A Fuzzy-Rough Feature Selection Based on Binary Shuffled Frog Leaping Algorithm

Feature selection and attribute reduction are crucial problems, and widely used techniques in the field of machine learning, data mining and pattern recognition to overcome the well-known phenomenon of the Curse of Dimensionality. This paper presents a feature selection method that efficiently carries out attribute reduction, thereby selecting the most informative features of a dataset. It consists of two components: 1) a measure for feature subset evaluation, and 2) a search strategy. For the evaluation measure, we have employed the fuzzy-rough dependency degree (FRFDD) of the lower approximation-based fuzzy-rough feature selection (L-FRFS) due to its effectiveness in feature selection. As for the search strategy, a modified version of a binary shuffled frog leaping algorithm is proposed (B-SFLA). The proposed feature selection method is obtained by hybridizing the B-SFLA with the FRDD. Nine classifiers have been employed to compare the proposed approach with several existing methods over twenty two datasets, including nine high dimensional and large ones, from the UCI repository. The experimental results demonstrate that the B-SFLA approach significantly outperforms other metaheuristic methods in terms of the number of selected features and the classification accuracy.

Synthetic Aperture Radar Remote Sensing Classification Using the Bag of Visual Words Model to Land Cover Studies

Classification of high resolution polarimetric Synthetic Aperture Radar (PolSAR) images plays an important role in land cover and land use management. Recently, classification algorithms based on Bag of Visual Words (BOVW) model have attracted significant interest among scholars and researchers in and out of the field of remote sensing. In this paper, BOVW model with pixel based low-level features has been implemented to classify a subset of San Francisco bay PolSAR image, acquired by RADARSAR 2 in C-band. We have used segment-based decision-making strategy and compared the result with the result of traditional Support Vector Machine (SVM) classifier. 90.95% overall accuracy of the classification with the proposed algorithm has shown that the proposed algorithm is comparable with the state-of-the-art methods. In addition to increase in the classification accuracy, the proposed method has decreased undesirable speckle effect of SAR images.

Evaluation of Systemic Immune-Inflammation Index in Obese Children

A growing list of cancers might be influenced by obesity. Obesity is associated with an increased risk for the occurrence and development of some cancers. Inflammation can lead to cancer. It is one of the characteristic features of cancer and plays a critical role in cancer development. C-reactive protein (CRP) is under evaluation related to the new and simple prognostic factors in patients with metastatic renal cell cancer. Obesity can predict and promote systemic inflammation in healthy adults. BMI is correlated with hs-CRP. In this study, SII index and CRP values were evaluated in children with normal BMI and those within the range of different obesity grades to detect the tendency towards cancer in pediatric obesity. A total of one hundred and ninety-four children; thirty-five children with normal BMI, twenty overweight (OW), forty-seven obese (OB) and ninety-two morbid obese (MO) participated in the study. Age- and sex-matched groups were constituted using BMI-for age percentiles. Informed consent was obtained. Ethical Committee approval was taken. Weight, height, waist circumference (C), hip C, head C and neck C of the children were measured. The complete blood count test was performed. C-reactive protein analysis was performed. Statistical analyses were performed using SPSS. The degree for statistical significance was p≤0.05. SII index values were progressively increasing starting from normal weight (NW) to MO children. There is a statistically significant difference between NW and OB as well as MO children. No significant difference was observed between NW and OW children, however, a correlation was observed between NW and OW children. MO constitutes the only group, which exhibited a statistically significant correlation between SII index and CRP. Obesity-related bladder, kidney, cervical, liver, colorectal, endometrial cancers are still being investigated. Obesity, characterized as a chronic low-grade inflammation, is a crucial risk factor for colon cancer. Elevated childhood BMI values may be indicative of processes leading to cancer, initiated early in life. Prevention of childhood adiposity may decrease the cancer incidence in adults. To authors’ best knowledge, this study is the first to introduce SII index values during obesity of varying degrees of severity. It is suggested that this index seems to affect all stages of obesity with an increasing tendency and may point out the concomitant status of obesity and cancer starting from very early periods of life.

