METHODS FOR DETERMINING SIMILARITY OF CATEGORICAL ORDERED DATA

This paper proposes to exploit heterogeneous data, i.e. data described by both numerical and categorical features, so as to gain knowledge about the categorical attributes from the numerical ones. More precisely, it aims at discovering whether, according to a given data set, based on information provided by the numerical attributes, some categorical attributes actually are ordinal ones and, additionally, at establishing ranking relations between the category values. To that aim, the paper proposes the 3-step methodology OSACA, standing for Order Seeking Algorithm for Categorical Attributes: it first consists in extracting gradual patterns from the numerical attributes, to identify rich ranking information about the data; it then applies mathematical morphology tools, more precisely alternated filters, to induce an associated order on the categorical attributes. The third step evaluates the quality of the candidate rankings through an original measure derived from the rank entropy discrimination.

Content Based Image Retrieval (CBIR) is a process in which for a given query image similar images will be retrieved based on the image content similarity. Image content refers to its visual features, which are mathematical representations of a digital image. The image retrieval task primarily depends on image feature extraction and similarity measurement between the feature vectors. The performance of CBIR process not only decided by the optimum features extracted from the image but also on the proper choice of the similarity/dissimilarity measures (distance metrics). As the image features broadly diversified in terms of color, texture and shape based, using the same distance metric may not work well for all of these features. In this paper, first we presented overview of geometric and statistical distance metrics used in CBIR along with the comparative analysis of these measures on color and texture features. Color features extracted by computing color histograms in HSV space and texture features by wavelet decompositions. Geometrical distances such as Manhattan, Chebyshev, Euclidean, statistical distance metrics such as Cosine Similarity, Chi-square, KullbackLeibler, Jeffrey and cumulative statistical distance metrics of Kolmogorov-Smirnov, Cramer von Mises and Earthmover's distances were analyzed for feature similarity. We gave certain conclusions on the performance of all these distance metrics in terms of Mean Average Precision (MAP) and Recall rates with color and texture features respectively.

Mixed feature selection based on granulation and approximation

The similarity metric between videos is integral to several key tasks, including video retrieval, classification and recommendation. Since there is no standard criterion for the similarity measurement between videos except measuring manually, it is difficult to collect large training dataset for distance metric learning algorithms. Moreover, the existing distance metric learning (DML) methods for multimedia data suffer from two critical limitations: (1) they typically attempt to learn a distance function on the single label setting, in which each item is only labeled with single label; (2) they are often designed for learning distance metrics on low-level features, which ignore the semantic similarity of the multimedia data. To address these problems, in this paper, we propose a novel framework of Intermediate Semantics based Distance Learning (ISDL) for video clips, which aims to integrate semantics of multiple modals optimally for distance metric learning. In particular, the proposed framework: (1) generates the training pairs automatically; (2) defines multi-modal concepts for similarity measure among videos; (3) learns the distance metric for video clips based on the intermediate semantics. We conduct an extensive set of experiments to evaluate the performance of the proposed algorithms, and the results validate the effectiveness of our proposed approach.

Clustering algorithms play a pivotal role in data mining, offering powerful tools for uncovering hidden patterns and structures within datasets. These algorithms aim to divide data points into coherent groups based on similarities or dissimilarities, making it easier to explore and understand complex data. Clustering algorithms typically rely on similarity measures to assess the likeness between data points. Consequently, selecting a suitable similarity measure is crucial for achieving satisfactory clustering outcomes. However, this decision can pose significant challenges, especially for non-experts, given the plethora of similarity measures available in the literature and their performance which is closely linked to the specific dataset, clustering algorithm, and cluster validity index employed. This difficulty is even more important when considering mixed data clustering. Mixed data refers to heterogeneous data characterized by both numerical and categorical attributes. In such a context, the same similarity measure cannot be used for both types of attributes due to their different nature. Commonly, two similarity measures are combined, one for numerical attributes and one for categorical attributes. This adds a layer of complexity to the problem since it requires the selection of two similarity measures instead of just one. This paper introduces SIMREC, a similarity measure recommendation system for mixed data clustering. The system uses meta-learning to mine the relationship between dataset characteristics and similarity measures performances for different mixed data clustering algorithms and cluster validity indices. Therefore, given a mixed dataset, a mixed data clustering algorithm, and a cluster validity index, the system can recommend suitable pairs of numerical and categorical similarity measures based on the characteristics of the dataset. We implemented the proposed system using 130 pairs of similarity measures (10 numerical and 13 categorical), 4 commonly used mixed data clustering algorithms (K-Prototypes, LSH-K-Prototypes, K-Medoids, and Hierarchical Clustering), and three cluster validity indices (Silhouette, Clustering Accuracy, and Adjusted Rand Index). Our experiments on 185 publicly available mixed datasets show that the pairs of similarity measures recommended by SIMREC outperform the baseline pairs, including classically used pairs of similarity measures in the literature.

