Clustering Mixed Data Using Spherical Representaion

<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>

In view of the considerable applications of data clustering techniques in various fields, such as engineering, artificial intelligence, machine learning, clinical medicine, biology, ecology, disease diagnosis, and business marketing, many data clustering algorithms and methods have been developed to deal with complicated data. These techniques include supervised learning methods and unsupervised learning methods such as density-based clustering, K-means clustering, and K-nearest neighbor clustering. This book reviews recently developed data clustering techniques and algorithms and discusses the development of data clustering, including measures of similarity or dissimilarity for data clustering, data clustering algorithms, assessment of clustering algorithms, and data clustering methods recently developed for insurance, psychology, pattern recognition, and survey data.

This paper briefly reports testing the use of multi-dimensional scaling as a method to illuminate the complex pattern of relationships existing between patients in a long-stay psychiatric setting. The results did not support the hypothesis that recently formed rehabilitation groups in the hostel would serve to explain the pattern of relationships between patients. The results did, however, promote a more informed discussion regarding the origin and implications of patient relationships in long-stay psychiatric care, which served to revise staff ideas and options regarding the organization of care. Relationships between long-stay disabled psychiatric patients are notoriously opaque to observers. The use of multi-dimensional scaling helped make them more transparent.

This work aims to expand the knowledge of the area of data analysis through persistence homology and representations of directed graphs. To be specific, we looked for how we can analyze homology cluster groups using agglomerative Hierarchical Clustering algorithms and methods. Additionally, the Wine data, which is offered in R studio, was analyzed using various cluster algorithms such as Hierarchical Clustering, K-Means Clustering, and PAM Clustering. The goal of the analysis was to find out which cluster's method is proper for a given numerical dataset. We tried to find the agglomerative hierarchical clustering method by testing the data that will be the optimal clustering algorithm among these three; K-Means, PAM, and Random Forest methods. By comparing each model's accuracy value with cultivar coefficients, we concluded that K-Means methods are the most helpful when working with numerical variables. On the other hand, PAM clustering and Gower with Random Forest are the most beneficial approaches when using categorical variables. These tests can determine the optimal number of clustering groups, given the data set, and by doing the proper analysis. Using those the project, we can apply our method to several industrial areas such that clinical, business, and others. For example, people can make different groups based on each patient who has a common disease, required therapy, and other things in the clinical society. Additionally, people can expect to get several clustered groups based on the marginal profit, marginal cost, or other economic indicators for the business area.

The mixed data clustering algorithms have been timidly emerging since the end of the last century. One of the last algorithms proposed for this data-type has been KAMILA (KAy-means for MIxed LArge data) algorithm. While the KAMILA has outperformed the previous mixed data algorithms results, it has some gaps. Among them is the definition of numerical and categorical variable weights, which is a user-defined parameter or, by default, equal to one for all features. Hence, we propose an optimization algorithm called Biased Random-Key Genetic Algorithm for Features Weighting (BRKGAFW) to accomplish the weighting of the numerical and categorical variables in the KAMILA algorithm. The experiment relied on six real-world mixed data sets and two baseline algorithms to perform the comparison, which are the KAMILA with default weight definition, and the KAMILA with weight definition done by the traditional genetic algorithm. The results have revealed the proposed algorithm overperformed the baseline algorithms results in all data sets.

Subject. This article discusses the application of the multidimensional scaling method to improve the methods of formation and effective management of a portfolio of securities. Objectives. The article aims to prove the rationality of using the multidimensional scaling method to assess the financial feasibility of including foreign exchange market assets in securities portfolios. Methods. For the study, we used the methods of correlation analysis and multidimensional scaling. Results. The article finds that the use of the multidimensional scaling method helps identify similar features of the assets of the securities market and the foreign exchange market, and confirms the rationality of using this method when assessing the financial feasibility of including foreign exchange market assets in securities portfolios. Conclusions. The article concludes that it is necessary to make changes to the traditional decision-making model in portfolio investment, recognizing the use of multidimensional scaling to assess the economic feasibility of including foreign exchange market assets denominated in the same currency as portfolio assets in securities portfolios as rational.

