scholarly journals A Study On High Dimensional Clustering By Using Clique

2011 ◽  
pp. 101-104
Author(s):  
Raghunath Kar ◽  
Susanta Kumar Das
Keyword(s):  
Input Parameter ◽  
High Dimensional Data ◽  
Real Life ◽  
Multidimensional Data ◽  
High Dimensional ◽  
Data Sets ◽  
Data Points ◽  
A Cell ◽  
Low Dimensional ◽  
Partition Method

In real life clustering of high dimensional data is a big problem. To find out the dense regions from increasing dimensions is one of them. We have already studied the clustering techniques of low dimensional data sets like k-means, k-mediod, BIRCH, CLARANS, CURE, DBScan, PAM etc. If a region is dense then it consists with number of data points with a minimum support of input parameter ø other wise it cannot take into clustering. So in this approach we have implemented CLIQUE to find out the clusters from multidimensional data sets. In dimension growth subspace clustering the clustering process start at single dimensional subspaces and grows upward to higher dimensional ones. It is a partition method where each dimension divided like a grid structure. The grid is a cell where the data points are present. We check the dense units from the structure by applying different algorithms. Finally the clusters are formed from the high dimensional data sets.

OLAP Visualization

2011 ◽  
pp. 1439-1446 ◽  
Author(s):  
Alfredo Cuzzocrea ◽  
Svetlana Mansmann
Keyword(s):  
Computer Science ◽  
High Dimensional Data ◽  
Real Life ◽  
Science Research ◽  
Research Field ◽  
Multidimensional Data ◽  
High Dimensional ◽  
Data Sets ◽  
Visualization Of Data ◽  
Multidimensional Data Sets

The problem of efficiently visualizing multidimensional data sets produced by scientific and statistical tasks/ processes is becoming increasingly challenging, and is attracting the attention of a wide multidisciplinary community of researchers and practitioners. Basically, this problem consists in visualizing multidimensional data sets by capturing the dimensionality of data, which is the most difficult aspect to be considered. Human analysts interacting with high-dimensional data often experience disorientation and cognitive overload. Analysis of high- dimensional data is a challenge encountered in a wide set of real-life applications such as (i) biological databases storing massive gene and protein data sets, (ii) real-time monitoring systems accumulating data sets produced by multiple, multi-rate streaming sources, (iii) advanced Business Intelligence (BI) systems collecting business data for decision making purposes etc. Traditional DBMS front-end tools, which are usually tuple-bag-oriented, are completely inadequate to fulfill the requirements posed by an interactive exploration of high-dimensional data sets due to two major reasons: (i) DBMS implement the OLTP paradigm, which is optimized for transaction processing and deliberately neglects the dimensionality of data; (ii) DBMS operators are very poor and offer nothing beyond the capability of conventional SQL statements, what makes such tools very inefficient with respect to the goal of visualizing and, above all, interacting with multidimensional data sets embedding a large number of dimensions. Despite the above-highlighted practical relevance of the problem of visualizing multidimensional data sets, the literature in this field is rather scarce, due to the fact that, for many years, this problem has been of relevance for life science research communities only, and interaction of the latter with the computer science research community has been insufficient. Following the enormous growth of scientific disciplines like Bio-Informatics, this problem has then become a fundamental field in the computer science academic as well as industrial research. At the same time, a number of proposals dealing with the multidimensional data visualization problem appeared in literature, with the amenity of stimulating novel and exciting application fields such as the visualization of Data Mining results generated by challenging techniques like clustering and association rule discovery. The above-mentioned issues are meant to facilitate understanding of the high relevance and attractiveness of the problem of visualizing multidimensional data sets at present and in the future, with challenging research findings accompanied by significant spin-offs in the Information Technology (IT) industrial field. A possible solution to tackle this problem is represented by well-known OLAP techniques (Codd et al., 1993; Chaudhuri & Dayal, 1997; Gray et al., 1997), focused on obtaining very efficient representations of multidimensional data sets, called data cubes, thus leading to the research field which is known in literature under the terms OLAP Visualization and Visual OLAP, which, in the remaining part of the article, are used interchangeably.

