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A Dendrite Method for Cluster Analysis



A method for identifying clusters of points in a multidimensional Euclidean space is described and its application to taxonomy considered. It reconciles, in a sense, two different approaches to the investigation of the spatial relationships between the points, viz., the agglomerative and the divisive methods. A graph, the shortest dendrite of Florek etal. (1951a), is constructed on a nearest neighbour basis and then divided into clusters by applying the criterion of minimum within cluster sum of squares. This procedure ensures an effective reduction of the number of possible splits. The method may be applied to a dichotomous division, but is perfectly suitable also for a global division into any number of clusters. An informal indicator of the "best number" of clusters is suggested. It is a"variance ratio criterion" giving some insight into the structure of the points. The method is illustrated by three examples, one of which is original. The results obtained by the dendrite method are compared with those obtained by using the agglomerative method or Ward (1963) and the divisive method of Edwards and Cavalli-Sforza (1965).
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... A higher score implies better performance. It is also known as the Variance Ratio Criterion [11]. It is calculated using the equation given below, of the clusters by a human expert or user. ...
... Whereas, clusters are evaluated based on similarity or dissimilarity measures where ground truths are unknown. One of the most popular cluster evaluation metrics Silhouette Coefficient [10], Calinski-Harabasz Index [11] and Davies Bouldin Index [12] are considered in this research. The analysis and comparison based on both datasets are as follows: According to the values of the cluster evaluation metrics mentioned in III the performance orders are as follows: ...
Conference Paper
Customer segmentation is a process that divides customers into groups based on common characteristics. The customer segmentation problem belongs to the domain of unsupervised learning, more specifically clustering. The effectiveness of customer segmentation distinctly depends on the chosen clustering algorithm. Moreover, the efficacy of a clustering algorithm is highly dependent on the dataset, type of data, utilised subspaces, and complexity, etc. However, different e-commerce or internet-based businesses collect and utilise their customer data differently and even the slightest difference in data might require a different clustering algorithm for effective customer segmentation. In this paper, we propose a system which consists of two modules, an unsupervised module and a supervised module. The unsupervised module will utilise unlabelled customer data and apply different categories of unsupervised clustering algorithms to find the most suitable algorithm for a given dataset. We use the acquired results to convert the unlabelled customer data into labelled data. After training a classification model using the labelled data, the supervised module can identify the groups of new customers using the trained model without further clustering. This system will work as a customer segmentation and identification system which will help businesses take data-driven decisions more efficiently.
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... Because FlowSOM requires knowledge about the final number of clusters, it was set to 24 (as the number of cell types identified by experts). The results were then compared in terms of the Calinski-Harabasz Index [20], Davies-Bouldin Index [21], and the number of clusters found (ClusterX and PARC). ...
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A procedure for forming hierarchical groups of mutually exclusive subsets, each of which has members that are maximally similar with respect to specified characteristics, is suggested for use in large-scale (n > 100) studies when a precise optimal solution for a specified number of groups is not practical. Given n sets, this procedure permits their reduction to n − 1 mutually exclusive sets by considering the union of all possible n(n − 1)/2 pairs and selecting a union having a maximal value for the functional relation, or objective function, that reflects the criterion chosen by the investigator. By repeating this process until only one group remains, the complete hierarchical structure and a quantitative estimate of the loss associated with each stage in the grouping can be obtained. A general flowchart helpful in computer programming and a numerical example are included.
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