Existing (dis)similarity measures for mixed data often ignore data distribution and ordering information along numerical and categorical features, respectively, during distance computation. Additionally, combining numerical and categorical (dis)similarities is often done naively, failing to judiciously assign relative weights. This work introduces a unified dissimilarity measure for mixed data (EDMIX) that addresses these challenges. It employs an entropy-based measure (SEND) for numerical attributes which utilizes intra-attribute inhomogeneity efficiently. A Boltzmann’s entropy-based measure (EDMD) is adopted for categorical features, which effectively handles both nominal and ordinal attributes. Decay of attribute weight is analyzed to determine the threshold weights for numerical and categorical parts. Number of attributes whose weights are above the threshold value in each part decides the mixing proportion of the respective parts. Notably, EDMIX requires no input parameters and is adaptable to diversified mixed data. Experimental results highlight its superiority in terms of cluster quality, accuracy, discrimination ability, and execution time across diverse mixed datasets for clustering applications.

The effectiveness of clustering techniques is significantly influenced by proximity measures irrespective of type of data and categorical data is no exception. Most of the existing proximity measures for categorical data assume that all attributes contribute equally to the distance measurement which is not true. Usually, frequency or probability-based approaches are better equipped in principle to counter this issue by appropriately weighting the attributes based on the intra-attribute statistical information. However, owing to the qualitative nature of categorical features, the intra-attribute disorder is not captured effectively by the popularly used continuum form of entropy known as Shannon or information entropy. If the categorical data contains ordinal features, then the problem multiplies because the existing measures treat all attributes as nominal. To address these issues, we propose a new Entropy-based Dissimilarity measure for Mixed categorical Data (EDMD) composed of both nominal and ordinal attributes. EDMD treats both nominal and ordinal attributes separately to capture the intrinsic information from the values of two different attribute types. We apply Boltzmann's definition of entropy, which is based on the principle of counting microstates, to exploit the intra-attribute statistical information of nominal attributes while preserving the order relationships among ordinal values in distance formulation. Additionally, the statistical significance of different attributes of the data towards dissimilarity computation is taken care of through attribute weighting. The proposed measure is free from any user-defined or domain-specific parameters and there is no prior assumption about the distribution of the data sets. Experimental results demonstrate the efficacy of EDMD in terms of cluster quality, accuracy, cluster discrimination ability, and execution time to handle mixed categorical data sets of different characteristics.

Clustering is an unsupervised learning technique that discovers intrinsic groups based on proximity between data points. Therefore, the performance of clustering techniques mainly relies on the proximity measures used to compute the (dis)similarity between the data objects. In general, it is relatively easier to compute the distance between numerical data points as numerical operations can directly be applied to values along features. However, for categorical datasets, computing the (dis)similarity between the data objects becomes a non-trivial problem. Therefore, in this paper, we propose a new distance metric based on the information theoretic approach to compute the dissimilarity between categorical data points. We compute entropy along each feature to capture the intra-attribute statistical information, based on which significance of attributes are decided during clustering. The proposed measure is free from any domain-dependent parameters and also does not rely on the distribution of data points. Experiment is conducted over diversified benchmark data sets, considering six competing proximity measures with three popular clustering algorithms and the clustering results are compared in terms of RI (Rand Index), ARI (Adjusted Rand Index), CA (Clustering Accuracy) and Cluster Discrimination Matrix (CDM). Over 85 percent of the data sets, the clustering accuracy of the proposed metric embedded with K-Mode and Weighted K-Mode outperforms its counterparts. Approximately, 0.2951 s is needed by the proposed metric to cluster a data set having 10,000 data points with 8 attributes and 2 clusters on a standard desktop machine. Overall, experimental results demonstrate the efficacy of the proposed metric to handle complex real datasets of different characteristics.

The clustering is an unsupervised learning technique for grouping the unlabeled data based on the proximity between the data points. Therefore, the performance of clustering techniques mainly depends on the proximity measures. The computation of dissimilarity in high dimensional and noisy datasets as well as datasets with imbalanced feature scale, which appear in various applications, is a challenging task. To counter these challenges, we propose a new distance metric to compute the dissimilarity between data points by combining the ensemble properties, entropy and weight information of feature vectors. We consider the statistical information and entropy along each features to compute the dissimilarity between the points. Then each feature is associated with weight based on its distribution information. The proposed Similarity measure based on Entropy for Numerical Datasets (SEND), is free from any domain specific parameters and there are no underlying assumptions about the distribution of the data. The proposed metric is applied on different type of clustering techniques to evaluate its performance. Experimental analyses on synthetic as well as real datasets demonstrate the efficacy of the proposed metric in terms of cluster quality, accuracy, execution time, robustness against noise and its ability to handle the high dimension datasets.

Handwritten signature has a key role in personnel authentication today. Institutions such as banks are using the handwritten signatures to control false transactions. Due to an increase in access by people to institutions such as banks, insurance companies etc., the volume of signatures are increasing day by day and need to be verified in real time. Hence, there is always a demand for a reliable and fast signature verification system. Researchers have contributed several techniques and ideas for signature verification. However, it has been investigated that the models are inefficient and their real-time implementation is a difficult task. In the present manuscript, a GPU based offline signature verification model has been proposed. The proposed signature verification model uses Hidden Markov Model (HMM) for both training and verification of the signatures. It has been found that the proposed GPU based model has more than 5 times faster response. The quantitative evaluations have been done using the average false rejection rate (FRR) and false acceptance rate (FAR). The lower values have been obtained which indicates that the proposed.