InitKmix -- A Novel Initial Partition Generation Algorithm for Clustering Mixed Data using k-means-based Clustering

Clustering algorithm for mixed datasets using density peaks and Self-Organizing Generative Adversarial Networks

Clustering algorithms play a pivotal role in data mining, offering powerful tools for uncovering hidden patterns and structures within datasets. These algorithms aim to divide data points into coherent groups based on similarities or dissimilarities, making it easier to explore and understand complex data. Clustering algorithms typically rely on similarity measures to assess the likeness between data points. Consequently, selecting a suitable similarity measure is crucial for achieving satisfactory clustering outcomes. However, this decision can pose significant challenges, especially for non-experts, given the plethora of similarity measures available in the literature and their performance which is closely linked to the specific dataset, clustering algorithm, and cluster validity index employed. This difficulty is even more important when considering mixed data clustering. Mixed data refers to heterogeneous data characterized by both numerical and categorical attributes. In such a context, the same similarity measure cannot be used for both types of attributes due to their different nature. Commonly, two similarity measures are combined, one for numerical attributes and one for categorical attributes. This adds a layer of complexity to the problem since it requires the selection of two similarity measures instead of just one. This paper introduces SIMREC, a similarity measure recommendation system for mixed data clustering. The system uses meta-learning to mine the relationship between dataset characteristics and similarity measures performances for different mixed data clustering algorithms and cluster validity indices. Therefore, given a mixed dataset, a mixed data clustering algorithm, and a cluster validity index, the system can recommend suitable pairs of numerical and categorical similarity measures based on the characteristics of the dataset. We implemented the proposed system using 130 pairs of similarity measures (10 numerical and 13 categorical), 4 commonly used mixed data clustering algorithms (K-Prototypes, LSH-K-Prototypes, K-Medoids, and Hierarchical Clustering), and three cluster validity indices (Silhouette, Clustering Accuracy, and Adjusted Rand Index). Our experiments on 185 publicly available mixed datasets show that the pairs of similarity measures recommended by SIMREC outperform the baseline pairs, including classically used pairs of similarity measures in the literature.

Nowadays many applications generate mixed data objects consisting of numerical and categorical attributes. Simultaneously dealing with mixed objects is more challenging and various approaches convert one type to another one to face this issue. But in many cases this leads to information loss. Therefore integrating categorical and numerical attributes sounds reasonable since it keeps the original format of any attribute. In this paper we focus on clustering and especially density-based clustering as one of the well-known clustering approaches well-performed on arbitrary shape clusters. Density-based clustering algorithms require a distance measure to discover dense regions. Therefore we introduce the distance hierarchy as a distance measure appropriate for both categorical and numerical attributes. However setting the parameters regarding any parametric clustering algorithm could be another issue. Therefore we employ minimum description length principle to automate this process.

Most clustering algorithms have been designed only for pure numerical or pure categorical data sets, while nowadays many applications generate mixed data. It raises the question how to integrate various types of attributes so that one could efficiently group objects without loss of information. It is already well understood that a simple conversion of categorical attributes into a numerical domain is not sufficient since relationships between values such as a certain order are artificially introduced. Leveraging the natural conceptual hierarchy among categorical information, concept trees summarize the categorical attributes. In this paper, we introduce the algorithm ClicoT (CLustering mixed-type data Including COncept Trees) as reported by Behzadi et al. (Advances in Knowledge Discovery and Data Mining, Springer, Cham, 2019) which is based on the minimum description length principle. Profiting of the conceptual hierarchies, ClicoT integrates categorical and numerical attributes by means of a MDL-based objective function. The result of ClicoT is well interpretable since concept trees provide insights into categorical data. Extensive experiments on synthetic and real data sets illustrate that ClicoT is noise-robust and yields well-interpretable results in a short runtime. Moreover, we investigate the impact of concept hierarchies as well as various data characteristics in this paper.

<span>Clustering is a significant approach in data mining, which seeks to find groups or clusters of data. Both numeric and categorical features are frequently used to define the data in real-world applications. Several different clustering algorithms are proposed for the numerical and categorical datasets. In clustering algorithms, the quality of clustering results is evaluated using cluster validation. This paper proposes an efficient clustering algorithm for mixed numerical and categorical data using re-clustering and cluster validation. Initially, the mixed dataset is clustered with four traditional clustering algorithms like expectation-maximization (EM), hierarchical cluster (HC), k-means (KM), and self-organizing map (SOM). These four algorithms are validated, and the best algorithm is selected for re-clustering. It is an iterative process for improving the quality of cluster results. The incorrectly clustered data is iteratively re-clustered and evaluated based on the cluster validation. The performance of the proposed clustering method is evaluated with a real-time dataset in terms of purity, normalized mutual information, rand index, precision, and recall. The experimental results have shown that the proposed reclust algorithm achieves better performance compared to other clustering algorithms.</span>