Stunting is one of the chronic nutritional problems that remains a serious issue in Indonesia, particularly in Bulungan Regency, North Kalimantan. This condition not only affects children's physical growth but also their cognitive development, which has implications for their quality of life and future prospects. This study aims to classify regions based on stunting risk levels to provide a more targeted framework for local governments in setting intervention priorities. The method used is K-Means Clustering, an effective data mining algorithm for non-hierarchical data clustering. The data used are secondary data from the Bulungan District Bappeda in 2021, covering 81 locations with 29 stunting risk factor variables. The analysis process was conducted through data processing, centroid initialization, Euclidean distance calculation, and the formation of convergent clusters. The results of the study show the formation of two main clusters: a cluster with moderate vulnerability and a cluster with high vulnerability. The moderate cluster is in a transitional state with fluctuating risks, while the high cluster has low health and sanitation indicators, requiring special attention. These findings indicate that the K-Means method can provide data-driven insights to support stunting prevention policies. This study is expected to serve as a reference for local governments in developing more targeted intervention programs and contribute academically to the application of data mining methods in public health.

The spread of Corono Virus 19 is very fast through effective human-to-human transmission through close contact and respiratory droplets such as coughing or sneezing. Various studies have been conducted to deal with COVID 19, but until now it has not been found how to stop the spread of this virus. Based on data obtained from the covid19.go.id page accessed on January 1, 2021 which was updated by the Ministry of Health, the overall number of confirmed cases was 1,078,314 active cases reaching 175,095 or 16.2% of confirmed cases, recovered 873,221 or 81.0% of cases confirmed, died 29,998 or 2.8% of the confirmed cases. In this study, comparing the two algorithms in the dataset which aims to analyze grouping patterns and determine the best method of data processing. The data used comes from the Ministry of Health, there are 4 attributes including confirmed cases, treatment, recovery and death, in this study only 2 attributes are used, namely confirmed cases and death. From the results of data analysis and processing through a comparison between the K-Means method and the K-Medoids for grouping the spread of the corona 19 virus in Indonesia, with the Davies Boulden index value from the K2 to K9 values, it turns out that the K-Means method gets the smallest value at the K-value. 5 is 0.064, while K-Medoids at the k-2 value is 0.411. Thus, from the two methods used, it can be found that the best method for clustering the spread of the corona 19 virus outbreak in Indonesia is the K-Means method.

PurposeThe K-means (KM) clustering algorithm is extremely responsive to the selection of initial centroids since the initial centroid of clusters determines computational effectiveness, efficiency and local optima issues. Numerous initialization strategies are to overcome these problems through the random and deterministic selection of initial centroids. The random initialization strategy suffers from local optimization issues with the worst clustering performance, while the deterministic initialization strategy achieves high computational cost. Big data clustering aims to reduce computation costs and improve cluster efficiency. The objective of this study is to achieve a better initial centroid for big data clustering on business management data without using random and deterministic initialization that avoids local optima and improves clustering efficiency with effectiveness in terms of cluster quality, computation cost, data comparisons and iterations on a single machine.Design/methodology/approachThis study presents the Normal Distribution Probability Density (NDPD) algorithm for big data clustering on a single machine to solve business management-related clustering issues. The NDPDKM algorithm resolves the KM clustering problem by probability density of each data point. The NDPDKM algorithm first identifies the most probable density data points by using the mean and standard deviation of the datasets through normal probability density. Thereafter, the NDPDKM determines K initial centroid by using sorting and linear systematic sampling heuristics.FindingsThe performance of the proposed algorithm is compared with KM, KM++, Var-Part, Murat-KM, Mean-KM and Sort-KM algorithms through Davies Bouldin score, Silhouette coefficient, SD Validity, S_Dbw Validity, Number of Iterations and CPU time validation indices on eight real business datasets. The experimental evaluation demonstrates that the NDPDKM algorithm reduces iterations, local optima, computing costs, and improves cluster performance, effectiveness, efficiency with stable convergence as compared to other algorithms. The NDPDKM algorithm minimizes the average computing time up to 34.83%, 90.28%, 71.83%, 92.67%, 69.53% and 76.03%, and reduces the average iterations up to 40.32%, 44.06%, 32.02%, 62.78%, 19.07% and 36.74% with reference to KM, KM++, Var-Part, Murat-KM, Mean-KM and Sort-KM algorithms.Originality/valueThe KM algorithm is the most widely used partitional clustering approach in data mining techniques that extract hidden knowledge, patterns and trends for decision-making strategies in business data. Business analytics is one of the applications of big data clustering where KM clustering is useful for the various subcategories of business analytics such as customer segmentation analysis, employee salary and performance analysis, document searching, delivery optimization, discount and offer analysis, chaplain management, manufacturing analysis, productivity analysis, specialized employee and investor searching and other decision-making strategies in business.