A Neuron Model of Facial Recognition and Detection of an Authorized Entity Using Machine Learning System

This paper has critically examined the use of Machine Learning procedures in curbing unauthorized access into valuable areas of an organization. The use of passwords, pin codes, user’s identification in recent times has been partially successful in curbing crimes involving identities, hence the need for the design of a system which incorporates biometric characteristics such as DNA and pattern recognition of variations in facial expressions. The facial model used is the OpenCV library which is based on the use of certain physiological features, the Raspberry Pi 3 module is used to compile the OpenCV library, which extracts and stores the detected faces into the datasets directory through the use of camera. The model is trained with 50 epoch run in the database and recognized by the Local Binary Pattern Histogram (LBPH) recognizer contained in the OpenCV. The training algorithm used by the neural network is back propagation coded using python algorithmic language with 200 epoch runs to identify specific resemblance in the exclusive OR (XOR) output neurons. The research however confirmed that physiological parameters are better effective measures to curb crimes relating to identities.

Lexical Based Method for Opinion Detection on Tripadvisor Collection

The massive development of online social networks allows users to post and share their opinions on various topics. With this huge volume of opinion, it is interesting to extract and interpret these information for different domains, e.g., product and service benchmarking, politic, system of recommendation. This is why opinion detection is one of the most important research tasks. It consists on differentiating between opinion data and factual data. The difficulty of this task is to determine an approach which returns opinionated document. Generally, there are two approaches used for opinion detection i.e. Lexical based approaches and Machine Learning based approaches. In Lexical based approaches, a dictionary of sentimental words is used, words are associated with weights. The opinion score of document is derived by the occurrence of words from this dictionary. In Machine learning approaches, usually a classifier is trained using a set of annotated document containing sentiment, and features such as n-grams of words, part-of-speech tags, and logical forms. Majority of these works are based on documents text to determine opinion score but dont take into account if these texts are really correct. Thus, it is interesting to exploit other information to improve opinion detection. In our work, we will develop a new way to consider the opinion score. We introduce the notion of trust score. We determine opinionated documents but also if these opinions are really trustable information in relation with topics. For that we use lexical SentiWordNet to calculate opinion and trust scores, we compute different features about users like (numbers of their comments, numbers of their useful comments, Average useful review). After that, we combine opinion score and trust score to obtain a final score. We applied our method to detect trust opinions in TRIPADVISOR collection. Our experimental results report that the combination between opinion score and trust score improves opinion detection.

Surface and Bulk Magnetization Behavior of Isolated Ferromagnetic NiFe Nanowires

The surface and bulk magnetization behavior of template released isolated ferromagnetic Ni60Fe40 nanowires of relatively thick diameters (~200 nm), deposited from a dilute suspension onto pre-patterned insulating chips have been investigated experimentally, using a highly sensitive Magneto-Optical Ker Effect (MOKE) magnetometry and Magneto-Resistance (MR) measurements, respectively. The MR data were consistent with the theoretical predictions of the anisotropic magneto-resistance (AMR) effect. The MR measurements, in all the angles of investigations, showed large features and a series of nonmonotonic "continuous small features" in the resistance profiles. The extracted switching fields from these features and from MOKE loops were compared with each other and with the switching fields reported in the literature that adopted the same analytical techniques on the similar compositions and dimensions of nanowires. A large difference between MOKE and MR measurments was noticed. The disparate between MOKE and MR results is attributed to the variance in the micro-magnetic structure of the surface and the bulk of such ferromagnetic nanowires. This result was ascertained using micro-magnetic simulations on an individual: cylindrical and rectangular cross sections NiFe nanowires, with the same diameter/thickness of the experimental wires, using the Object Oriented Micro-magnetic Framework (OOMMF) package where the simulated loops showed different switching events, indicating that such wires have different magnetic states in the reversal process and the micro-magnetic spin structures during switching behavior was complicated. These results further supported the difference between surface and bulk magnetization behavior in these nanowires. This work suggests that a combination of MOKE and MR measurements is required to fully understand the magnetization behavior of such relatively thick isolated cylindrical ferromagnetic nanowires.

Effects of Fermentation Techniques on the Quality of Cocoa Beans

Fermentation as an important operation in the processing of cocoa beans is now affected by the recent climate change across the globe. The major requirement for effective fermentation is the ability of the material used to retain sufficient heat for the required microbial activities. Apart from the effects of climate on the rate of heat retention, the materials used for fermentation plays an important role. Most Farmers still restrict fermentation activities to the use of traditional methods. Improving on cocoa fermentation in this era of climate change makes it necessary to work on other materials that can be suitable for cocoa fermentation. Therefore, the objective of this study was to determine the effects of fermentation techniques on the quality of cocoa beans. The materials used in this fermentation research were heap-leaves (traditional), stainless steel, plastic tin, plastic basket and wooden box. The period of fermentation varies from zero days to 10 days. Physical and chemical tests were carried out for variables in quality determination in the samples. The weight per bean varied from 1.0-1.2 g after drying across the samples and the major color of the dry beans observed was brown except with the samples from stainless steel. The moisture content varied from 5.5-7%. The mineral content and the heavy metals decreased with increase in the fermentation period. A wooden box can conclusively be used as an alternative to heap-leaves as there was no significant difference in the physical features of the samples fermented with the two methods. The use of a wooden box as an alternative for cocoa fermentation is therefore recommended for cocoa farmers.

