Scott and Szewczyk in Technometrics, 2001, have introduced a similarity measure for two densities ¦1 and  ¦2 , bySIM(¦1 ¦2)=< ¦1 ¦2>/Ö<¦1 ¦2> <¦1 ¦2>Where<¦1 ¦2>ò+¥-¥¦1(c,q1) ¦2(c,q2)dc sim(¦1 ¦2) has some appropriate properties that can be suitable measures for the similarity of ¦1 and ¦2 . However, due to some restrictions on the value of parameters and the kind of densities, discrete or continuous, it cannot be used in general. The purpose of this article is to give some other measures, based on modified Scott's measure, and Kullback information, which may be better than sim (¦1 ¦2) in some cases. The properties of these new measures are studied and some examples are provided.

In this paper, we first of all define the distance measure entitled generalized Hausdorff distance between two trapezoidal generalized fuzzy numbers (TGFNs) that has been introduced by Chen [10]. Then using a other distance and combining with generalized Hausdorff distance, we define the similarity measure. The basic properties of the above mentioned similarity measure are proved in detail. Finally we rank two generalized fuzzy numbers using distance measure and similarity measure between them.

Document clustering has been widely used in information retrieval systems in order to improve the efficiency and also the effectiveness of ranked output systems using clustering hypothesis. Based on this hypothesis, documents relevant to a query tend to be highly similar in the context defined by the query. In this way, a pair of documents has an overall similarity (ignoring the query) and a specific similarity (similarity of a pair of documents given a query). A Query-Sensitive similarity measure (QSSM) is a mechanism to measure the similarity of two documents given a query. In this paper, in the first step, we identify the sources of information that may be used for this purpose. In the second step, we propose a QSSM based on these information sources. Finally, we propose a parametric QSSM that simultaneously makes use of the product and weighted sum to fuse the information from the identified sources. A genetic algorithm is used to learn the optimal values of parameters in this measure for a specific collection. The leave-one-out method is used to evaluate the proposed learning scheme. Our motivation for this is to see whether the learning scheme can perform significantly better than the measure proposed in the second step. Using several document collections, the performance of each measure is evaluated and the results are compared with other QSSMs proposed in the past research.

Recommender Systems (RS) provide personalized recommendation according to the user need by analyzing behavior of users and gathering their information. One of the algorithms used in recommender systems is user-based Collaborative Filtering (CF) method. The idea is that if users have similar preferences in the past, they will probably have similar preferences in the future. The important part of collaborative filtering algorithms is allocated to determine similarity between objects. Similarities between objects are classified to user-based similarity and item-based similarity. The most popular used similarity metrics in recommender systems are Pearson correlation coefficient, Spearman rank correlation, and Cosine similarity measure.Until now, little computation has been made for optimal similarity in collaborative filtering by researchers. For this reason, in this research, we propose an optimal similarity measure via a simple linear combination of values and ratio of ratings for user-based collaborative filtering by the use of Firefly algorithm; and we compare our experimental results with Pearson traditional similarity measure and optimal similarity measure based on genetic algorithm. Experimental results on real datasets show that proposed method not only improves recommendation accuracy significantly but also increases quality of prediction and recommendation performance.

The most important issue with trajectory analysis is calculating similarity between trajectories. In this paper a novel method for measuring similarity between trajectories based on the cost to match a set of trajectories segments was introduced. The similarity between two trajectories is defined as a minimum cost to match a trajectory to the other one. For this purpose, the segment based distance was introduced to as a cost of matching two trajectories segments. In addition, the dynamic programming technique is used to implement the time warp method. We performed some experiments to compare the proposed similarity measure with the similar approaches in the application of trajectory classification. The empirical quality of the proposed similarity measure was evaluated on 1-nearest neighbor (1-NN) classification task using 13 publicly available data sets. Compared to the other well-known similarity measures, the proposed method proved to be effective in the considered experiments based on the accuracy of classification.

Distance size, similarity size, and entropy size provide useful results for decision makers to make decisions about problems with uncertain data. The main focus of this research is to introduce a new measure for interval-valued intuitive fuzzy numbers. Many of the defined measures have shortcomings such as not being comprehensive, high volume of calculations and application in limited cases. Therefore, the main goal of this research is to introduce a measure of distance and similarity with a new and reduced approach for intuitive fuzzy numbers with a value interval. After presenting the structure and effective indicators in the proposed size, it can be seen that the amount of calculations is clearly reduced in the defined interval size. In addition, the proof that size properties hold for it is shown correctly. The presented size structure has the ability to be combined with the process related to multi-criteria decision making and medical diagnosis problems. For this purpose, while presenting hybrid algorithms, effective applications of it have been given by mentioning several prominent examples.

Background and Objectives: Neuroscience research can benefit greatly from the fusion of simultaneous recordings of electroencephalogram (EEG) and functional magnetic resonance imaging (fMRI) data due to their complementary properties. We can extract shared information by coupling two modalities in a symmetric data fusion.Methods: This paper proposed an approach based on the advanced coupled matrix tensor factorization (ACMTF) method for analyzing simultaneous EEG-fMRI data. To alleviate the strict equality assumption of shared factors in the common dimension of the ACMTF, the proposed method used a similarity criterion based on normalized mutual information (NMI). This similarity criterion effectively revealed the underlying relationships between the modalities, resulting in more accurate factorization results.Results: The suggested method was utilized on simulated data with various levels of correlation between the components of the two modalities. Despite different noise levels, the average match score improved compared to the ACMTF model, as demonstrated by the results.Conclusion: By relaxing the strict equality assumption, we can identify shared components in a common mode and extract shared components with higher performance than the traditional methods. The suggested method offers a more robust and effective way to analyze multimodal data sets. The findings highlight the potential of the ACMTF method with NMI-based similarity criterion for uncovering hidden patterns in EEG and fMRI data.

Introduction With the developments in navigation, positioning, and tracking technologies, a large amount of moving point data (e.g., human, vehicle, animal) have been produced. Through moving an object in the course of time, a sequence of its position is recorded which is known as trajectory. Studying the behaviors of point objects and analyzing their trajectories have recently received great attentions among researchers in different fields of science, especially in geographic information science. Such studies contribute to better understanding of movement-behavior patterns of moving objects. Data mining, as one of the main approaches in geographic knowledge discovery, is normally used in moving databases to extract information from moving point objects’ trajectories. Analyzing the similarity of trajectories as one of the frequently used approaches in geographic data mining, is of great importance, which is normally performed by distance functions.

One of the biggest challenges in this field is classification problems which refers to the number of different samples in each class. If a data set includes two classes, imbalance distribution occurs when one class has a large number of samples while the other is represented by a small number of samples. In general, the methods of solving these problems are divided into two categories: under-sampling and over-sampling. In this research, it is focused on under-sampling and the advantages of this method will be analyzed by considering the efficiency of classifying imbalanced data and it’s supposed to provide a method for sampling a majority data class by using subtractive clustering and fuzzy similarity measure. For this purpose, at first the subtractive clustering is conducted and the majority data class is clustered. Then, using fuzzy similarity measure, samples of each cluster will be ranked and appropriate samples are selected based on these rankings. The selected samples with the minority class create the final dataset. In this research, MATLAB software is used for implementation, the results are evaluated by using AUC criterion and analyzing the results has been performed by standard statistical tools. The experimental results show that the proposed method is superior to other methods of under-sampling.