Subsidized fertilizer is a form of the government's commitment to increasing agricultural productivity, increasing food production and sustainable food security, now the price of fertilizer in Bojonegoro district is getting more expensive, this encourages researchers to raise it as the title of the thesis. The purpose of the K-Means Clustering method is to increase knowledge and understanding of computer-based systems. The K-Means algorithm is an iterative clustering algorithm that partitions datasets into a number of K Clusters that have been set at the beginning. The K-Means algorithm is simple to implement and execute, relatively fast, adaptable, commonly used in practice. From the problem of clustering subsidized fertilizers in Bojonegoro Regency, it can be solved using the ¬K-Means method. The K-Means algorithm can precisely group large amounts of data. The determination of the central point (centroid) in the initial process of the K-Means algorithm has a significant influence on the cluster yield. Based on the research conducted, the authors tested the best cluster grouping using the Davies Bouldin Index (DBI). It was found that the results of 3 clusters were the best with a DBI value of 0.527 while 4 clusters with a DBI value of 0.649 and 5 clusters with a DBI value of 0.677. The smaller the resulting value in the test, the better the result will be. Meanwhile, the Mean Square Error (MSE) produced in fertilizer clustering is 0.588 and RMSE is 0.962.

Floods are natural events or phenomena that can cause environmental damage, loss of property, psychological effects, and death or casualties. One way to control flooding non-structurally is by mapping areas that are prone to flooding. This study builds a geographic-based information system to map flood-prone areas in Manado City using the K-Means Clustering algorithm. The main objective of this research is to identify and map areas with a high risk of flooding using spatial data. Slope, land cover type, soil type, water discharge (discharge), and rainfall are independent variables that will be used and processed using the K-Means Clustering algorithm. There are four clusters in the mapping results of flood-prone areas, namely: high vulnerability, medium vulnerability, low vulnerability, and not vulnerable. By using the K-Means method, the results obtained are Paal Dua and Wenang sub-districts are high-vulnerability groups, followed by Mapanget, Tuminting, and Singkil subdistricts with medium vulnerability groups. Tikala District is the only area with low vulnerability. Meanwhile, Bunaken, Sario, Wanea, and Malayayang sub-districts are areas that are not potentially prone to flooding.

