scholarly journals Robust K-Median and K-Means Clustering Algorithms for Incomplete Data

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Jinhua Li ◽  
Shiji Song ◽  
Yuli Zhang ◽  
Zhen Zhou
Keyword(s):  
Incomplete Data ◽  
Missing Values ◽  
Clustering Algorithms ◽  
Interval Data ◽  
Accurate Estimation ◽  
Data Sets ◽  
Clustering Methods ◽  
Estimation Errors ◽  
Feature Values ◽  
Time And Space Complexity

Incomplete data with missing feature values are prevalent in clustering problems. Traditional clustering methods first estimate the missing values by imputation and then apply the classical clustering algorithms for complete data, such as K-median and K-means. However, in practice, it is often hard to obtain accurate estimation of the missing values, which deteriorates the performance of clustering. To enhance the robustness of clustering algorithms, this paper represents the missing values by interval data and introduces the concept of robust cluster objective function. A minimax robust optimization (RO) formulation is presented to provide clustering results, which are insensitive to estimation errors. To solve the proposed RO problem, we propose robust K-median and K-means clustering algorithms with low time and space complexity. Comparisons and analysis of experimental results on both artificially generated and real-world incomplete data sets validate the robustness and effectiveness of the proposed algorithms.

A New semi-supervised clustering for incomplete data

2021 ◽  
pp. 1-13
Author(s):  
Sonia Goel ◽  
Meena Tushir
Keyword(s):  
Incomplete Data ◽  
Missing Values ◽  
Clustering Algorithms ◽  
Complete Data ◽  
Unlabeled Data ◽  
Misclassification Rate ◽  
Data Sets ◽  
Clustering Methods ◽  
Data Set ◽  
Supervised Clustering

Semi-supervised clustering technique partitions the unlabeled data based on prior knowledge of labeled data. Most of the semi-supervised clustering algorithms exist only for the clustering of complete data, i.e., the data sets with no missing features. In this paper, an effort has been made to check the effectiveness of semi-supervised clustering when applied to incomplete data sets. The novelty of this approach is that it considers the missing features along with available knowledge (labels) of the data set. The linear interpolation imputation technique initially imputes the missing features of the data set, thus completing the data set. A semi-supervised clustering is now employed on this complete data set, and missing features are regularly updated within the clustering process. In the proposed work, the labeled percentage range used is 30, 40, 50, and 60% of the total data. Data is further altered by arbitrarily eliminating certain features of its components, which makes the data incomplete with partial labeling. The proposed algorithm utilizes both labeled and unlabeled data, along with certain missing values in the data. The proposed algorithm is evaluated using three performance indices, namely the misclassification rate, random index metric, and error rate. Despite the additional missing features, the proposed algorithm has been successfully implemented on real data sets and showed better/competing results than well-known standard semi-supervised clustering methods.

scholarly journals A General Framework for Mixed and Incomplete Data Clustering Based on Swarm Intelligence Algorithms

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 786
Author(s):  
Yenny Villuendas-Rey ◽  
Eley Barroso-Cubas ◽  
Oscar Camacho-Nieto ◽  
Cornelio Yáñez-Márquez
Keyword(s):  
Swarm Intelligence ◽  
Data Clustering ◽  
Incomplete Data ◽  
Missing Values ◽  
Clustering Algorithms ◽  
Bat Algorithm ◽  
Hybrid Features ◽  
Bee Colony ◽  
Learning Tasks ◽  
Clustering Data

Swarm intelligence has appeared as an active field for solving numerous machine-learning tasks. In this paper, we address the problem of clustering data with missing values, where the patterns are described by mixed (or hybrid) features. We introduce a generic modification to three swarm intelligence algorithms (Artificial Bee Colony, Firefly Algorithm, and Novel Bat Algorithm). We experimentally obtain the adequate values of the parameters for these three modified algorithms, with the purpose of applying them in the clustering task. We also provide an unbiased comparison among several metaheuristics based clustering algorithms, concluding that the clusters obtained by our proposals are highly representative of the “natural structure” of data.

