**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**1015

# Search results for: Distance metric

##### 1015 Graphs with Metric Dimension Two-A Characterization

**Authors:**
Sudhakara G,
Hemanth Kumar A.R

**Abstract:**

In this paper, we define distance partition of vertex set of a graph G with reference to a vertex in it and with the help of the same, a graph with metric dimension two (i.e. β (G) = 2 ) is characterized. In the process, we develop a polynomial time algorithm that verifies if the metric dimension of a given graph G is two. The same algorithm explores all metric bases of graph G whenever β (G) = 2 . We also find a bound for cardinality of any distance partite set with reference to a given vertex, when ever β (G) = 2 . Also, in a graph G with β (G) = 2 , a bound for cardinality of any distance partite set as well as a bound for number of vertices in any sub graph H of G is obtained in terms of diam H .

**Keywords:**
Metric basis,
Distance partition,
Metric dimension.

##### 1014 A Distance Function for Data with Missing Values and Its Application

**Authors:**
Loai AbdAllah,
Ilan Shimshoni

**Abstract:**

Missing values in data are common in real world applications. Since the performance of many data mining algorithms depend critically on it being given a good metric over the input space, we decided in this paper to define a distance function for unlabeled datasets with missing values. We use the Bhattacharyya distance, which measures the similarity of two probability distributions, to define our new distance function. According to this distance, the distance between two points without missing attributes values is simply the Mahalanobis distance. When on the other hand there is a missing value of one of the coordinates, the distance is computed according to the distribution of the missing coordinate. Our distance is general and can be used as part of any algorithm that computes the distance between data points. Because its performance depends strongly on the chosen distance measure, we opted for the k nearest neighbor classifier to evaluate its ability to accurately reflect object similarity. We experimented on standard numerical datasets from the UCI repository from different fields. On these datasets we simulated missing values and compared the performance of the kNN classifier using our distance to other three basic methods. Our experiments show that kNN using our distance function outperforms the kNN using other methods. Moreover, the runtime performance of our method is only slightly higher than the other methods.

**Keywords:**
Missing values,
Distance metric,
Bhattacharyya distance.

##### 1013 Adaptive Few-Shot Deep Metric Learning

**Authors:**
Wentian Shi,
Daming Shi,
Maysam Orouskhani,
Feng Tian

**Abstract:**

Currently the most prevalent deep learning methods require a large amount of data for training, whereas few-shot learning tries to learn a model from limited data without extensive retraining. In this paper, we present a loss function based on triplet loss for solving few-shot problem using metric based learning. Instead of setting the margin distance in triplet loss as a constant number empirically, we propose an adaptive margin distance strategy to obtain the appropriate margin distance automatically. We implement the strategy in the deep siamese network for deep metric embedding, by utilizing an optimization approach by penalizing the worst case and rewarding the best. Our experiments on image recognition and co-segmentation model demonstrate that using our proposed triplet loss with adaptive margin distance can significantly improve the performance.

**Keywords:**
Few-shot learning,
triplet network,
adaptive margin,
deep learning.

##### 1012 Metric Dimension on Line Graph of Honeycomb Networks

**Authors:**
M. Hussain,
Aqsa Farooq

**Abstract:**

**Keywords:**
Resolving set,
metric dimension,
honeycomb network,
line graph.

##### 1011 Method of Moments Applied to a Cuboidal Cavity Resonator: Effect of Gravitational Field Produced by a Black Hole

**Authors:**
Arti Vaish,
Harish Parthasarathy

**Abstract:**

This paper deals with the formulation of Maxwell-s equations in a cavity resonator in the presence of the gravitational field produced by a blackhole. The metric of space-time due to the blackhole is the Schwarzchild metric. Conventionally, this is expressed in spherical polar coordinates. In order to adapt this metric to our problem, we have considered this metric in a small region close to the blackhole and expressed this metric in a cartesian system locally.

**Keywords:**
Method of moments,
General theory of relativity,
Electromagnetism,
Metric tensor,
schwarzchild metric,
Wave Equation.

##### 1010 A Design-Based Cohesion Metric for Object-Oriented Classes

**Authors:**
Jehad Al Dallal

**Abstract:**

**Keywords:**
Object-oriented software quality,
object-orienteddesign,
class cohesion.

##### 1009 A Supervised Text-Independent Speaker Recognition Approach

**Authors:**
Tudor Barbu

**Abstract:**

We provide a supervised speech-independent voice recognition technique in this paper. In the feature extraction stage we propose a mel-cepstral based approach. Our feature vector classification method uses a special nonlinear metric, derived from the Hausdorff distance for sets, and a minimum mean distance classifier.