Development of a Biomaterial from Naturally Occurring Chloroapatite Mineral for Biomedical Applications

Hydroxyapatite is a bioceramic which can be used for applications in orthopedics and dentistry due to its structural similarity with the mineral phase of mammalian bones and teeth. In this study, it was synthesized, chemically changing natural Eppawala chloroapatite mineral as a value-added product. Sol-gel approach and solid state sintering were used to synthesize products using diluted nitric acid, ethanol and calcium hydroxide under different conditions. Synthesized Eppawala hydroxyapatite powder was characterized using X-ray Fluorescence (XRF), X-ray Powder Diffraction (XRD), Fourier-transform Infrared Spectroscopy (FTIR), Scanning Electron Microscopy (SEM), Thermogravimetric Analysis (TGA) and Differential Scanning Calorimetry (DSC) in order to find out its composition, crystallinity, presence of functional groups, bonding type, surface morphology, microstructural features, and thermal dependence and stability, respectively. The XRD results reflected the formation of a hexagonal crystal structure of hydroxyapatite. Elementary composition and microstructural features of products were discussed based on the XRF and SEM results of the synthesized hydroxyapatite powder. TGA and DSC results of synthesized products showed high thermal stability and good material stability in nature. Also, FTIR spectroscopy results confirmed the formation of hydroxyapatite from apatite via the presence of hydroxyl groups. Those results coincided with the FTIR results of mammalian bones including human bones. The study concludes that there is a possibility of producing hydroxyapatite using commercially available Eppawala chloroapatite in Sri Lanka.

Understanding the Programming Techniques Using a Complex Case Study to Teach Advanced Object-Oriented Programming

Teaching Object-Oriented Programming (OOP) as part of a Computing-related university degree is a very difficult task; the road to ensuring that students are actually learning object oriented concepts is unclear, as students often find it difficult to understand the concept of objects and their behavior. This problem is especially obvious in advanced programming modules where Design Pattern and advanced programming features such as Multi-threading and animated GUI are introduced. Looking at the students’ performance at their final year on a university course, it was obvious that the level of students’ understanding of OOP varies to a high degree from one student to another. Students who aim at the production of Games do very well in the advanced programming module. However, the students’ assessment results of the last few years were relatively low; for example, in 2016-2017, the first quartile of marks were as low as 24.5 and the third quartile was 63.5. It is obvious that many students were not confident or competent enough in their programming skills. In this paper, the reasons behind poor performance in Advanced OOP modules are investigated, and a suggested practice for teaching OOP based on a complex case study is described and evaluated.

Pareidolia and Perception of Anger in Vehicle Styles: Survey Results

Most people see human faces in car front and back ends because of the process of pareidolia. 96 people were surveyed to see how many of them saw a face in the vehicle styling. Participants were aged 18 to 72 years. 94% of the participants saw faces in the front-end design of production models. All participants that recognized faces indicated that most styles showed some degree of an angry expression. It was found that women were more likely to see faces in inanimate objects. However, with respect to whether women were more likely to perceive anger in the vehicle design, the results need further clarification. Survey responses were correlated to the design features of vehicles to determine what cues the respondents were likely looking at when responding. Whether the features looked anthropomorphic was key to anger perception. Features such as the headlights which could represent eyes and the air intake that could represent a mouth had high correlations to trends in scores. Results are compared among models, makers, by groupings of body styles classifications for the top 12 brands sold in the US, and by year for the top 20 models sold in the US in 2016. All of the top models sold increased in perception of an angry expression over the last 20 years or since the model was introduced, but the relative change varied by body style grouping.