On Fuzzy Non-Metric Model for Data with Tolerance and its Application to Incomplete Data Clustering

2016 ◽  
Vol 20 (4) ◽  
pp. 571-579 ◽  
Author(s):  
Yasunori Endo ◽  
◽  
Tomoyuki Suzuki ◽  
Naohiko Kinoshita ◽  
Yukihiro Hamasuna ◽  
...  
Keyword(s):  
Data Clustering ◽  
Incomplete Data ◽  
Clustering Algorithm ◽  
Uncertain Data ◽  
Data Sets ◽  
Membership Degree ◽  
Clustering Methods ◽  
Clustering Method ◽  
Numerical Examples ◽  
Metric Model

The fuzzy non-metric model (FNM) is a representative non-hierarchical clustering method, which is very useful because the belongingness or the membership degree of each datum to each cluster can be calculated directly from the dissimilarities between data and the cluster centers are not used. However, the original FNM cannot handle data with uncertainty. In this study, we refer to the data with uncertainty as “uncertain data,” e.g., incomplete data or data that have errors. Previously, a methods was proposed based on the concept of a tolerance vector for handling uncertain data and some clustering methods were constructed according to this concept, e.g. fuzzyc-means for data with tolerance. These methods can handle uncertain data in the framework of optimization. Thus, in the present study, we apply the concept to FNM. First, we propose a new clustering algorithm based on FNM using the concept of tolerance, which we refer to as the fuzzy non-metric model for data with tolerance. Second, we show that the proposed algorithm can handle incomplete data sets. Third, we verify the effectiveness of the proposed algorithm based on comparisons with conventional methods for incomplete data sets in some numerical examples.

scholarly journals Comparison of Algorithms for Clustering Incomplete Data

2014 ◽  
Vol 39 (2) ◽  
pp. 107-127 ◽  
Author(s):  
Artur Matyja ◽  
Krzysztof Siminski
Keyword(s):  
Data Analysis ◽  
Incomplete Data ◽  
Missing Values ◽  
Real Data ◽  
Complete Data ◽  
The Other ◽  
Data Sets ◽  
Missing Value ◽  
Comparison Of Algorithms ◽  
New Algorithms

Abstract The missing values are not uncommon in real data sets. The algorithms and methods used for the data analysis of complete data sets cannot always be applied to missing value data. In order to use the existing methods for complete data, the missing value data sets are preprocessed. The other solution to this problem is creation of new algorithms dedicated to missing value data sets. The objective of our research is to compare the preprocessing techniques and specialised algorithms and to find their most advantageous usage.

scholarly journals CLUSTERING INCOMPLETE SPECTRAL DATA WITH ROBUST METHODS

2017 ◽  
Vol XLII-3/W3 ◽  
pp. 13-17
Author(s):  
S. Äyrämö ◽  
I. Pölönen ◽  
M. A. Eskelinen
Keyword(s):  
Incomplete Data ◽  
Missing Values ◽  
Robust Statistics ◽  
Hyperspectral Image ◽  
Underlying Structure ◽  
Clustering Methods ◽  
Full Data ◽  
Robust Clustering ◽  
Data Cubes ◽  
Classical Statistics

Missing value imputation is a common approach for preprocessing incomplete data sets. In case of data clustering, imputation methods may cause unexpected bias because they may change the underlying structure of the data. In order to avoid prior imputation of missing values the computational operations must be projected on the available data values. In this paper, we apply a robust nan-K-spatmed algorithm to the clustering problem on hyperspectral image data. Robust statistics, such as multivariate medians, are more insensitive to outliers than classical statistics relying on the Gaussian assumptions. They are, however, computationally more intractable due to the lack of closed-form solutions. We will compare robust clustering methods on the bands incomplete data cubes to standard K-means with full data cubes.