**Keywords:**
Text-independent speaker recognition,
mel cepstral
analysis,
speech feature vector,
Hausdorff-based metric,
supervised
classification.

##### 1008 Accelerating GLA with an M-Tree

**Authors:**
Olli Luoma,
Johannes Tuikkala,
Olli Nevalainen

**Abstract:**

**Keywords:**
Clustering,
GLA,
M-Tree,
Vector
Quantization .

##### 1007 A New Concept for Deriving the Expected Value of Fuzzy Random Variables

**Authors:**
Liang-Hsuan Chen,
Chia-Jung Chang

**Abstract:**

Fuzzy random variables have been introduced as an imprecise concept of numeric values for characterizing the imprecise knowledge. The descriptive parameters can be used to describe the primary features of a set of fuzzy random observations. In fuzzy environments, the expected values are usually represented as fuzzy-valued, interval-valued or numeric-valued descriptive parameters using various metrics. Instead of the concept of area metric that is usually adopted in the relevant studies, the numeric expected value is proposed by the concept of distance metric in this study based on two characters (fuzziness and randomness) of FRVs. Comparing with the existing measures, although the results show that the proposed numeric expected value is same with those using the different metric, if only triangular membership functions are used. However, the proposed approach has the advantages of intuitiveness and computational efficiency, when the membership functions are not triangular types. An example with three datasets is provided for verifying the proposed approach.

**Keywords:**
Fuzzy random variables,
Distance measure,
Expected value.

##### 1006 Distances over Incomplete Diabetes and Breast Cancer Data Based on Bhattacharyya Distance

**Authors:**
Loai AbdAllah,
Mahmoud Kaiyal

**Abstract:**

**Keywords:**
Missing values,
distance metric,
Bhattacharyya
distance.

##### 1005 Analysis on Fractals in Intuitionistic Fuzzy Metric Spaces

**Authors:**
R. Uthayakumar,
D. Easwaramoorthy

**Abstract:**

**Keywords:**
Fractal Analysis,
Fixed Point,
Contraction,
Iterated Function System,
Intuitionistic Fuzzy Metric Space.

##### 1004 Hutchinson-Barnsley Operator in Intuitionistic Fuzzy Metric Spaces

**Authors:**
R. Uthayakumar,
D. Easwaramoorthy

**Abstract:**

The main purpose of this paper is to prove the intuitionistic fuzzy contraction properties of the Hutchinson-Barnsley operator on the intuitionistic fuzzy hyperspace with respect to the Hausdorff intuitionistic fuzzy metrics. Also we discuss about the relationships between the Hausdorff intuitionistic fuzzy metrics on the intuitionistic fuzzy hyperspaces. Our theorems generalize and extend some recent results related with Hutchinson-Barnsley operator in the metric spaces to the intuitionistic fuzzy metric spaces.

**Keywords:**
Contraction,
Iterated Function System,
Hutchinson- Barnsley Operator,
Intuitionistic Fuzzy Metric Space,
Hausdorff Intuitionistic Fuzzy Metric.

##### 1003 Application of l1-Norm Minimization Technique to Image Retrieval

**Authors:**
C. S. Sastry,
Saurabh Jain,
Ashish Mishra

**Abstract:**

Image retrieval is a topic where scientific interest is currently high. The important steps associated with image retrieval system are the extraction of discriminative features and a feasible similarity metric for retrieving the database images that are similar in content with the search image. Gabor filtering is a widely adopted technique for feature extraction from the texture images. The recently proposed sparsity promoting l1-norm minimization technique finds the sparsest solution of an under-determined system of linear equations. In the present paper, the l1-norm minimization technique as a similarity metric is used in image retrieval. It is demonstrated through simulation results that the l1-norm minimization technique provides a promising alternative to existing similarity metrics. In particular, the cases where the l1-norm minimization technique works better than the Euclidean distance metric are singled out.

**Keywords:**
l1-norm minimization,
content based retrieval,
modified Gabor function.

##### 1002 Hutchinson-Barnsley Operator in Fuzzy Metric Spaces

**Authors:**
R. Uthayakumar,
D. Easwaramoorthy

**Abstract:**

**Keywords:**
Fractals,
Iterated Function System,
Hutchinson- Barnsley Operator,
Fuzzy Metric Space,
Hausdorff Fuzzy Metric.