Data mining discloses hidden, previously unknown, and potentially useful information from large amounts of data. As comparison to the traditional statistical and machine learning data analysis techniques, data mining emphasizes to provide a convenient and complete environment for the data analysis. Data mining has become a popular technology in analyzing complex data. Clustering is one of the data mining core techniques. In the field of data mining and data clustering, it is a highly desirable task to perform cluster analysis on large data sets with mixed numeric, categorical, ordinal, and ratio-scaled with binary and nominal values. However, most already available data merging and grouping through clustering algorithms are effective for the numeric data rather than the mixed data set. For this purpose, this paper makes efforts to present a new amalgamation algorithm for these mixed data sets by modifying the common cost function, trace of the within cluster dispersion matrix. The genetic algorithm (GA) is used to optimize the new cost function to obtain valid clustering result. We can compare and analyze that the GA-based clustering algorithm is feasible for the high-dimensional data sets with mixed data values that are obtained in real life results. Core Idea of Our Paper: By this paper, we try to describe a technique for estimating the cost function metrics from mixed numeric, categorical and other type databases by using an uncertain grade-of-membership clustering model with the efficiency of Genetic Algorithm. This technique can be applied to the problem of opportunity analysis for business decision-making. This general approach could be adapted to many other applications where a decision agent needs to assess the value of items from a set of opportunities with respect to a reference set representing its business. For processing numeric attributes, instead of generalizing them, a prototype may be developed for experiments with synthetic and real data sets, and comparison with those of the traditional approaches. The results confirmed the feasibility of the framework and the superiority of the extended techniques.

Microarray data are a rich source of information, containing the collected expression values of thousands of genes for well defined states of a cell or tissue. Vast amounts of data (thousands of arrays) are publicly available and ready for analysis, e.g. to scrutinise correlations between genes at the level of gene expression. The large variety of arrays available makes it possible to combine different independent experiments to extract new knowledge. Starting with a large set of data, relevant information can be isolated for further analysis. To extract the required information from data sets of such size and complexity requires an appropriate and powerful analysis method. In this study, we chose to use an unsupervised hierarchical clustering algorithm, Chaotic Map Clustering (CMC), in a coupled two-way approach to analyse such data. However, the clustering approach is intrinsically difficult, both in terms of the unknown structure of the data and interpretation of the clustering results. It is therefore critical to evaluate the quality of any unsupervised procedure for such a complex set of data and to validate the clustering results, separating those clusters that are due simply to noise or statistical fluctuations. We used a resampling method to perform this validation. The resampling procedure applies the clustering algorithm to a large number of random sub-samples of the original data matrix and, consequently, the whole process becomes computationally intensive and time consuming. Using Grid technology, we show that we can drastically speed up this process by distributing the clustering of each matrix to a separate worker node, and thus retrieve resampling results within a few hours instead of several days. Further, we offer an online service to cluster large microarray data sets and conduct the subsequent validation described in this paper.

Modified FDP cluster algorithm and its application in protein conformation clustering analysis

One of the major drawbacks of OFDM system is the high peak-to-average power ratio (PAPR). This high PAPR causes nonlinear distortion of the high power amplifier (HPA). Among the studies for PAPR reduction, the partial transmit sequence (PTS) is an attractive technique to prevent nonlinear distortion. However, it causes high computational complexity. Moreover, although the random sub-block partition method can obtain the optimum PAPR reduction, it is difficult to design the random sub-block partition method in a systematic manner. In this paper, we propose a new systematic sub-block partition method which shows low computational complexity and effective PAPR reduction. Simulation results show that the PAPR performance of the proposed PTS is closely similar to the random partitioning PTS, while it has low computational complexity.

In the field of cluster analysis, the fuzzy k-means, k-modes and k-prototypes algorithms were designed for numerical, categorical and mixed data sets respectively. However, all the above algorithms assume that each feature of the samples plays an uniform contribution for cluster analysis. To consider the particular contributions of different features, a novel feature weighted fuzzy clustering algorithm is proposed in this paper, in which the ReliefF algorithm is used to assign the weights for every feature. By weighting the features of samples, the above three clustering algorithms can be unified, and better classification results can be also achieved. The experimental results with various real data sets illustrate the effectiveness of the proposed algorithm.