This paper represents a new approach for face recognition that incorporates Prewitt edge detection, Gabor filter and Zernike moments to transform the image into a unified domain. On this joint domain, five distance metrics are constructed using Schoenberg transform for the purpose of defining efficient similarity measures for holistic face recognition. The proposed Schoenberg similarity applies Schoenberg transform to the logarithm of five existing distance metrics: Minkowski, City-Block, Euclidean, Soergel and Lorentzian metrics. The constructed Schoenberg logarithmic metrics are called SL-Minkowski, SL-City-Block, SL-Euclidean, SL-Soergel and SL-Lorentzian. These distance metrics are utilized as similarity measures after being normalized over the range [0,1] for fair comparison with existing measures. The proposed Schoenberg system can resist three problems: Change in illumination, pose and facial expression. Simulation results show that the proposed distance measures have superior performance as compared to the classical metrics: Structural Similarity Index Measure (SSIM) and Feature-based Similarity Measure (FSIM). Performance criteria are the recognition rate and the recognition confidence, defined as the similarity difference between the best match and the second-best match in the face database.

In the current years, advancements in medical imaging have prompted the rise of some massive databases, including the pictures from a different scope of modalities. Content based image retrieval (CBIR) is a kind of search that selects examples from an image set that have a similar content to an input query image. Each CBIR system consists of two substantial factors, feature extraction and similarity measure. Based on the type of these parts, many CBIR systems are proposed. In this paper we present not only how to design a CBIR system for MRI brain Tumor images, but also a comparison between the different implemented CBIR systems and ours. Furthermore, in this research, using a DML (Distance Metric Learning) instead of the rigid distance metric such as Euclidean distance as the Similarity measure has helped the researchers to obtain a better mAP (mean Average Precision) as the result. The experimental results of our CBIR system show that it has a better performance than other rivals in the field. The obtained mean average precision of our CBIR system is 92.41 that is significant in MRI brain tumor.

Clustering is a difficult and widely studied data mining task, with many varieties of clustering algorithms proposed in the literature. Nearly all algorithms use a similarity measure such as a distance metric (e.g., Euclidean distance) to decide which instances to assign to the same cluster. These similarity measures are generally predefined and cannot be easily tailored to the properties of a particular dataset, which leads to limitations in the quality and the interpretability of the clusters produced. In this article, we propose a new approach to automatically evolving similarity functions for a given clustering algorithm by using genetic programming. We introduce a new genetic programming-based method which automatically selects a small subset of features (feature selection) and then combines them using a variety of functions (feature construction) to produce dynamic and flexible similarity functions that are specifically designed for a given dataset. We demonstrate how the evolved similarity functions can be used to perform clustering using a graph-based representation. The results of a variety of experiments across a range of large, high-dimensional datasets show that the proposed approach can achieve higher and more consistent performance than the benchmark methods. We further extend the proposed approach to automatically produce multiple complementary similarity functions by using a multi-tree approach, which gives further performance improvements. We also analyse the interpretability and structure of the automatically evolved similarity functions to provide insight into how and why they are superior to standard distance metrics.

Similarity measurement plays an important role to solve many pattern recognition problems such as classification, clustering and particularly the content based image retrieval problems. In this paper, a detailed comparison of 10 similarity measures has been presented for medical image retrieval. Different types of medical images from databases such as NEMA, OASIS and EXACT09 are used to evaluate the performance. Features of all the medical images are extracted using Log-Gabor wavelet. The effectiveness of all the distance metrics are investigated and tested on more than 800 medical images from the databases. It is observed from the experimental results that the retrieval performance can be improved by the distance measures like Bray- Curtis and Canberra distance metric as compared to other existing distance based approach.