Mahalanobis distance informed by clustering

2018 ◽  
Vol 8 (2) ◽  
pp. 377-406
Author(s):  
Almog Lahav ◽  
Ronen Talmon ◽  
Yuval Kluger
Keyword(s):  
Mahalanobis Distance ◽  
High Dimensional Data ◽  
Hidden Variables ◽  
Real Data ◽  
Risk Groups ◽  
High Dimensional ◽  
Data Sets ◽  
Kaplan Meier ◽  
Data Points ◽  
Survival Plot

Abstract A fundamental question in data analysis, machine learning and signal processing is how to compare between data points. The choice of the distance metric is specifically challenging for high-dimensional data sets, where the problem of meaningfulness is more prominent (e.g. the Euclidean distance between images). In this paper, we propose to exploit a property of high-dimensional data that is usually ignored, which is the structure stemming from the relationships between the coordinates. Specifically, we show that organizing similar coordinates in clusters can be exploited for the construction of the Mahalanobis distance between samples. When the observable samples are generated by a nonlinear transformation of hidden variables, the Mahalanobis distance allows the recovery of the Euclidean distances in the hidden space. We illustrate the advantage of our approach on a synthetic example where the discovery of clusters of correlated coordinates improves the estimation of the principal directions of the samples. Our method was applied to real data of gene expression for lung adenocarcinomas (lung cancer). By using the proposed metric we found a partition of subjects to risk groups with a good separation between their Kaplan–Meier survival plot.

scholarly journals A Novel Density-based Technique for Outlier Detection of High Dimensional Data Utilizing Full Feature Space

2021 ◽  
Vol 50 (1) ◽  
pp. 138-152
Author(s):  
Mujeeb Ur Rehman ◽  
Dost Muhammad Khan
Keyword(s):  
Data Mining ◽  
Outlier Detection ◽  
High Dimensional Data ◽  
Research Work ◽  
Feature Space ◽  
High Dimensional ◽  
Data Set ◽  
Data Points ◽  
Low Dimensional ◽  
Intrinsic Feature

Recently, anomaly detection has acquired a realistic response from data mining scientists as a graph of its reputation has increased smoothly in various practical domains like product marketing, fraud detection, medical diagnosis, fault detection and so many other fields. High dimensional data subjected to outlier detection poses exceptional challenges for data mining experts and it is because of natural problems of the curse of dimensionality and resemblance of distant and adjoining points. Traditional algorithms and techniques were experimented on full feature space regarding outlier detection. Customary methodologies concentrate largely on low dimensional data and hence show ineffectiveness while discovering anomalies in a data set comprised of a high number of dimensions. It becomes a very difficult and tiresome job to dig out anomalies present in high dimensional data set when all subsets of projections need to be explored. All data points in high dimensional data behave like similar observations because of its intrinsic feature i.e., the distance between observations approaches to zero as the number of dimensions extends towards infinity. This research work proposes a novel technique that explores deviation among all data points and embeds its findings inside well established density-based techniques. This is a state of art technique as it gives a new breadth of research towards resolving inherent problems of high dimensional data where outliers reside within clusters having different densities. A high dimensional dataset from UCI Machine Learning Repository is chosen to test the proposed technique and then its results are compared with that of density-based techniques to evaluate its efficiency.

scholarly journals A Preview on Subspace Clustering of High Dimensional Data

2013 ◽  
Vol 6 (3) ◽  
pp. 441-448 ◽  
Author(s):  
Sajid Nagi ◽  
Dhruba Kumar Bhattacharyya ◽  
Jugal K. Kalita
Keyword(s):  
Search Strategy ◽  
High Dimensional Data ◽  
Subspace Clustering ◽  
High Dimensional ◽  
Expression Data ◽  
Clustering Methods ◽  
Top Down ◽  
Data Points ◽  
Low Dimensional ◽  
Entire Dataset