Specialized Translation Teaching Strategies: A Corpus-Based Approach

This study presents a methodology of specialized translation with the objective of helping teachers to improve the strategies in teaching translation. In order to allow students to acquire skills to translate specialized texts, they need to become familiar with the semantic and syntactic features of source texts and target texts. The aim of our study is to use a corpus-based approach in the teaching of specialized translation between Chinese and Italian. This study proposes to construct a specialized Chinese - Italian comparable corpus that consists of 50 economic contracts from the domain of food. With the help of AntConc, we propose to compile a comparable corpus in for translation teaching purposes. This paper attempts to provide insight into how teachers could benefit from comparable corpus in the teaching of specialized translation from Italian into Chinese and through some examples of passive sentences how students could learn to apply different strategies for translating appropriately the voice.

A Design for Customer Preferences Model by Cluster Analysis of Geometric Features and Customer Preferences

In the design cycle, a main design task is to determine the external shape of the product. The external shape of a product is one of the key factors that can affect the customers’ preferences linking to the motivation to buy the product, especially in the case of a consumer electronic product such as a mobile phone. The relationship between the external shape and the customer preferences needs to be studied to enhance the customer’s purchase desire and action. In this research, a design for customer preferences model is developed for investigating the relationships between the external shape and the customer preferences of a product. In the first stage, the names of the geometric features are collected and evaluated from the data of the specified internet web pages using the developed text miner. The key geometric features can be determined if the number of occurrence on the web pages is relatively high. For each key geometric feature, the numerical values are explored using the text miner to collect the internet data from the web pages. In the second stage, a cluster analysis model is developed to evaluate the numerical values of the key geometric features to divide the external shapes into several groups. Several design suggestion cases can be proposed, for example, large model, mid-size model, and mini model, for designing a mobile phone. A customer preference index is developed by evaluating the numerical data of each of the key geometric features of the design suggestion cases. The design suggestion case with the top ranking of the customer preference index can be selected as the final design of the product. In this paper, an example product of a notebook computer is illustrated. It shows that the external shape of a product can be used to drive customer preferences. The presented design for customer preferences model is useful for determining a suitable external shape of the product to increase customer preferences.

Automated Heart Sound Classification from Unsegmented Phonocardiogram Signals Using Time Frequency Features

Cardiologists perform cardiac auscultation to detect abnormalities in heart sounds. Since accurate auscultation is a crucial first step in screening patients with heart diseases, there is a need to develop computer-aided detection/diagnosis (CAD) systems to assist cardiologists in interpreting heart sounds and provide second opinions. In this paper different algorithms are implemented for automated heart sound classification using unsegmented phonocardiogram (PCG) signals. Support vector machine (SVM), artificial neural network (ANN) and cartesian genetic programming evolved artificial neural network (CGPANN) without the application of any segmentation algorithm has been explored in this study. The signals are first pre-processed to remove any unwanted frequencies. Both time and frequency domain features are then extracted for training the different models. The different algorithms are tested in multiple scenarios and their strengths and weaknesses are discussed. Results indicate that SVM outperforms the rest with an accuracy of 73.64%.

A Taxonomy Proposal on Criterion Structure for Evaluating Freight Village Concepts in Early-Stage Design Projects

The early-stage design and development projects for the freight village initiatives require a comprehensive analysis of both qualitative and quantitative data. Considering the literature review on structural and operational management requirements, this study proposed an original taxonomy on criterion structure to assess freight village conceptualization. The potential challenges and uncertainties of the developed taxonomy are extended. Besides requirement analysis, this study is also expected to contribute to forthcoming research on benchmarking of freight villages in different regions. The methodology used in this research is a systematic review on several articles as per their modelling approaches, sustainability, entities and decisions made together with the uncertainties and features of their models taken into consideration. The major findings of the study that are the categories for assessing the projects attributes on their environmental, socio-economical, accessibility and location aspects.

Accessible Facilities in Home Environment for Elderly Family Members in Sri Lanka