Residency training programs vary across characteristics such as their didactic and clinical experiences, attributes of the incoming residents, faculty characteristics, research conducted, community service performed by the program, and eventual practice choices of graduates. Which of these characteristics are most salient for evaluating the quality of a program? Elliott1 lists characteristics of graduates, cost—effectiveness, fair and ethical treatment of trainees, and meeting societal needs as important quality indicators. Iverson2 takes a dimensional approach. His dimensions, with metrics, are: intake [U.S. Medical Licensing Examination (USMLE) scores of matched applicants]; customer satisfaction [percentage of available positions filled by match, and percentage filled by U.S. medical school graduates (USMGs)]; residency review committee (RRC) quintile scores; and outcome (specialty board pass rates). The Accreditation Council for Graduate Medical Education (ACGME) recently switched its focus from process variables to outcomes, and is encouraging RRCs to evaluate a program on how well it provides for six core competencies: patient care, clinical science; interpersonal skills and communication, professionalism, practice-based learning and improvement, and systems-based practice.3 In 1997, a task force of the American Association of Directors of Psychiatry Residency Training (AADPRT) developed a survey to define the variables important to determining a program's quality from the psychiatry resident's perspective. The 41-item questionnaire was based on feedback from focus groups of psychiatry residents and program directors and a review of the literature. A total of 180 psychiatry residents from 16 programs completed the survey. Quality of supervision and teaching conferences, respect of faculty for residents, responsiveness of the program to feedback from residents, and morale in the department were the items most important to residents' satisfaction. A detailed description of the construction of the survey and its results was published by Elliott.4 In 1998, the AADPRT's survey was repeated with psychiatry residency directors and heads of major rotations to see whether their values agreed with those of the residents.5 This paper describes the use of multidimensional scaling (MDS) of the survey's results to establish whether there were distinct groupings of program directors with different opinions about the determinants of quality in psychiatry residency programs. These groupings might represent types of psychiatry programs (or market niches) as reflected in the values and priorities of their faculty and directors. Method Multidimensional scaling is an analytic technique frequently used in marketing research to identify the psychological dimensions underlying customers' preferences with respect to multiple variables or features of a product.6 In MDS the difference between clusters or groups of variables is predicted by the distance between the variables in psychological "space," with the dimensionality of the space equal to the number of relevant dimensions underlying the data. These dimensions can be thought of as analogous to the latent constructs derived in factor analysis. The scaling algorithm derives the dimensions and plots the coordinates of the variables in the resulting multidimensional space. MDS is an inherently interpretive procedure—it locates variables on dimensions but requires the investigator to determine whether the dimensions can be intelligibly labeled. Individual Differences Scaling (INDSCAL) is an MDS algorithm that models both the overall dimensions that underlie the perceptions of the group of respondents and individual weights on those dimensions for each respondent, allowing individuals to vary in the importance they attach to each of the dimensions. For example, for one individual, dimension A (the educational resources available, for example) may be highly salient, while dimension B (the administration of the program, for example) is relatively unimportant. For another individual, these priorities may be reversed. By examining the distribution of subject weights one can identify clusters of subjects who share similar values regarding the relative importances of the various dimensions. The questionnaire was sent in late 1998 to all psychiatry residency directors listed in the American Medical Association's 1998–1999 Directory of Accredited Graduate Medical Education (GME) Programs. The faculty members who served as the heads of the inpatient and outpatient psychiatry rotations of each program were also surveyed. These are the two major rotations of psychiatry training programs, and the opinions of the heads of these rotations (henceforth referred to as service chiefs) would most likely represent the dominant values of the program. The survey asked directors and service chiefs to rate how important the 41 items of the questionnaire were in determining the quality of a residency program. The anchors were 1 = least important, 4 = average importance, and 7 = most important. Multidimensional scaling using INDSCAL was done on the survey responses. Solutions in two to six dimensions were generated. Results Of the 186 active programs listed in the GME directory, 117 programs (63%) responded to the survey. There were 234 individual responses from the 117 programs. Of these, 142 (61%) were from program directors and 92 (39%) were from service chiefs who were not identified as directors. For some programs the head of inpatient or outpatient services also served as an associate program director, confirming our supposition that these faculty members represent the administrative backbone of the program. The Pearson correlation between the responses of the residency directors and those of the service chiefs was 0.98 (p < 0.01). We therefore pooled data from both chiefs' and residency directors' responses for the following analysis. The two-dimensional INDSCAL solution was degenerate and was discarded. The solutions in three to six dimensions were inspected for goodness of fit and interpretability. The three-dimensional configuration provided the most interpretable dimensions, and accounted for 46.4% of the variance in the data; higher-dimensional solutions accounted for only slightly more variance. Based on examination of the locations of the items, particularly those that had particularly high or low coordinates in each dimension, the dimensions seemed to correspond to three constructs: "curriculum," "quality of the institution," and "supportiveness of the administration of the program." The three dimensions, and the highest-loading items on each, are given in Table 1.TABLE 1: Three Dimensions of Quality of Psychiatry Residency Programs, Based on Multidimensional Scaling of Responses by Residency Directors and Service Chiefs to a 1998 Questionnaire*Subject weights measure the importance or salience of each dimension to each respondent; they range from 0 (completely ignored) to 1 (overwhelmingly important), and need not sum to 1. In addition, each respondent is assigned a "weirdness' value, which measures the similarity of his or her responses to those of the typical respondent, based on the relative importance of each dimension and the goodness of fit for that respondent. There was a great deal of variation in individual preferences, but no distinct clusters were