Academic literature on the topic 'Generalized cosine similarity'

The paper proposes a generalized ordered weighted simplified neutrosophic cosine similarity (GOWSNCS) measure by combining the cosine similarity measure of simplified neutrosophic sets (SNSs) with the generalized ordered weighted averaging (GOWA) operator and investigates its properties and special cases. Then, the author develops a simplified neutrosophic group decision-making method based on the GOWSNCS measure to handle multiple attribute group decision-making problems with simplified neutrosophic information. The prominent characteristics of the GOWSNCS measure are that it not only is a generalization of the cosine similarity measure but also considers the associated weights for attributes and decision makers in the aggregation of the cosine similarity measures of SNSs to alleviate the influence of unduly large or small similarities in the process of information aggregation. Finally, an illustrative example of investment alternatives is provided to demonstrate the application and effectiveness of the developed approach.

We present the interval-valued intuitionistic fuzzy ordered weighted cosine similarity (IVIFOWCS) measure in this paper, which combines the interval-valued intuitionistic fuzzy cosine similarity measure with the generalized ordered weighted averaging operator. The main advantage of the IVIFOWCS measure provides a parameterized family of similarity measures, and the decision maker can use the IVIFOWCS measure to consider a lot of possibilities and select the aggregation operator in accordance with his interests. We have studied some of its main properties and particular cases such as the interval-valued intuitionistic fuzzy ordered weighted arithmetic cosine similarity (IVIFOWACS) measure and the interval-valued intuitionistic fuzzy maximum cosine similarity (IVIFMAXCS) measure. The IVIFOWCS measure not only is a generalization of some similarity measure, but also it can deal with the correlation of different decision matrices for interval-valued intuitionistic fuzzy values. Furthermore, we present an application of IVIFOWCS measure to the group decision-making problem. Finally the existing similarity measures are compared with the IVIFOWCS measure by an illustrative example.

To enhance the credibility level/measure of an intuitionistic fuzzy set (IFS), this study proposes the notion of an intuitionistic fuzzy credibility set (IFCS) to express the hybrid information of a pair of a membership degree and a credibility degree and a pair of a nonmembership degree and a credibility degree. Next, we propose generalized distance and similarity measures between IFCSs and then further generalize the weighted generalized distance measure of IFCSs to the trigonometric function-based similarity measures of IFCSs, including the cosine, sine, tangent, and cotangent similarity measures based on the weighted generalized distance measure of IFCSs. Then, a multicriteria decision making (MCDM) method using the proposed similarity measures is developed in the environment of IFCSs. An illustrative example about the performance evaluation of industrial robots and comparative analysis are presented to indicate the applicability and efficiency of the developed method in the setting of IFCSs.

This paper proposes a neutrosophic hesitant fuzzy linguistic term set (NHFLTS) based on hesitant fuzzy linguistic term set (HFLTS) and neutrosophic set (NS), which can express the inconsistent and uncertainty information flexibly in multiple criteria decision making problems. The basic operational laws of NHFLTS based on linguistic scale function are also discussed. Then we propose the generalized neutrosophic hesitant fuzzy linguistic distance measure and discuss its properties. Furthermore, a new similarity measure of NHFLTS combines the generalized neutrosophic hesitant fuzzy linguistic distance measure and the cosine function is given. A corresponding cosine distance measure between NHFLTSs is proposed according to the relationship between the similarity measure and the distance measure, and we develop the technique for order preference by similarity to an ideal solution (TOPSIS) method to the obtained cosine distance measure. The main advantages of the proposed NHFLTS is defined on linguistic scale function, the decision makers can flexibly convert the linguistic information to semantic values, and the proposed cosine distance measure between NHFLTSs with TOPSIS method can deal with the related decision information not only from the point of view of algebra, but also from the point of view of geometry. Finally, the reasonableness and effectiveness of the proposed method is demonstrated by the illustrative example, which is also compared to the other existing methods.

This article introduces the concept of Heronian mean operators, geometric Heronian mean operators, neutrosophic cubic number–improved generalized weighted Heronian mean operators, neutrosophic cubic number–improved generalized weighted geometric Heronian mean operators. These operators actually generalize the operators of fuzzy sets, cubic sets, and neutrosophic sets. We investigate the average weighted operator on neutrosophic cubic sets and weighted geometric operator on neutrosophic cubic sets to aggregate the neutrosophic cubic information. After this, based on average weighted and geometric weighted and cosine similarity function in neutrosophic cubic sets, we developed a multiple attribute group decision-making method. Finally, we give a mathematical example to illustrate the usefulness and application of the proposed method.