An efficient heuristic algorithm for solving cluster problems associated with partitioning of power networks is presented. The algorithm is divided into two stages. The first stage creates an initial partition based on the electrical distance between system buses. The second stage involves interchanging pairs of buses among the various clusters of the initial partition. The first stage solves the placement problem of n connected buses in an r-dimensional Euclidean space; such a problem is reduced to finding r eigenvectors of a connectivity matrix, defined as the bus admittance matrix. The second stage is based on a node interchange technique. The node interchange is an iterative heuristic method that can be used to improve an initial partition. The method moves one bus at a time, from one cluster of the initial partition to another, in an attempt to maximize the total electrical distance between clusters of the final partition. Applications of the proposed algorithm to both small and medium-size power systems are illustrated.

Clustering, in data mining, is useful for discovering groups and identifying interesting distributions in the underlying data. Traditional clustering algorithms either favor clusters with spherical shapes and similar sizes, or are very fragile in the presence of outliers. We propose a new clustering algorithm called CURE that is more robust to outliers, and identifies clusters having non-spherical shapes and wide variances in size. CURE achieves this by representing each cluster by a certain fixed number of points that are generated by selecting well scattered points from the cluster and then shrinking them toward the center of the cluster by a specified fraction. Having more than one representative point per cluster allows CURE to adjust well to the geometry of non-spherical shapes and the shrinking helps to dampen the effects of outliers. To handle large databases, CURE employs a combination of random sampling and partitioning. A random sample drawn from the data set is first partitioned and each partition is partially clustered. The partial clusters are then clustered in a second pass to yield the desired clusters. Our experimental results confirm that the quality of clusters produced by CURE is much better than those found by existing algorithms. Furthermore, they demonstrate that random sampling and partitioning enable CURE to not only outperform existing algorithms but also to scale well for large databases without sacrificing clustering quality.

The first synchronization clustering (SynC) algorithm based on an extensive Kuromato model was presented in 2010. In 2017, an effective synchronization clustering (ESynC) algorithm, inspired by SynC algorithm and a linear version of Vicsek model, was proposed. When facing complex data distributions, ESynC algorithm may regard an irregular and whole cluster as some micro-clusters. To conquer this shortcoming, a combined clustering algorithm based on ESynC algorithm and a merging judgement process of micro-clusters (CESynC) is presented. CESynC algorithm first uses ESynC algorithm to detect clusters or micro-clusters, then merges those conjoint micro-clusters by using a merging judgement process. For some datasets that ESynC and SynC cannot detect correct clusters, CESynC can capture natural clusters. From the simulation experiments, we observe that CESynC can get better (or the same) clustering results than (or as) that of ESynC in many cases. We also observe that the clustering results of CESynC and ESynC are often better than that of SynC. Therefore, we can say CESynC can often obtain better clustering quality than ESynC and SynC in some kinds of datasets. Further comparison experiments with some classical clustering algorithms demonstrate the clustering effect of CESynC.

We propose a Seed-based Inter-Domain Supervised (IDS) framework to handle possibly diverse data formats, mixed-type attributes and different sources of data. This approach can be used for combining diverse representations of the data, in particular where data comes from different sources, some of which may be unreliable or uncertain, or for exploiting optional external concept set labels to guide the clustering of the main data set in its original domain. Unlike semi-supervised clustering, our approach exploits the synergy between different domains instead of external labels. Also ensemble clustering and our proposed IDS clustering are different mechanisms with distinct goals: (i) the former aims to combine independent clustering results from many independent subsets sampled from the same data set or from different clustering algorithm results on the same data set, into one consensus, (ii) while the latter (IDS) aims to exploit a mutual synergy between different data domains or sources to guide the clustering in these different domains or sources. Our preliminary results in clustering data with mixed numerical and categorical attributes show that the proposed IDS framework gives better clustering results in the categorical domain. Thus the seeds or the constraints obtained from clustering the numerical domain give an additional knowledge to the categorical clustering algorithm. Additional results show that our approach outperforms clustering either domain on its own or clustering both domains converted to the same target domain.

Data mining means extracting knowledge from big amount of data. Data mining techniques include clustering, Association, classification, Prediction, etc. Clustering is an unsupervised technique that is useful for finding groups in data. Most traditional clustering algorithms are limited to handling datasets that contain either numeric or categorical attributes. However, datasets with mixed numeric and categorical types of attributes are common in real life data mining applications. The K-Prototype clustering algorithm is one of the most important algorithms for clustering this type of data. This algorithm produces the locally optimal solution that is dependent on the initial prototype selection. This paper presents a new algorithm for data clustering based on K-Prototype and cuckoo search optimization to attain the global optimization.