evident. Notably, although weights for the supportiveness of the administration of the program dimension fell between 0.25 and 0.40 for nearly all respondents, the importance attributed to the dimensions of curriculum and quality of the institution varied extensively across individuals. Figure 1 plots the weights of curriculum and quality of the institution against one another for each respondent. The unshaded polygon encloses data for more typical respondents with less than the median weirdness, represented as circles; the two shaded polygons identify two groups of less typical respondents with more than the median weirdness, represented as crosses. Two respondents in the upper left had extreme (outlier) weirdness values.Figure 1: Subject weights for the "curriculum" and "quality of the institution" dimensions of the three-dimensional INDSCAL solution. The unshaded polygon encloses subjects with less than the median weirdness (based on weights in all three dimensions), represented as circles; the two shaded polygons identify two groups of subjects with greater than median weirdness, represented as crosses. Two subjects in the upper left had extreme (outlier) weirdness values."Weirdness" measures how similar each respondent is to the typical respondent, based on the relative importance of each dimension and the goodness of fit for that respondent.While the most typical respondents gave curriculum weights between 0.3 and 0.6, and quality of the institution weights between 0.2 and 0.4, two groups of respondents displayed different weight patterns. One group (lower right) gave curriculum substantially higher weights than typical (ranging from 0.5 to 0.75); the other group (upper left) gave quality of the institution substantially higher weights than typical (ranging from 0.25 to 0.65). On the average, most respondents' data displayed a continuum of weight patterns in which curriculum was considered to be more important than either quality of the institution or supportiveness of the administration of the program; the respondents with the lowest weirdness scores weighted these dimensions in the proportions 1.3:1:1, respectively. Discussion The three dimensions that emerged from the MDS are consistent with the many suggested quality indicators reviewed above.1,2,3 How might we conceptualize this triad? The dimensions of curriculum and supportiveness reflect two different aspects of the process of residency training. The curriculum dimension describes the content of the educational program; the supportiveness dimension reflects the culture or ambiance within which the training occurs. Residency directors and their faculty seem to differentiate between these two aspects of the program, and value both as indicators of the quality of the program. The dimension of institutional quality includes items reflecting the reputation and resources of the institution as well as items generally considered to be outcomes (i.e., board scores of graduates and graduates' job satisfaction). In this instance, these "outcome" items probably serve as proxies for (and a reflection of) the reputation of the institution and the quality of the residents it attracts, rather than as true outcome measures. This dimension could represent a general context factor, reflecting the quality of the facilities, the faculty, and of the residents themselves. This general factor could itself modify the effects of the process variables either up or down, thereby affecting the expected outcomes. Thus, this dimension may reflect the expectation of program directors and chiefs that equivalent processes (curriculum and supportiveness) could lead to better outcomes if they are provided in the context of a higher-quality institution. Donabedian lists input, process, and product as the dimensions of quality in healthcare.7 Interestingly, product (outcomes) did not emerge as a dimension of the quality of a program. Perhaps residency directors and service chiefs focus on process variables as indicators of quality since it is in the process of residency training that they deal. The neglect of outcome measures may also reflect a philosophy that, while the program is responsible for teaching, it is the residents' responsibility to learn. Outcome measures are highly confounded by the abilities and characteristics of the individual residents and, thus, may not be considered an accurate or reliable measure of the quality of the program per se. The ACGME and others who have begun the move towards outcome evaluation may wish to take this as a word of caution. Outcomes should not be considered in a vacuum. For at least some key stakeholders—the residents and faculty of the program—the context, content, and culture of the program are significant as well. No truly distinct clusters or groups of respondents emerged from the multidimensional scaling of the data. While there may be programs with different missions—programs oriented towards research or community psychiatry, for example—these missions do not seem to result in drastically different definitions of quality. This suggests that there is a core concept of quality that holds across contexts and across missions—consistent with the RRC's model of minimum standards. On the other hand, there seems to be a continuum of individual variation, rather than variation based on group membership. The individual respondents differed widely in the dimensions they considered most important. Since the individuals in this case are the faculty leaders and directors of the programs, these priorities are most likely reflected in the programs as a whole. The individual variation can be usefully segregated into three "market niches," corresponding to the three polygons in Figure 1. Thus we could describe three types of programs: (1) programs in which the quality of the sponsoring institution (context) is paramount, (2) programs in which the quality of the curriculum (content) is paramount, and (3) programs with a more typical weighting of the three dimensions. While there was less variability in the importance attached to the supportiveness (culture) of the program, this should not be construed as lack of salience. Rather, all programs should be alert to the importance of this dimension. Residents, too, vary in the levels of importance they attribute to the various features of a training program.4 The context, content, and culture of a program may provide a good conceptual model of the dimensions along which the market varies. Programs may find it useful to identify and market themselves on the basis of these dimensions. This study focused on only one of the many stakeholder groups of residency programs. The needs and expectations of other stake-holders, such as program funders and employers of a program's graduates, remain to be defined. This study also focused only on psychiatry programs, but the dimensions of context, content, and culture would seem to be potentially applicable to other specialties as well. Repeating the study with other specialties will tell us whether indeed this triad is relevant to the quality of programs across specialties. The method of multidimensional scaling is a novel one for determining quality measures in graduate medical education. Repeated use of this technique, across stakeholders and across specialties, can help elucidate the factors most important to the evaluation of residency programs.