Abstract Background Variations of clinical terms are very commonly encountered in clinical texts. Normalization methods that use similarity measures or hand-coded approximation rules for matching clinical terms to standard terminologies have limited accuracy and coverage. Materials and Methods In this paper, a novel method is presented that automatically learns patterns of variations of clinical terms from known variations from a resource such as the Unified Medical Language System (UMLS). The patterns are first learned by computing edit distances between the known variations, which are then appropriately generalized for normalizing previously unseen terms. The method was applied and evaluated on the disease and disorder mention normalization task using the dataset of SemEval 2014 and compared with the normalization ability of the MetaMap system and a method based on cosine similarity. Results Excluding the mentions that already exactly match in UMLS and the training dataset, the proposed method obtained 64.7% accuracy on the rest of the test dataset. The accuracy was calculated as the number of mentions that correctly matched the gold-standard concept unique identifiers (CUIs) or correctly matched to be without a CUI. In comparison, MetaMap’s accuracy was 41.9% and cosine similarity’s accuracy was 44.6%. When only the output CUIs were evaluated, the proposed method obtained 54.4% best F -measure (at 92.1% precision and 38.6% recall) while MetaMap obtained 19.4% best F -measure (at 38.0% precision and 13.0% recall) and cosine similarity obtained 38.1% best F -measure (at 70.3% precision and 26.1% recall). Conclusions The novel method was found to perform much better than the MetaMap system and the cosine similarity based method in normalizing disease mentions in clinical text that did not exactly match in UMLS. The method is also general and can be used for normalizing clinical terms of other semantic types as well.

The aim of the study was to design and implement automatic testing of online essay examinations using the Generalized Vector Space Model (GVSM) method. This data is obtained through (1) Literature Study (2) Observation (3) Documentation. The results of this study indicate that the automatic scoring system with the GVSM weighting method and the cosine similarity similarity calculation method have the accuracy of the assessment with an average of 66%.

In this paper a nonlinear Gabor Wavelet Transform (GWT) discriminant feature extraction approach for enhanced face recognition is proposed. Firstly, the low-energized blocks from Gabor wavelet transformed images are extracted. Secondly, the nonlinear discriminating features are analyzed and extracted from the selected low-energized blocks by the generalized Kernel Discriminative Common Vector (KDCV) method. The KDCV method is extended to include cosine kernel function in the discriminating method. The KDCV with the cosine kernels is then applied on the extracted low-energized discriminating feature vectors to obtain the real component of a complex quantity for face recognition. In order to derive positive kernel discriminative vectors, we apply only those kernel discriminative eigenvectors that are associated with nonzero eigenvalues. The feasibility of the low-energized Gabor-block-based generalized KDCV method with cosine kernel function models has been successfully tested for classification using theL1, L2distance measures; and the cosine similarity measure on both frontal and pose-angled face recognition. Experimental results on the FRAV2D and the FERET database demonstrate the effectiveness of this new approach.

Similarity measures, distance measures and entropy measures are some common tools considered to be applied to some interesting real-life phenomena including pattern recognition, decision making, medical diagnosis and clustering. Further, interval-valued picture fuzzy sets (IVPFSs) are effective and useful to describe the fuzzy information. Therefore, this manuscript aims to develop some similarity measures for IVPFSs due to the significance of describing the membership grades of picture fuzzy set in terms of intervals. Several types cosine similarity measures, cotangent similarity measures, set-theoretic and grey similarity measures, four types of dice similarity measures and generalized dice similarity measures are developed. All the developed similarity measures are validated, and their properties are demonstrated. Two well-known problems, including mineral field recognition problems and multi-attribute decision making problems, are solved using the newly developed similarity measures. The superiorities of developed similarity measures over the similarity measures of picture fuzzy sets, interval-valued intuitionistic fuzzy sets and intuitionistic fuzzy sets are demonstrated through a comparison and numerical examples.

Power from solar energy is not reliable, due to weather-related factors, which diminishes the power system’s reliability. Therefore, this study suggests a way to predict the intensity of solar irradiance using various statistical algorithms and artificial intelligence. In particular, we suggest the use of a hybrid predictive model, combining statistical properties and historical data training. In order to evaluate the maximum prediction steps of solar irradiance, the maximum Lyapunov exponent was applied. Then, we used the cosine similarity algorithm in the hidden Markov model for the initial prediction. The combination of the Hurst exponent and tail parameter revealed the self-similarity and long-range dependence of the fractional generalized Pareto motion, which enabled us to consider the iterative predictive model. The initial prediction was substituted into a stochastic differential equation to achieve the final prediction, which prevents error propagation. The effectiveness of the hybrid model was demonstrated in the case study.

