Clustering Text for Marketing Segmentation, Similarity Measures, and Grouping

In this review of existing similarity measures of intuitionistic fuzzy sets (IFSs), we apply some numerical examples showing that not all existing similarity measures are effective and reasonable in some cases. We propose properties based on intuition and the human thinking process that should be satisfied by all dissimilarity and similarity measures, together with new similarity measures of IFSs that overcome drawbacks of existing measures. In examples, we compare the proposed similarity measures to existing measures and present two propositions on the relationship between similarity and dissimilarity measures of IFSs. We also propose that a suitable combination of similarity measures may be a similarity measure.

Many similarity measures (SMs) were proposed to measure the similarity between multimodal remote sensing (RS) images. Each SM is efficient to a different degree in different registration cases (we consider visible-to-infrared, visible-to-radar, visible-to-digital elevation model (DEM), and radar-to-DEM ones), but no SM was shown to outperform all other SMs in all cases. In this article, we investigate the possibility of deriving a more powerful SM by combining two or more existing SMs. This combined SM relies on a binary linear support vector machine (SVM) classifier trained using real RS images. In the general registration case, we order SMs according to their impact on the combined SM performance. The three most important SMs include two structural SMs based on modality independent neighborhood descriptor (MIND) and scale-invariant feature transform-octave (SIFT-OCT) descriptors and one area-based logarithmic likelihood ratio (logLR) SM: the former ones are more robust to structural changes of image intensity between registered modes, the latter one is to image noise. Importantly, we demonstrate that a single combined SM can be applied in the general case as well as in each particular considered registration case. As compared to existing multimodal SMs, the proposed combined SM [based on five existing SMs, namely, MIND, logLR, SIFT-OCT, phase correlation (PC), histogram of orientated phase congruency (HOPC)] increases the area under the curve (AUC) by from 1% to 21%. From a practical point of view, we demonstrate that complex multimodal image pairs can be successfully registered with the proposed combined SM, while existing single SMs fail to detect enough correspondences for registration. Our results demonstrate that MIND, SIFT, and logLR SMs capture essential aspects of the similarity between RS modes, and their properties are complementary for designing a new more efficient multimodal SM.

The exploding number of computational models produced by Systems Biologists over the last years is an invitation to structure and exploit this new wealth of information. Researchers would like to trace models relevant to specific scientific questions, to explore their biological content, to align and combine them, and to match them with experimental data. To automate these processes, it is essential to consider semantic annotations, which describe their biological meaning. As a prerequisite for a wide range of computational methods, we propose general and flexible similarity measures for Systems Biology models computed from semantic annotations. By using these measures and a large extensible ontology, we implement a platform that can retrieve, cluster, and align Systems Biology models and experimental data sets. At present, its major application is the search for relevant models in the BioModels Database, starting from initial models, data sets, or lists of biological concepts. Beyond similarity searches, the representation of models by semantic feature vectors may pave the way for visualisation, exploration, and statistical analysis of large collections of models and corresponding data.

Interval-valued intuitionistic fuzzy environment is appropriate for most of the practical scenarios involving uncertainty, vagueness, and insufficient information. Entropy, similarity, distance, inclusion, and cross entropy measures are a few methods used for measuring uncertainty and classifying fuzzy sets and its generalizations. Entropy of a fuzzy set describes fuzziness degree of the set and similarity measure measures similarity between two fuzzy or members of its extended family. This paper presents generalized entropy and similarity measures for interval-valued intuitionistic fuzzy sets. Further, the proposed similarity measure is compared with some existing measure of similarity with the help of an illustrative example, and a method is used to define optimal point using the existing information. Finally, entropy and similarity measures are used to identify best alternatives to solve multi-attribute decision making.

Cosine similarity and information measures of [formula omitted] spherical fuzzy sets: Application in selecting migration destination

Defining similarity measures is a requirement for some machine learning methods. One such method is case-based reasoning (CBR) where the similarity measure is used to retrieve the stored case or a set of cases most similar to the query case. Describing a similarity measure analytically is challenging, even for domain experts working with CBR experts. However, datasets are typically gathered as part of constructing a CBR or machine learning system. These datasets are assumed to contain the features that correctly identify the solution from the problem features; thus, they may also contain the knowledge to construct or learn such a similarity measure. The main motivation for this work is to automate the construction of similarity measures using machine learning. Additionally, we would like to do this while keeping training time as low as possible. Working toward this, our objective is to investigate how to apply machine learning to effectively learn a similarity measure. Such a learned similarity measure could be used for CBR systems, but also for clustering data in semi-supervised learning, or one-shot learning tasks. Recent work has advanced toward this goal which relies on either very long training times or manually modeling parts of the similarity measure. We created a framework to help us analyze the current methods for learning similarity measures. This analysis resulted in two novel similarity measure designs: The first design uses a pre-trained classifier as basis for a similarity measure, and the second design uses as little modeling as possible while learning the similarity measure from data and keeping training time low. Both similarity measures were evaluated on 14 different datasets. The evaluation shows that using a classifier as basis for a similarity measure gives state-of-the-art performance. Finally, the evaluation shows that our fully data-driven similarity measure design outperforms state-of-the-art methods while keeping training time low.