There are many successful experiences employing texture analysis to improve the accuracy and robustness of image segmentation. Usually, per-pixel based texture analysis is required, which involves intensive computation especially for large images. Precomputation and storing of the texture features involves large file space which is not cost effective. To adopt to these novel needs, we propose the use of multidimensional scaling (MDS) technique to reduce the size of per-pixel texture features of an image while preserving the textural discrminiability for segmentation. Per-pixel texture features will create very large dissimilarity matrix, making the solving of MDS intractable. A sampling-based MDS is therefore introduced to tackle the problem with a divide-and-conquer approach. A compression ratio of 1:24 can be achieved with an average error rate lower than 7%. Preliminary experiments on segmentation using the compressed data show satisfactory results as good as using the uncompressed features. We foresee that such a method will allow texture features to be stored and transferred more efficiently on low processing power devices or embedded systems like mobile phones.

The k-means method is a widely used technique for clustering points in Euclidean space. While it is extremely fast in practice, its worst-case running time is exponential in the number of data points. We prove that the k-means method can implicitly solve PSPACE-complete problems, providing a complexity-theoretic explanation for its worst-case running time. Our result parallels recent work on the complexity of the simplex method for linear programming.

In recent years, huge different biological databases have been stored in various locations. Using distinct data sets from multiple sources results in more reliable data analysis. However, it is so difficult to combine heterogeneous data in one single server. The most obvious reasons include data privacy, large data sizes, costs, and different geographical locations of data sources. In this paper, we present two new algorithms for clustering data from multiple remote data sources using kernel k-means. The first algorithm is the center-based algorithm built on k-means algorithm. The second algorithm uses distributed kernel k-means over multiple data sources. In the distributed scheme, clustering methods are executed only on their local data sources themselves. Partial clustering results are synched between data sources. To evaluate performance of our proposed algorithms, we merged all data from different sources into one large data set to perform kernel k-means. The results showed that our center-based algorithm greatly reduced transmission data between data sources while still yielding acceptable clustering results. Our distributed kernel k-means algorithm achieved even better performance. The clustering results are very close to those generated by kernel k-means on one merged data set.