Competición vídeo: ¿cómo puedo saber si el resultado de un clustering es lo suficientemente bueno?

En este vídeo divulgativo se hace una introducción a una de las técnicas de análisis de datos más usada, el clustering. En él, se explica a través de sencillos ejemplos qué es el clustering y cómo se analizan las distintas soluciones que ofrece a través de diferentes índices de validació

Understanding the Evaluation Abilities of External Cluster Validity Indices to Internal Ones

Evaluating internal Cluster Validity Index (CVI) is a critical task in clustering research. Existing studies mainly employ the number of clusters (NC-based method) or external CVIs (external CVIs-based method) to evaluate internal CVIs, which are not always reasonable in all scenarios. Additionally, there is no guideline of choosing appropriate methods to evaluate internal CVIs in different cases. In this paper, we focus on the evaluation abilities of external CVIs to internal CVIs, and propose a novel approach, named external CVI\u27s evaluation Ability MEasurement approach through Ranking consistency (CAMER), to measure the evaluation abilities of external CVIs quantitatively, for assisting in selecting appropriate external CVIs to evaluate internal CVIs. Specifically, we formulate the evaluation ability measurement problem as a ranking consistency task, by measuring the consistency between the evaluation results of external CVIs to internal CVIs and the ground truth performance of internal CVIs. Then, the superiority of CAMER is validated through a real-world case. Moreover, the evaluation abilities of seven popular external CVIs to internal CVIs in six different scenarios are explored by CAMER. Finally, these explored evaluation abilities are validated on four real-world datasets, demonstrating the effectiveness of CAMER

CUBOS: An Internal Cluster Validity Index for Categorical Data

Internal cluster validity index is a powerful tool for evaluating clustering performance. The study on internal cluster validity indices for categorical data has been a challenging task due to the difficulty in measuring distance between categorical attribute values. While some efforts have been made, they ignore the relationship between different categorical attribute values and the detailed distribution information between data objects. To solve these problems, we propose a novel index called Categorical data cluster Utility Based On Silhouette (CUBOS). Specifically, we first make clear the superiority of the paradigm of Silhouette index in exploring the details of clustering results. Then, we raise the Improved Distance metric for Categorical data (IDC) inspired by Category Distance to measure distance between categorical data exactly. Finally, the paradigm of Silhouette index and IDC are combined to construct the CUBOS, which can overcome the aforementioned shortcomings and produce more accurate evaluation results than other baselines, as shown by the experimental results on several UCI datasets

External clustering validity index based on chi-squared statistical test

Clustering is one of the most commonly used techniques in data mining. Its main goal is to group objects into clusters so that each group contains objects that are more similar to each other than to objects in other clusters. The evaluation of a clustering solution is a task carried out through the application of validity indices. These indices measure the quality of the solution and can be classified as either internal that calculate the quality of the solution through the data of the clusters, or as external indices that measure the quality by means of external information such as the class. Generally, indices from the literature determine their optimal result through graphical representation, whose results could be imprecisely interpreted. The aim of this paper is to present a new external validity index based on the chi-squared statistical test named Chi Index, which presents accurate results that require no further interpretation. Chi Index was analyzed using the clustering results of 3 clustering methods in 47 public datasets. Results indicate a better hit rate and a lower percentage of error against 15 external validity indices from the literature.Ministerio de Economía y Competitividad TIN2014-55894-C2-RMinisterio de Economía y Competitividad TIN2017-88209-C2-2-

The Hyperspherical Geometry of Community Detection:Modularity as a Distance

We introduce a metric space of clusterings, where clusterings are described by a binary vector indexed by the vertex-pairs. We extend this geometry to a hypersphere and prove that maximizing modularity is equivalent to minimizing the angular distance to some modularity vector over the set of clustering vectors. In that sense, modularity-based community detection methods can be seen as a subclass of a more general class of projection methods, which we define as the community detection methods that adhere to the following two-step procedure: first, mapping the network to a point on the hypersphere; second, projecting this point to the set of clustering vectors. We show that this class of projection methods contains many interesting community detection methods. Many of these new methods cannot be described in terms of null models and resolution parameters, as is customary for modularity-based methods. We provide a new characterization of such methods in terms of meridians and latitudes of the hypersphere. In addition, by relating the modularity resolution parameter to the latitude of the corresponding modularity vector, we obtain a new interpretation of the resolution limit that modularity maximization is known to suffer from

Ground truth bias in external cluster validity indices

External cluster validity indices (CVIs) are used to quantify the quality of a clustering by comparing the similarity between the clustering and a ground truth partition. However, some external CVIs show a biased behavior when selecting the most similar clustering. Users may consequently be misguided by such results. Recognizing and understanding the bias behavior of CVIs is therefore crucial. It has been noticed that, some external CVIs exhibit a preferential bias towards a larger or smaller number of clusters which is monotonic (directly or inversely) in the number of clusters in candidate partitions. This type of bias is caused by the functional form of the CVI model. For example, the popular Rand Index (RI) exhibits a monotone increasing (NCinc) bias, while the Jaccard Index (JI) index suffers from a monotone decreasing (NCdec) bias. This type of bias has been previously recognized in the literature. In this work, we identify a new type of bias arising from the distribution of the ground truth (reference) partition against which candidate partitions are compared. We call this new type of bias ground truth (GT) bias. This type of bias occurs if a change in the reference partition causes a change in the bias status (e.g., NCinc, NCdec) of a CVI. For example, NCinc bias in the RI can be changed to NCdec bias by skewing the distribution of clusters in the ground truth partition. It is important for users to be aware of this new type of biased behavior, since it may affect the interpretations of CVI results. The objective of this article is to study the empirical and theoretical implications of GT bias. To the best of our knowledge, this is the first extensive study of such a property for external CVIs. Our computational experiments show that 5 of 26 pair-counting based CVIs studied in this paper, which are all functions of the RI, exhibit GT bias. Following the numerical examples, we provide a theoretical analysis of GT bias based on the relatio