The world is facing several problems due to increasing elderly population. In Sri Lanka, along with the complexity of the modern society and structural and functional changes of the family, “caring for elders” seems as an emerging social problem. This situation may intensify as the county is moving into a middle income society. Seeking higher education and related career opportunities, and urban living in modern housing are new trends, through which several problems are generated. Among many issues related with elders, “lack of accessible and appropriate facilities in their houses as well as public buildings” can be identified as a major problem. This study argues that welfare facilities provided for the elderly people, particularly in the home environment, in the country are not adequate. Modern housing features such as bathrooms, pantries, lobbies, and leisure areas etc. are questionable as to whether they match with elders’ physical and mental needs. Consequently, elders have to face domestic accidents and many other difficulties within their living environments. Records of hospitals in the country also proved this fact. Therefore, this study tries to identify how far modern houses are suited with elders’ needs. The study further questioned whether “aging” is a considerable matter when people are buying, planning and renovating houses. A randomly selected sample of 50 houses were observed and 50 persons were interviewed around the Maharagama urban area in Colombo district to obtain primary data, while relevant secondary data and information were used to have a depth analysis. The study clearly found that none of the houses included to the sample are considering elders’ needs in planning, renovating, or arranging the home. Instead, most of the families were giving priority to the rich and elegant appearance and modern facilities of the houses. Particularly, to the bathrooms, pantry, large setting areas, balcony, parking slots for two vehicles, ad parapet walls with roller-gates are the main concerns. A significant factor found here is that even though, many children of the aged are in middle age and reaching their older years at present, they do not plan their future living within a safe and comfortable home, despite that they are hoping to spent the latter part of their lives in the their current homes. This fact highlights that not only the other responsible parts of the society, but also those who are reaching their older ages are ignoring the problems of the aged. At the same time, it was found that more than 80% of old parents do not like to stay at their children’s homes as the living environments in such modern homes are not familiar or convenient for them. Due to this context, the aged in Sri Lanka may have to be alone in their own homes due to current trend of society of migrating to urban living in modern houses. At the same time, current urban families who live in modern houses may have to face adding accessible facilities in their home environment, as current modern housing facilities may not be appropriate them for a better life in their latter part of life.

Meta-Learning for Hierarchical Classification and Applications in Bioinformatics

Hierarchical classification is a special type of classification task where the class labels are organised into a hierarchy, with more generic class labels being ancestors of more specific ones. Meta-learning for classification-algorithm recommendation consists of recommending to the user a classification algorithm, from a pool of candidate algorithms, for a dataset, based on the past performance of the candidate algorithms in other datasets. Meta-learning is normally used in conventional, non-hierarchical classification. By contrast, this paper proposes a meta-learning approach for more challenging task of hierarchical classification, and evaluates it in a large number of bioinformatics datasets. Hierarchical classification is especially relevant for bioinformatics problems, as protein and gene functions tend to be organised into a hierarchy of class labels. This work proposes meta-learning approach for recommending the best hierarchical classification algorithm to a hierarchical classification dataset. This work’s contributions are: 1) proposing an algorithm for splitting hierarchical datasets into new datasets to increase the number of meta-instances, 2) proposing meta-features for hierarchical classification, and 3) interpreting decision-tree meta-models for hierarchical classification algorithm recommendation.

Improving Similarity Search Using Clustered Data

This paper presents a method for improving object search accuracy using a deep learning model. A major limitation to provide accurate similarity with deep learning is the requirement of huge amount of data for training pairwise similarity scores (metrics), which is impractical to collect. Thus, similarity scores are usually trained with a relatively small dataset, which comes from a different domain, causing limited accuracy on measuring similarity. For this reason, this paper proposes a deep learning model that can be trained with a significantly small amount of data, a clustered data which of each cluster contains a set of visually similar images. In order to measure similarity distance with the proposed method, visual features of two images are extracted from intermediate layers of a convolutional neural network with various pooling methods, and the network is trained with pairwise similarity scores which is defined zero for images in identical cluster. The proposed method outperforms the state-of-the-art object similarity scoring techniques on evaluation for finding exact items. The proposed method achieves 86.5% of accuracy compared to the accuracy of the state-of-the-art technique, which is 59.9%. That is, an exact item can be found among four retrieved images with an accuracy of 86.5%, and the rest can possibly be similar products more than the accuracy. Therefore, the proposed method can greatly reduce the amount of training data with an order of magnitude as well as providing a reliable similarity metric.

Inorganic Anion Removal from Water Using Natural Adsorbents

There is a need for new systems that can be attached to drinking water treatment plants and have the required treatment capacity as well as the selectivity regarding components derived from anthropogenic activities. In a context of high volumes of water and low concentration of contaminants, adsorption/interchange processes are appealing since they meet the required features. Iron oxides such as siderite and molysite, which are respectively based on FeCO3 and FeCl3, can be found in nature. In this work, their observed performance, raw or roasted at different temperatures, as adsorbents of some inorganic anions is discussed. Roasted 1:1 FeCO3: FeCl3 mixture was very selective for arsenic and allowed a 100% removal of As from a 10 mg L-1 As solution. Besides, the 1:1 FeCO3 and FeCl3 mixture roasted at 500 ºC showed good selectivity for, in order of preference, arsenate, bromate, phosphate, fluoride and nitrate anions with distribution coefficients of, respectively, 4200, 2800, 2500 0.4 and 0.03 L g-1.