##### 1001 Feature Extraction for Surface Classification – An Approach with Wavelets

**Authors:**
Smriti H. Bhandari,
S. M. Deshpande

**Abstract:**

Surface metrology with image processing is a challenging task having wide applications in industry. Surface roughness can be evaluated using texture classification approach. Important aspect here is appropriate selection of features that characterize the surface. We propose an effective combination of features for multi-scale and multi-directional analysis of engineering surfaces. The features include standard deviation, kurtosis and the Canny edge detector. We apply the method by analyzing the surfaces with Discrete Wavelet Transform (DWT) and Dual-Tree Complex Wavelet Transform (DT-CWT). We used Canberra distance metric for similarity comparison between the surface classes. Our database includes the surface textures manufactured by three machining processes namely Milling, Casting and Shaping. The comparative study shows that DT-CWT outperforms DWT giving correct classification performance of 91.27% with Canberra distance metric.

**Keywords:**
Dual-tree complex wavelet transform,
surface metrology,
surface roughness,
texture classification.

##### 1000 Cognitive Weighted Polymorphism Factor: A Comprehension Augmented Complexity Metric

**Authors:**
T. Francis Thamburaj,
A. Aloysius

**Abstract:**

**Keywords:**
Cognitive complexity metric,
cognitive weighted
polymorphism factor,
object-oriented metrics,
polymorphism factor,
software metrics.

##### 999 A New Approach for Image Segmentation using Pillar-Kmeans Algorithm

**Authors:**
Ali Ridho Barakbah,
Yasushi Kiyoki

**Abstract:**

**Keywords:**
Image segmentation,
K-means clustering,
Pillaralgorithm,
color spaces.

##### 998 A Geometrical Perspective on the Insulin Evolution

**Authors:**
Yuhei Kunihiro,
Sorin V. Sabau,
Kazuhiro Shibuya

**Abstract:**

We study the molecular evolution of insulin from metric geometry point of view. In mathematics, and in particular in geometry, distances and metrics between objects are of fundamental importance. Using a weaker notion than the classical distance, namely the weighted quasi-metrics, one can study the geometry of biological sequences (DNA, mRNA, or proteins) space. We analyze from geometrical point of view a family of 60 insulin homologous sequences ranging on a large variety of living organisms from human to the nematode C. elegans. We show that the distances between sequences provide important information about the evolution and function of insulin.

**Keywords:**
Metric geometry,
evolution,
insulin.

##### 997 The Validity Range of LSDP Robust Controller by Exploiting the Gap Metric Theory

**Authors:**
Ali Ameur Haj Salah,
Tarek Garna,
Hassani Messaoud

**Abstract:**

This paper attempts to define the validity domain of LSDP (Loop Shaping Design Procedure) controller system, by determining the suitable uncertainty region, so that linear system be stable. Indeed the LSDP controller cannot provide stability for any perturbed system. For this, we will use the gap metric tool that is introduced into the control literature for studying robustness properties of feedback systems with uncertainty. A 2nd order electric linear system example is given to define the validity domain of LSDP controller and effectiveness gap metric.

**Keywords:**
LSDP,
Gap metric,
Robust Control.

##### 996 Fixed Point Theorems for Set Valued Mappings in Partially Ordered Metric Spaces

**Authors:**
Ismat Beg,
Asma Rashid Butt

**Abstract:**

Let (X,) be a partially ordered set and d be a metric on X such that (X, d) is a complete metric space. Assume that X satisfies; if a non-decreasing sequence xn → x in X, then xn x, for all n. Let F be a set valued mapping from X into X with nonempty closed bounded values satisfying; (i) there exists κ ∈ (0, 1) with D(F(x), F(y)) ≤ κd(x, y), for all x y, (ii) if d(x, y) < ε < 1 for some y ∈ F(x) then x y, (iii) there exists x0 ∈ X, and some x1 ∈ F(x0) with x0 x1 such that d(x0, x1) < 1. It is shown that F has a fixed point. Several consequences are also obtained.

