Benchmarking distance-based partitioning methods for mixed-type data

Clustering mixed-type data, that is, observation by variable data that consist of both continuous and categorical variables poses novel challenges. Foremost among these challenges is the choice of the most appropriate clustering method for the data. This paper presents a benchmarking study comparing eight distance-based partitioning methods for mixed-type data in terms of cluster recovery performance. A series of simulations carried out by a full factorial design are presented that examined the effect of a variety of factors on cluster recovery. The amount of cluster overlap, the percentage of categorical variables in the data set, the number of clusters and the number of observations had the largest effects on cluster recovery and in most of the tested scenarios. KAMILA, K-Prototypes and sequential Factor Analysis and K-Means clustering typically performed better than other methods. The study can be a useful reference for practitioners in the choice of the most appropriate method

Beyond pairwise clustering

We consider the problem of clustering in domains where the affinity relations are not dyadic (pairwise), but rather triadic, tetradic or higher. The problem is an instance of the hypergraph partitioning problem. We propose a two-step algorithm for solving this problem. In the first step we use a novel scheme to approximate the hypergraph using a weighted graph. In the second step a spectral partitioning algorithm is used to partition the vertices of this graph. The algorithm is capable of handling hyperedges of all orders including order two, thus incorporating information of all orders simultaneously. We present a theoretical analysis that relates our algorithm to an existing hypergraph partitioning algorithm and explain the reasons for its superior performance. We report the performance of our algorithm on a variety of computer vision problems and compare it to several existing hypergraph partitioning algorithms

Multiple Imputation Ensembles (MIE) for dealing with missing data

Missing data is a significant issue in many real-world datasets, yet there are no robust methods for dealing with it appropriately. In this paper, we propose a robust approach to dealing with missing data in classification problems: Multiple Imputation Ensembles (MIE). Our method integrates two approaches: multiple imputation and ensemble methods and compares two types of ensembles: bagging and stacking. We also propose a robust experimental set-up using 20 benchmark datasets from the UCI machine learning repository. For each dataset, we introduce increasing amounts of data Missing Completely at Random. Firstly, we use a number of single/multiple imputation methods to recover the missing values and then ensemble a number of different classifiers built on the imputed data. We assess the quality of the imputation by using dissimilarity measures. We also evaluate the MIE performance by comparing classification accuracy on the complete and imputed data. Furthermore, we use the accuracy of simple imputation as a benchmark for comparison. We find that our proposed approach combining multiple imputation with ensemble techniques outperform others, particularly as missing data increases

Similarity networks for classification: a case study in the Horse Colic problem

This paper develops a two-layer neural network in which the neuron model computes a user-defined similarity function between inputs and weights. The neuron transfer function is formed by composition of an adapted logistic function with the mean of the partial input-weight similarities. The resulting neuron model is capable of dealing directly with variables of potentially different nature (continuous, fuzzy, ordinal, categorical). There is also provision for missing values. The network is trained using a two-stage procedure very similar to that used to train a radial basis function (RBF) neural network. The network is compared to two types of RBF networks in a non-trivial dataset: the Horse Colic problem, taken as a case study and analyzed in detail.Postprint (published version