In the study of intuitionistic fuzzy clustering, the construction of an intuitionistic fuzzy similarity matrix (IFSM) is a fundamental and important issue in the direct clustering analysis, since it determines clustering results and computational efforts. Many methods based on the axioms of intuitionistic fuzzy similarity relations are applicable to IFSM construction. However, most of existing methods may yield a “counterintuitive result” in some cases and consume much computational time. In this paper, we propose a novel intuitionistic fuzzy clustering method to deal with such problems. First, based on the normalized Hamming distance, we define a similarity measure between intuitionistic fuzzy numbers (IFNs), by which a similarity measure between intuitionistic fuzzy sets (IFSs) is induced. Second, a divergence measure between IFSs is obtained by extending the dissimilarity of IFNs. Third, we construct an IFSM by using together the similarity and divergence measures so as to cluster the intuitionistic fuzzy information. Finally, two examples are presented to show the effectiveness and advantages of our method.

Information and similarity measures have a vital place in the fuzzy set theory. It has been investigated by many researchers with different aspects. In this paper, new intuitionistic fuzzy similarity and information measures based on sine function are proposed. Comparison of proposed information measures with the existing ones is listed. Numerical results clearly indicate the efficiencies of these measures over others. New technique for multi-criteria decision-making (MCDM) quandaries to rank the alternatives is introduced. This technique is developed on the application intuitionistic fuzzy information measure and weighted averaging operator (IFWAO). A case of five colleges ranking of a district region is studied and discussed.

The paper focuses on similarity and distance measures for binary data and their application in cluster analysis. There are 66 measures for binary data analyzed in the paper in order to provide a comprehensive insight into the problematics and to create their well-arranged overview. For this purpose, formulas by which they were defined are studied. In the next part of the research, the results of object clustering on generated datasets are compared, and the ability of measures to create similar or identical clustering solutions is evaluated. This is done by using chosen internal and external evaluation criteria, and comparing the assignments of objects into clusters in the process of hierarchical clustering. The paper shows which similarity measures and distance measures for binary data lead to similar or even identical results in hierarchical cluster analysis.

Randomized Similarity Analysis of Multispecies Laboratory and Field Studies

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 explains about similarity measure and the relationship between the knowledge repositories. This paper also describes the significance of document similarity measures, algorithms and to which type of text it can be applied Document similarity measures are of full text similarity, paragraph similarity, sentence similarity, semantic similarity, structural similarity and statistical measures. Two different frameworks had been proposed in this paper, one for measuring document to document similarity and the other model which measures similarity between documents to multiple documents. These two proposed models can use any one of the similarity measures in implementation aspect, which is been put forth for further research.

Semantic similarity is an essential concept that widen across various fields such as artificial intelligence, natural language processing, information retrieval, relation extraction, document clustering and automatic data extraction. The study proposed in this paper focus on semantic similarity and counter measure on question answering task. Despite the usefulness of semantic similarity in these applications, finding the exact meaning between the words from question and answer pair has become a major challenge in question answering system. To recognize various relationships those exist between question and answer pair, measuring semantically is essential. We present study using a match maker algorithm for similarity measurement between question-answer pair. The study compares similarity measurement using match maker algorithm as against semantic similarity measure on Miller-Charles bench marked data set. This paper present study about different types of algorithm used to measure the semantic similarity between the words and those result compare with match maker algorithm. The experiments on real datasets shows matchmaker algorithm works better than web-based semantic similarity measure.

The measurement of uncertainty is an important topic for the theories dealing with uncertainty. The definition of similarity measure between two IFSs is one of the most interesting topics in IFSs theory. A similarity measure is defined to compare the information carried by IFSs. Many similarity measures have been proposed. A few of them come from the well-known distance measures. In this work, a new similarity measure between IFSs was proposed by the consideration of the information carried by the membership degree, the non-membership degree, and hesitancy degree in intuitionistic fuzzy sets (IFSs). To demonstrate the efficiency of the proposed similarity measure, various similarity measures between IFSs were compared with the proposed similarity measure between IFSs by numerical examples. The compared results demonstrated that the new similarity measure is reasonable and has stronger discrimination among them. Finally, the similarity measure was applied to pattern recognition and medical diagnosis. Two illustrative examples were provided to show the effectiveness of the pattern recognition and medical diagnosis.

Similarity measure is an important key in image registration. Most traditional intensity-based similarity measures (e.g. sum-of-squared-differences, correlation coefficient, mutual information and correlation ratio) assume a stationary image and pixel-by-pixel independence. These similarity measures ignore the correlation among pixel intensities; hence, a perfect image registration cannot be achieved especially in the presence of spatially varying intensity distortions and outlier objects that appear in one image but not in the other. It is supposed here that non-stationary intensity distortion (such as bias field) has a sparse representation in the transformation domain. Based on this assumption, a novel similarity measure is proposed here based on sparse representation in a mono-modal setting. The zero norm (l 0 ) in the transform domain is introduced as a new similarity measure in the presence of non-stationary intensity distortion. The present study defines a sparsity similarity measure that indicates the complexity of the residual image between two registered images in the transform domain such as discrete cosine transform or wavelet. It is attempted here to analytically and statistically illustrate that the proposed similarity measure has important properties such as metric properties in vector space, from correntropy perspective. This measure produces accurate registration results on both artificial and real-world problems which are examined in the present study.