When clustering high dimensional data, traditional clustering methods are found to be lacking since they consider all of the dimensions of the dataset in discovering clusters whereas only some of the dimensions are relevant. This may give rise to subspaces within the dataset where clusters may be found. Using feature selection, we can remove irrelevant and redundant dimensions by analyzing the entire dataset. The problem of automatically identifying clusters that exist in multiple and maybe overlapping subspaces of high dimensional data, allowing better clustering of the data points, is known as Subspace Clustering. There are two major approaches to subspace clustering based on search strategy. Top-down algorithms find an initial clustering in the full set of dimensions and evaluate the subspaces of each cluster, iteratively improving the results. Bottom-up approaches start from finding low dimensional dense regions, and then use them to form clusters. Based on a survey on subspace clustering, we identify the challenges and issues involved with clustering gene expression data.

scholarly journals Subspace Clustering of High-Dimensional Data: An Evolutionary Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Singh Vijendra ◽  
Sahoo Laxman
Keyword(s):  
Clustering Algorithm ◽  
Dimensional Space ◽  
Clustering Algorithms ◽  
High Dimensional Data ◽  
Subspace Clustering ◽  
High Dimensional ◽  
Data Sets ◽  
Real World Data ◽  
Data Set ◽  
Data Points

Clustering high-dimensional data has been a major challenge due to the inherent sparsity of the points. Most existing clustering algorithms become substantially inefficient if the required similarity measure is computed between data points in the full-dimensional space. In this paper, we have presented a robust multi objective subspace clustering (MOSCL) algorithm for the challenging problem of high-dimensional clustering. The first phase of MOSCL performs subspace relevance analysis by detecting dense and sparse regions with their locations in data set. After detection of dense regions it eliminates outliers. MOSCL discovers subspaces in dense regions of data set and produces subspace clusters. In thorough experiments on synthetic and real-world data sets, we demonstrate that MOSCL for subspace clustering is superior to PROCLUS clustering algorithm. Additionally we investigate the effects of first phase for detecting dense regions on the results of subspace clustering. Our results indicate that removing outliers improves the accuracy of subspace clustering. The clustering results are validated by clustering error (CE) distance on various data sets. MOSCL can discover the clusters in all subspaces with high quality, and the efficiency of MOSCL outperforms PROCLUS.

scholarly journals Visualization of Very Large High-Dimensional Data Sets as Minimum Spanning Trees

2019 ◽  
Author(s):  
Daniel Probst ◽  
Jean-Louis Reymond
Keyword(s):  
Particle Physics ◽  
Spanning Trees ◽  
High Dimensional Data ◽  
Large Data ◽  
High Dimensional ◽  
Data Sets ◽  
Chemical Structures ◽  
Data Points ◽  
Global And Local ◽  
Human Inspection

<p>The chemical sciences are producing an unprecedented amount of large, high-dimensional data sets containing chemical structures and associated properties. However, there are currently no algorithms to visualize such data while preserving both global and local features with a sufficient level of detail to allow for human inspection and interpretation. Here, we propose a solution to this problem with a new data visualization method, TMAP, capable of representing data sets of up to millions of data points and arbitrary high dimensionality as a two-dimensional tree (http://tmap.gdb.tools). Visualizations based on TMAP are better suited than t-SNE or UMAP for the exploration and interpretation of large data sets due to their tree-like nature, increased local and global neighborhood and structure preservation, and the transparency of the methods the algorithm is based on. We apply TMAP to the most used chemistry data sets including databases of molecules such as ChEMBL, FDB17, the Natural Products Atlas, DSSTox, DrugBank, as well as to the MoleculeNet benchmark collection of data sets. We also show its broad applicability with further examples from biology, particle physics, and literature.</p>

scholarly journals Detection of Outliers in High Dimensional Data with Lasso Regression

2019 ◽  
Vol 9 (1) ◽  
pp. 7342-7346
Keyword(s):  
High Dimensional Data ◽  
Real Life ◽  
Research Area ◽  
High Dimensional ◽  
Data Sets ◽  
Lasso Regression ◽  
Internet Users ◽  
Huge Data ◽  
Significant Research ◽  
Detection Of Outliers