Cobalamin, Folate and Metabolic Syndrome Parameters in Pediatric Morbid Obesity and Metabolic Syndrome

Obesity is known to be associated with many clinically important diseases including metabolic syndrome (MetS). Vitamin B12 plays essential roles in fat and protein metabolisms and its cooperation with vitamin B9 is well-known. The aim of this study is to investigate the possible contributions as well as associations of these micronutrients upon obesity and MetS during childhood. A total of 128 children admitted to Namik Kemal University, Medical Faculty, Department of Pediatrics Outpatient Clinics were included into the scope of this study. The mean age±SEM of 92 morbid obese (MO) children and 36 with MetS were 118.3±3.8 months and 129.5±6.4 months, respectively (p > 0.05). The study was approved by Namık Kemal University, Medical Faculty Ethics Committee. Written informed consent forms were obtained from the parents. Demographic features and anthropometric measurements were recorded. WHO BMI-for age percentiles were used. The values above 99 percentile were defined as MO. Components of MetS [waist circumference (WC), fasting blood glucose (FBG), triacylglycerol (TRG), high density lipoprotein cholesterol (HDL-Chol), systolic pressure (SP), diastolic pressure (DP)] were determined. Routine laboratory tests were performed. Serum vitamin B12 concentrations were measured using electrochemiluminescence immunoassay. Vitamin B9 was analyzed by an immunoassay analyzer. Values for vitamin B12 < 148 pmol/L, 148-221 pmol/L, > 221 pmol/L were accepted as low, borderline and normal, respectively. Vitamin B9 levels ≤ 4 mcg/L defined deficiency state. Statistical evaluations were performed by SPSSx Version 16.0. p≤0.05 was accepted as statistical significance level. Statistically higher body mass index (BMI), WC, hip circumference (C) and neck C were calculated in MetS group compared to children with MO. No difference was noted for head C. All MetS components differed between the groups (SP, DP p < 0.001; WC, FBG, TRG p < 0.01; HDL-Chol p < 0.05). Significantly decreased vitamin B9 and vitamin B12 levels were detected (p < 0.05) in children with MetS. In both groups percentage of folate deficiency was 5.5%. No cases were below < 148 pmol/L. However, in MO group 14.3% and in MetS group 22.2% of the cases were of borderline status. In MO group B12 levels were negatively correlated with BMI, WC, hip C and head C, but not with neck C. WC, hip C, head C and neck C were all negatively correlated with HDL-Chol. None of these correlations were observed in the group of children with MetS. Strong positive correlation between FBG and insulin as well as strong negative correlation between TRG and HDL-Chol detected in MO children were lost in MetS group. Deficiency state end-products of both B9 and B12 may interfere with the expected profiles of MetS components. In this study, the alterations in MetS components affected vitamin B12 metabolism and also its associations with anthropometric body measurements. Further increases in vitamin B12 and vitamin B9 deficiency in MetS associated with the increased vitamin B12 as well as vitamin B9 deficiency metabolites may add to MetS parameters.

Generating a Functional Grammar for Architectural Design from Structural Hierarchy in Combination of Square and Equal Triangle

Islamic culture was accountable for a plethora of development in astronomy and science in the medieval term, and in geometry likewise. Geometric patterns are reputable in a considerable number of cultures, but in the Islamic culture the patterns have specific features that connect the Islamic faith to mathematics. In Islamic art, three fundamental shapes are generated from the circle shape: triangle, square and hexagon. Originating from their quiddity, each of these geometric shapes has its own specific structure. Even though the geometric patterns were generated from such simple forms as the circle and the square, they can be combined, duplicated, interlaced, and arranged in intricate combinations. So in order to explain geometrical interaction principles between square and equal triangle, in the first definition step, all types of their linear forces individually and in the second step, between them, would be illustrated. In this analysis, some angles will be created from intersection of their directions. All angles are categorized to some groups and the mathematical expressions among them are analyzed. Since the most geometric patterns in Islamic art and architecture are based on the repetition of a single motif, the evaluation results which are obtained from a small portion, is attributable to a large-scale domain while the development of infinitely repeating patterns can represent the unchanging laws. Geometric ornamentation in Islamic art offers the possibility of infinite growth and can accommodate the incorporation of other types of architectural layout as well, so the logic and mathematical relationships which have been obtained from this analysis are applicable in designing some architecture layers and developing the plan design.