scholarly journals A COMPARISON OF CLUSTERING BY IMPUTATION AND SPECIAL CLUSTERING ALGORITHMS ON THE REAL INCOMPLETE DATA

2020 ◽  
Vol 13 (2) ◽  
pp. 65-75
Author(s):  
Ridho Ananda ◽  
Atika Ratna Dewi ◽  
Nurlaili Nurlaili
Keyword(s):  
Expectation Maximization ◽  
Incomplete Data ◽  
Missing Values ◽  
Clustering Algorithms ◽  
Distance Estimation ◽  
Soft Constraints ◽  
Fuzzy C Means ◽  
Environmental Performance Index ◽  
Silhouette Index ◽  
Value Decomposition

The existence of missing values will really inhibit process of clustering. To overcome it, some of scientists have found several solutions. Both of them are imputation and special clustering algorithms. This paper compared the results of clustering by using them in incomplete data. K-means algorithms was utilized in the imputation data. The algorithms used were distribution free multiple imputation (DFMI), Gabriel eigen (GE), expectation maximization-singular value decomposition (EM-SVD), biplot imputation (BI), four algorithms of modified fuzzy c-means (FCM), k-means soft constraints (KSC), distance estimation strategy fuzzy c-means (DESFCM), k-means soft constraints imputed-observed (KSC-IO). The data used were the 2018 environmental performance index (EPI) and the simulation data. The optimal clustering on the 2018 EPI data would be chosen based on Silhouette index, where previously, it had been tested its capability in simulation dataset. The results showed that Silhouette index have the good capability to validate the clustering results in the incomplete dataset and the optimal clustering in the 2018 EPI dataset was obtained by k-means using BI where the silhouette index and time complexity were 0.613 and 0.063 respectively. Based on the results, k-means by using BI is suggested processing clustering analysis in the 2018 EPI dataset.

scholarly journals MODIFIED POSSIBILISTIC FUZZY C-MEANS ALGORITHM FOR CLUSTERING INCOMPLETE DATA SETS

2021 ◽  
Vol 61 (2) ◽  
pp. 364-377
Author(s):  
. Rustam ◽  
Koredianto Usman ◽  
Mudyawati Kamaruddin ◽  
Dina Chamidah ◽  
. Nopendri ◽  
...  
Keyword(s):  
Experimental Data ◽  
Incomplete Data ◽  
Missing Values ◽  
Complete Data ◽  
Noise Sensitivity ◽  
Data Sets ◽  
Fuzzy C Means ◽  
Number Of Iterations ◽  
Fuzzy C Means Algorithm

A possibilistic fuzzy c-means (PFCM) algorithm is a reliable algorithm proposed to deal with the weaknesses associated with handling noise sensitivity and coincidence clusters in fuzzy c-means (FCM) and possibilistic c-means (PCM). However, the PFCM algorithm is only applicable to complete data sets. Therefore, this research modified the PFCM for clustering incomplete data sets to OCSPFCM and NPSPFCM with the performance evaluated based on three aspects, 1) accuracy percentage, 2) the number of iterations, and 3) centroid errors. The results showed that the NPSPFCM outperforms the OCSPFCM with missing values ranging from 5% − 30% for all experimental data sets. Furthermore, both algorithms provide average accuracies between 97.75%−78.98% and 98.86%−92.49%, respectively.