We define a new family of similarity and distance measures on graphs, and explore their theoretical properties in comparison to conventional distance metrics. These measures are defined by the solution(s) to an optimization problem which attempts find a map minimizing the discrepancy between two graph Laplacian exponential matrices, under norm-preserving and sparsity constraints. Variants of the distance metric are introduced to consider such optimized maps under sparsity constraints as well as fixed time-scaling between the two Laplacians. The objective function of this optimization is multimodal and has discontinuous slope, and is hence difficult for univariate optimizers to solve. We demonstrate a novel procedure for efficiently calculating these optima for two of our distance measure variants. We present numerical experiments demonstrating that (a) upper bounds of our distance metrics can be used to distinguish between lineages of related graphs; (b) our procedure is faster at finding the required optima, by as much as a factor of 103; and (c) the upper bounds satisfy the triangle inequality exactly under some assumptions and approximately under others. We also derive an upper bound for the distance between two graph products, in terms of the distance between the two pairs of factors. Additionally, we present several possible applications, including the construction of infinite “graph limits” by means of Cauchy sequences of graphs related to one another by our distance measure.

We define a new family of similarity and distance measures on graphs, and explore their theoretical properties in comparison to conventional distance metrics. These measures are defined by the solution(s) to an optimization problem which attempts find a map minimizing the discrepancy between two graph Laplacian exponential matrices, under norm-preserving and sparsity constraints. Variants of the distance metric are introduced to consider such optimized maps under sparsity constraints as well as fixed time-scaling between the two Laplacians. The objective function of this optimization is multimodal and has discontinuous slope, and is hence difficult for univariate optimizers to solve. We demonstrate a novel procedure for efficiently calculating these optima for two of our distance measure variants. We present numerical experiments demonstrating that (a) upper bounds of our distance metrics can be used to distinguish between lineages of related graphs; (b) our procedure is faster at finding the required optima, by as much as a factor of 103; and (c) the upper bounds satisfy the triangle inequality exactly under some assumptions and approximately under others. We also derive an upper bound for the distance between two graph products, in terms of the distance between the two pairs of factors. Additionally, we present several possible applications, including the construction of infinite "graph limits" by means of Cauchy sequences of graphs related to one another by our distance measure.

This paper proposes a distance metric for motion vector histograms. Of a number of existing distance metrics for histograms, the weighted quadratic form distance is known to be efficient because of its flexibility. In order for the distance to be efficient, however, a suitable selection for its weighting matrix is necessary. Proposed in this paper is a determination technique for the weighting matrix which can reflect human perceptual characteristics for motion similarity. Experimental results have confirmed that the proposed technique is useful as a similarity measure in video retrieval.

Distance metric is widely used in similarity estimation. The smaller the distance is, the greater the similarity is. The Minkowski distance metric are usually chosen as the similarity measure in the conventional similarity metrics. In this paper, the most popular Euclidean and Manhattan distance, and the morphology similarity distance we have proposed are compared as similarity estimation measure distance. We cluster thirty random datasets using the fuzzy c-mean algorithm, recognize the Iris data from the UCI repository, and the experiment results are compared and analyzed.

Mining, discovering, and integrating process-oriented services has attracted growing attention in the recent years. Workflow precedence graph and workflow block structures are two important factors for comparing and mining processes based on distance similarity measure. Some existing work has done on comparing workflow designs based on their precedence graphs. However, there lacks of standard distance metrics for comparing workflows that contain complex block structures such as parallel OR, parallel AND. In this paper we present a quantitative approach to modeling and capturing the similarity and dissimilarity between different workflow designs, focusing on similarity and dissimilarity between the block structures of different workflow designs. We derive the distance-based similarity measures by analyzing the workflow block structure of the participating workflow processes in four consecutive phases. We first convert each workflow dependency graph into a block tree by using our block detection algorithm. Second, we transform the block tree into a binary tree to provide a normalized reference structure for distance based similarity analysis. Third, we construct a binary branch vector by encoding the binary tree. Finally, we calculate the distance metric between two binary branch vectors.KeywordsBusiness ProcessBinary TreeDependency GraphBusiness Process ManagementBlock TreeThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Clustering algorithm for mixed datasets using density peaks and Self-Organizing Generative Adversarial Networks