Detecting Outliers has become a significant research area in data mining in last few years. The focus of this research has been to identify patterns or objects in huge data sets of a database that are exceptional from normal pattern, specifically dissimilar, and unpredictable with reference to the most of the datasets. As billions of personal computers, and internet users rose phenomenally, huge data sets of real life applications have been created for new challenges as well as explorations in research for Outlier detection. Many traditional techniques to detect outliers have unable to yield good results in such environments. So, developing a method to detect Outliers has become a critical task. A method to identify anomalies in high dimensional data based on Lasso Regression has been study in this research. This framework has been implemented in the open source JMP software. The parameters such as RSquare 0.001162, RMSE 0.031806 and Mean Response 0.007889 are calculated using Spambase dataset. The results from the experiments have shown that the proposed method detects Outliers in high dimensional data with potentially higher accuracy.

scholarly journals Visualization of Very Large High-Dimensional Data Sets as Minimum Spanning Trees

2019 ◽  
Author(s):  
Daniel Probst ◽  
Jean-Louis Reymond
Keyword(s):  
Particle Physics ◽  
Spanning Trees ◽  
High Dimensional Data ◽  
Large Data ◽  
High Dimensional ◽  
Data Sets ◽  
Chemical Structures ◽  
Data Points ◽  
Global And Local ◽  
Human Inspection

<p>The chemical sciences are producing an unprecedented amount of large, high-dimensional data sets containing chemical structures and associated properties. However, there are currently no algorithms to visualize such data while preserving both global and local features with a sufficient level of detail to allow for human inspection and interpretation. Here, we propose a solution to this problem with a new data visualization method, TMAP, capable of representing data sets of up to millions of data points and arbitrary high dimensionality as a two-dimensional tree (http://tmap.gdb.tools). Visualizations based on TMAP are better suited than t-SNE or UMAP for the exploration and interpretation of large data sets due to their tree-like nature, increased local and global neighborhood and structure preservation, and the transparency of the methods the algorithm is based on. We apply TMAP to the most used chemistry data sets including databases of molecules such as ChEMBL, FDB17, the Natural Products Atlas, DSSTox, DrugBank, as well as to the MoleculeNet benchmark collection of data sets. We also show its broad applicability with further examples from biology, particle physics, and literature.</p>

scholarly journals ReliefE: feature ranking in high-dimensional spaces via manifold embeddings

2021 ◽  
Author(s):  
Blaž Škrlj ◽  
Sašo Džeroski ◽  
Nada Lavrač ◽  
Matej Petković
Keyword(s):  
Sparse Matrix ◽  
Real Life ◽  
High Dimensional ◽  
Feature Ranking ◽  
Data Sets ◽  
Data Set ◽  
Learning Capabilities ◽  
Machine Learning Applications ◽  
High Utility ◽  
Low Dimensional

AbstractFeature ranking has been widely adopted in machine learning applications such as high-throughput biology and social sciences. The approaches of the popular Relief family of algorithms assign importances to features by iteratively accounting for nearest relevant and irrelevant instances. Despite their high utility, these algorithms can be computationally expensive and not-well suited for high-dimensional sparse input spaces. In contrast, recent embedding-based methods learn compact, low-dimensional representations, potentially facilitating down-stream learning capabilities of conventional learners. This paper explores how the Relief branch of algorithms can be adapted to benefit from (Riemannian) manifold-based embeddings of instance and target spaces, where a given embedding’s dimensionality is intrinsic to the dimensionality of the considered data set. The developed ReliefE algorithm is faster and can result in better feature rankings, as shown by our evaluation on 20 real-life data sets for multi-class and multi-label classification tasks. The utility of ReliefE for high-dimensional data sets is ensured by its implementation that utilizes sparse matrix algebraic operations. Finally, the relation of ReliefE to other ranking algorithms is studied via the Fuzzy Jaccard Index.

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