A Joint Optimization Framework Integrated with Biological Knowledge for Clustering Incomplete Gene Expression Data

2021 ◽  
Author(s):  
Dan Li ◽  
Hong Gu ◽  
Qiaozhen Chang ◽  
Jia Wang ◽  
Pan Qin
Keyword(s):  
Gene Expression ◽  
Gene Expression Data ◽  
Missing Values ◽  
Clustering Algorithms ◽  
Joint Optimization ◽  
Gene Clustering ◽  
Biological Knowledge ◽  
Data Sets ◽  
Expression Data ◽  
Optimization Framework

Abstract Clustering algorithms have been successfully applied to identify co-expressed gene groups from gene expression data. Missing values often occur in gene expression data, which presents a challenge for gene clustering. When partitioning incomplete gene expression data into co-expressed gene groups, missing value imputation and clustering are generally performed as two separate processes. These two-stage methods are likely to result in unsuitable imputation values for clustering task and unsatisfying clustering performance. This paper proposes a multi-objective joint optimization framework for clustering incomplete gene expression data that addresses this problem. The proposed framework can impute the missing expression values under the guidance of clustering, and therefore realize the synergistic improvement of imputation and clustering. In addition, gene expression similarity and gene semantic similarity extracted from the Gene Ontology are combined, as the form of functional neighbor interval for each missing expression value, to provide reasonable constraints for the joint optimization framework. Experiments on several benchmark data sets confirm the effectiveness of the proposed framework.

Missing Values Compensation in Duplicates Detection Using Hot Deck

2021 ◽  
Author(s):  
Abdulrazzak Ali ◽  
Nurul A. Emran ◽  
Siti A. Asmai
Keyword(s):  
Performance Improvement ◽  
Incomplete Data ◽  
Missing Values ◽  
Detection Method ◽  
Data Sets ◽  
Data Set ◽  
Removal Process ◽  
Matching Process ◽  
A Performance

Abstract Duplicate record is a known problem within the datasets especially within databases of huge volumes. The accuracy of duplicates detection determines the efficiency of the duplicates removal process. Unfortunately, the effort to detect duplicates becomes more challenging due to the presence of missing values within the records. This is because, during the clustering and matching process, missing values can cause records that are similar to be assigned in a wrong group, causing the duplicates left undetected. In this paper, we present how duplicates detection can be improved even though missing values are present within a data set using our Duplicates Detection within the Incomplete Data set (DDID) method. We hypothetically add the missing values to the key attributes of two datasets under study, using an arbitrary pattern to simulate both complete and incomplete data sets. We analyze the results to evaluate the performance of duplicates detection using the Hot Deck method to compensate for the missing values in the key attributes. We hypothesize that by using Hot Deck, there is a performance improvement in duplicates detection. The performance of the DDID is compared with an early duplicates detection method (called DuDe) in terms of its accuracy and speed. The findings of the experiment show that, even though the data sets are incomplete, DDID is capable to offer better accuracy and faster duplicates detection as compared to a benchmark method (called DuDe). The results of this study contribute to duplicates detection under incomplete data sets constraint.

Hard c-Means Using Quadratic Penalty-Vector Regularization for Uncertain Data

2012 ◽  
Vol 16 (7) ◽  
pp. 831-840 ◽  
Author(s):  
Yasunori Endo ◽  
◽  
Arisa Taniguchi ◽  
Yukihiro Hamasuna ◽  
◽  
...  
Keyword(s):  
Missing Values ◽  
Clustering Algorithm ◽  
Clustering Algorithms ◽  
Uncertain Data ◽  
Unsupervised Classification ◽  
Real Space ◽  
Clustering Methods ◽  
Cluster Number ◽  
Numerical Examples ◽  
Classification Technique

Clustering is an unsupervised classification technique for data analysis. In general, each datum in real space is transformed into a point in a pattern space to apply clustering methods. Data cannot often be represented by a point, however, because of its uncertainty, e.g., measurement error margin and missing values in data. In this paper, we will introduce quadratic penalty-vector regularization to handle such uncertain data using Hard c-Means (HCM), which is one of the most typical clustering algorithms. We first propose a new clustering algorithm called hard c-means using quadratic penalty-vector regularization for uncertain data (HCMP). Second, we propose sequential extraction hard c-means using quadratic penalty-vector regularization (SHCMP) to handle datasets whose cluster number is unknown. Furthermore, we verify the effectiveness of our proposed algorithms through numerical examples.

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