analysis. However, the results of traditional K-means clustering algorithms are greatly affected by the initial clustering center, with unstable accuracy and low speed, which makes the algorithm hard to meet the requirements for Big Data. In this paper, a modernized version of the K-means algorithm based on density to select the initial seed of clustering is proposed. Firstly, Kd-tree is used to divide the hyper-rectangle space, so those points close to each other are grouped into the same sub-tree during data pre-processing, and the generalized information is stored in the tree structure. Besides, an improved Kd-tree nearest neighbor search is used in the K-means algorithm to prune the search space and optimize the operation for speedup. The clustering results show that the clusters are stable and accurate when the numbers of clusters and iterations are constant. Experimental results in the network intrusion detection case show that the improved version of the K-means algorithms performs better in terms of detection rate and false rate.

The Earth Mover’s Distance as a Metric for the Space of Inorganic Compositions

2020 ◽  
Author(s):  
Cameron Hargreaves ◽  
Matthew Dyer ◽  
Michael Gaultois ◽  
Vitaliy Kurlin ◽  
Matthew J Rosseinsky
Keyword(s):  
Euclidean Distance ◽  
Nearest Neighbor ◽  
Nearest Neighbor Search ◽  
Inorganic Crystal Structure Database ◽  
Earth Mover’S Distance ◽  
Chemical Similarity ◽  
Earth Mover's Distance ◽  
Neighbor Search ◽  
The Earth ◽  
Binary Compounds

It is a core problem in any field to reliably tell how close two objects are to being the same, and once this relation has been established we can use this information to precisely quantify potential relationships, both analytically and with machine learning (ML). For inorganic solids, the chemical composition is a fundamental descriptor, which can be represented by assigning the ratio of each element in the material to a vector. These vectors are a convenient mathematical data structure for measuring similarity, but unfortunately, the standard metric (the Euclidean distance) gives little to no variance in the resultant distances between chemically dissimilar compositions. We present the Earth Mover’s Distance (EMD) for inorganic compositions, a well-defined metric which enables the measure of chemical similarity in an explainable fashion. We compute the EMD between two compositions from the ratio of each of the elements and the absolute distance between the elements on the modified Pettifor scale. This simple metric shows clear strength at distinguishing compounds and is efficient to compute in practice. The resultant distances have greater alignment with chemical understanding than the Euclidean distance, which is demonstrated on the binary compositions of the Inorganic Crystal Structure Database (ICSD). The EMD is a reliable numeric measure of chemical similarity that can be incorporated into automated workflows for a range of ML techniques. We have found that with no supervision the use of this metric gives a distinct partitioning of binary compounds into clear trends and families of chemical property, with future applications for nearest neighbor search queries in chemical database retrieval systems and supervised ML techniques.

DRSA: a non-hierarchical clustering algorithm using k-NN graph and its application in vegetation classification

2015 ◽  
pp. 125-138 ◽  
Author(s):  
I. V. Goncharenko
Keyword(s):  
Cluster Analysis ◽  
Clustering Algorithm ◽  
Nearest Neighbor ◽  
Clustering Algorithms ◽  
Protein Structures ◽  
Hierarchical Cluster ◽  
Vegetation Classification ◽  
K Nearest Neighbor ◽  
Neighbor Graph ◽  
Nearest Neighbor Graph

In this article we proposed a new method of non-hierarchical cluster analysis using k-nearest-neighbor graph and discussed it with respect to vegetation classification. The method of k-nearest neighbor (k-NN) classification was originally developed in 1951 (Fix, Hodges, 1951). Later a term “k-NN graph” and a few algorithms of k-NN clustering appeared (Cover, Hart, 1967; Brito et al., 1997). In biology k-NN is used in analysis of protein structures and genome sequences. Most of k-NN clustering algorithms build «excessive» graph firstly, so called hypergraph, and then truncate it to subgraphs, just partitioning and coarsening hypergraph. We developed other strategy, the “upward” clustering in forming (assembling consequentially) one cluster after the other. Until today graph-based cluster analysis has not been considered concerning classification of vegetation datasets.

scholarly journals PCT: Point cloud transformer

2021 ◽  
Vol 7 (2) ◽  
pp. 187-199
Author(s):  
Meng-Hao Guo ◽  
Jun-Xiong Cai ◽  
Zheng-Ning Liu ◽  
Tai-Jiang Mu ◽  
Ralph R. Martin ◽  
...  
Keyword(s):  
Language Processing ◽  
Point Cloud ◽  
Nearest Neighbor ◽  
Semantic Segmentation ◽  
Nearest Neighbor Search ◽  
Local Context ◽  
Irregular Domain ◽  
Cloud Processing ◽  
Neighbor Search ◽  
Farthest Point

AbstractThe irregular domain and lack of ordering make it challenging to design deep neural networks for point cloud processing. This paper presents a novel framework named Point Cloud Transformer (PCT) for point cloud learning. PCT is based on Transformer, which achieves huge success in natural language processing and displays great potential in image processing. It is inherently permutation invariant for processing a sequence of points, making it well-suited for point cloud learning. To better capture local context within the point cloud, we enhance input embedding with the support of farthest point sampling and nearest neighbor search. Extensive experiments demonstrate that the PCT achieves the state-of-the-art performance on shape classification, part segmentation, semantic segmentation, and normal estimation tasks.

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