Les performances des algorithmes d'apprentissage automatique dépendent de la métrique utilisée pour comparer deux objets, et beaucoup de travaux ont montré qu'il était préférable d'apprendre une métrique à partir des données plutôt que se reposer sur une métrique simple fondée sur la matrice identité. Ces résultats ont fourni la base au domaine maintenant qualifié d'apprentissage de métrique. Toutefois, dans ce domaine, la très grande majorité des développements concerne l'apprentissage de distances. Toutefois, dans certaines situations, il est préférable d'utiliser des similarités (par exemple le cosinus) que des distances. Il est donc important, dans ces situations, d'apprendre correctement les métriques à la base des mesures de similarité. Il n'existe pas à notre connaissance de travaux complets sur le sujet, et c'est une des motivations de cette thèse. Dans le cas des systèmes de filtrage d'information où le but est d'affecter un flot de documents à un ou plusieurs thèmes prédéfinis et où peu d'information de supervision est disponible, des seuils peuvent être appris pour améliorer les mesures de similarité standard telles que le cosinus. L'apprentissage de tels seuils représente le premier pas vers un apprentissage complet des mesures de similarité. Nous avons utilisé cette stratégie au cours des campagnes CLEF INFILE 2008 et 2009, en proposant des versions en ligne et batch de nos algorithmes. Cependant, dans le cas où l'on dispose de suffisamment d'information de supervision, comme en catégorisation, il est préférable d'apprendre des métriques complètes, et pas seulement des seuils. Nous avons développé plusieurs algorithmes qui visent à ce but dans le cadre de la catégorisation à base de k plus proches voisins. Nous avons tout d'abord développé un algorithme, SiLA, qui permet d'apprendre des similarités non contraintes (c'est-à-dire que la mesure peut être symétrique ou non). SiLA est une extension du perceptron par vote et permet d'apprendre des similarités qui généralisent le cosinus, ou les coefficients de Dice ou de Jaccard. Nous avons ensuite comparé SiLA avec RELIEF, un algorithme standard de re-pondération d'attributs, dont le but n'est pas sans lien avec l'apprentissage de métrique. En effet, il a récemment été suggéré par Sun et Wu que RELIEF pouvait être considéré comme un algorithme d'apprentissage de métrique avec pour fonction objectif une approximation de la fonction de perte 0-1. Nous montrons ici que cette approximation est relativement mauvaise et peut être avantageusement remplacée par une autre, qui conduit à un algorithme dont les performances sont meilleures. Nous nous sommes enfin intéressés à une extension directe du cosinus, extension définie comme la forme normalisée d'un produit scalaire dans un espace projeté. Ce travail a donné lieu à l'algorithme gCosLA. Nous avons testé tous nos algorithmes sur plusieurs bases de données. Un test statistique, le s-test, est utilisé pour déterminer si les différences entre résultats sont significatives ou non. GCosLA est l'algorithme qui a fourni les meilleurs résultats. De plus, SiLA et gCosLA se comparent avantageusement à plusieurs algorithmes standard, ce qui illustre leur bien fondé
Almost all machine learning problems depend heavily on the metric used. Many works have proved that it is a far better approach to learn the metric structure from the data rather than assuming a simple geometry based on the identity matrix. This has paved the way for a new research theme called metric learning. Most of the works in this domain have based their approaches on distance learning only. However some other works have shown that similarity should be preferred over distance metrics while dealing with textual datasets as well as with non-textual ones. Being able to efficiently learn appropriate similarity measures, as opposed to distances, is thus of high importance for various collections. If several works have partially addressed this problem for different applications, no previous work is known which has fully addressed it in the context of learning similarity metrics for kNN classification. This is exactly the focus of the current study. In the case of information filtering systems where the aim is to filter an incoming stream of documents into a set of predefined topics with little supervision, cosine based category specific thresholds can be learned. Learning such thresholds can be seen as a first step towards learning a complete similarity measure. This strategy was used to develop Online and Batch algorithms for information filtering during the INFILE (Information Filtering) track of the CLEF (Cross Language Evaluation Forum) campaign during the years 2008 and 2009. However, provided enough supervised information is available, as is the case in classification settings, it is usually beneficial to learn a complete metric as opposed to learning thresholds. To this end, we developed numerous algorithms for learning complete similarity metrics for kNN classification. An unconstrained similarity learning algorithm called SiLA is developed in which case the normalization is independent of the similarity matrix. SiLA encompasses, among others, the standard cosine measure, as well as the Dice and Jaccard coefficients. SiLA is an extension of the voted perceptron algorithm and allows to learn different types of similarity functions (based on diagonal, symmetric or asymmetric matrices). We then compare SiLA with RELIEF, a well known feature re-weighting algorithm. It has recently been suggested by Sun and Wu that RELIEF can be seen as a distance metric learning algorithm optimizing a cost function which is an approximation of the 0-1 loss. We show here that this approximation is loose, and propose a stricter version closer to the the 0-1 loss, leading to a new, and better, RELIEF-based algorithm for classification. We then focus on a direct extension of the cosine similarity measure, defined as a normalized scalar product in a projected space. The associated algorithm is called generalized Cosine simiLarity Algorithm (gCosLA). All of the algorithms are tested on many different datasets. A statistical test, the s-test, is employed to assess whether the results are significantly different. GCosLA performed statistically much better than SiLA on many of the datasets. Furthermore, SiLA and gCosLA were compared with many state of the art algorithms, illustrating their well-foundedness

It was recently shown that there is a formal similarity between 1- and 2-D canonical operators.1 This immediately generalizes all previous results in 2-D Fourier optics to nonorthogonal systems. In particular, the analysis of Nazarathy and Goodman2 goes through as before with no change in the logic. The spatial dispersion relation now expresses p z as a function of p x and p y , where p i is the optical direction cosine in the ith direction. This leads to the linear scalar transfer function for Fourier optics in three dimensions. Similar results can be derived in related fields, such as for anisotropic Gaussian-Schell model sources.