**Keywords:**
Fixed point,
partially ordered set,
metric space,
set
valued mapping.

##### 995 IFS on the Multi-Fuzzy Fractal Space

**Authors:**
Nadia M. G. AL-Sa'idi,
Muhammad Rushdan Md. Sd.,
Adil M. Ahmed

**Abstract:**

The IFS is a scheme for describing and manipulating complex fractal attractors using simple mathematical models. More precisely, the most popular “fractal –based" algorithms for both representation and compression of computer images have involved some implementation of the method of Iterated Function Systems (IFS) on complete metric spaces. In this paper a new generalized space called Multi-Fuzzy Fractal Space was constructed. On these spases a distance function is defined, and its completeness is proved. The completeness property of this space ensures the existence of a fixed-point theorem for the family of continuous mappings. This theorem is the fundamental result on which the IFS methods are based and the fractals are built. The defined mappings are proved to satisfy some generalizations of the contraction condition.

**Keywords:**
Fuzzy metric space,
Fuzzy fractal space,
Multi fuzzy
fractal space.

##### 994 An Iterated Function System for Reich Contraction in Complete b Metric Space

**Authors:**
R. Uthayakumar,
G. Arockia Prabakar

**Abstract:**

In this paper, we introduce R Iterated Function System and employ the Hutchinson Barnsley theory (HB) to construct a fractal set as its unique fixed point by using Reich contractions in a complete b metric space. We discuss about well posedness of fixed point problem for b metric space.

**Keywords:**
Fractals,
Iterated Function System,
Compact set,
Reich
Contraction,
Well posedness.

##### 993 Best Proximity Point Theorems for MT-K and MT-C Rational Cyclic Contractions in Metric Spaces

**Authors:**
M. R. Yadav,
A. K. Sharma,
B. S. Thakur

**Abstract:**

The purpose of this paper is to present a best proximity point theorems through rational expression for a combination of contraction condition, Kannan and Chatterjea nonlinear cyclic contraction in what we call MT-K and MT-C rational cyclic contraction. Some best proximity point theorems for a mapping satisfy these conditions have been established in metric spaces. We also give some examples to support our work.

**Keywords:**
Cyclic contraction,
rational cyclic contraction,
best proximity point and complete metric space.

##### 992 Differences in Students` Satisfaction with Distance Learning Studies

**Authors:**
Ana Horvat,
Maja Krsmanovic,
Mladen Djuric

**Abstract:**

**Keywords:**
distance learning,
students' satisfaction

##### 991 A P2P File Sharing Technique by Indexed-Priority Metric

**Authors:**
Toshinori Takabatake,
Yoshikazu Komano

**Abstract:**

**Keywords:**
peer-to-peer,
file-sharing system,
load-balancing,
dependability

##### 990 OWA Operators in Generalized Distances

**Authors:**
José M. Merigó,
Anna M. Gil-Lafuente

**Abstract:**

**Keywords:**
Aggregation operators,
Distance measures,
Quasi- OWA operator.

##### 989 Analyzing Methods of the Relation between Concepts based on a Concept Hierarchy

**Authors:**
Ke Lu,
Tetsuya Furukawa

**Abstract:**

**Keywords:**
Concept Hierarchy,
Horizontal Distance,
Relation
Analysis,
Vertical Distance

##### 988 Using the OWA Operator in the Minkowski Distance

**Authors:**
José M. Merigó,
Anna M. Gil-Lafuente

**Abstract:**

**Keywords:**
Aggregation operators,
Minkowski distance,
OWA
operators,
Selection of strategies.

##### 987 The Distance between a Point and a Bezier Curveon a Bezier Surface

**Authors:**
Wen-Haw Chen,
Sheng-Gwo Chen

**Abstract:**

**Keywords:**
Geodesic-like curve,
distance,
projection,
Bezier.

##### 986 The Content Based Objective Metrics for Video Quality Evaluation

**Authors:**
Michal Mardiak,
Jaroslav Polec

**Abstract:**

In this paper we proposed comparison of four content based objective metrics with results of subjective tests from 80 video sequences. We also include two objective metrics VQM and SSIM to our comparison to serve as “reference” objective metrics because their pros and cons have already been published. Each of the video sequence was preprocessed by the region recognition algorithm and then the particular objective video quality metric were calculated i.e. mutual information, angular distance, moment of angle and normalized cross-correlation measure. The Pearson coefficient was calculated to express metrics relationship to accuracy of the model and the Spearman rank order correlation coefficient to represent the metrics relationship to monotonicity. The results show that model with the mutual information as objective metric provides best result and it is suitable for evaluating quality of video sequences.

**Keywords:**
Objective quality metrics,
mutual information,
region recognition,
content based metrics