A New Support Vector Finder Method Based on Triangular Calculations 9th International Conference on Information and Knowledge Technology (IKT 2017) A New Support Vector Finder Method Based on Triangular Calculations and K-means Clustering Seyed Muhammad Hossein Mousavi S.Younes MiriNezhad Atiye Mirmoini Bu Ali Sina University Department of Computer Engineering

ABSTRACT Classification SVM Least Squares Linear discriminant analysis K-means clustering Find the best Support vectors

INTRODUCTION Pattern Recognition K-means Clustering Support Vector Pattern recognition methods separate intended patterns out of a bunch of data, using prior knowledge about patterns or statistical information of data. By reducing classification samples, make classification process easier and faster. Finding Support vector samples is a pre-processing for some classification algorithms.

K-means Clustering Solve clustering problem Unsupervised learning algorithms K-means Procedure Place K points into the space represented by the objects that are being clustered. These points represent initial group centroids. Assign each object to the group that has the closest centroid. When all objects have been assigned, recalculate the positions of the K centroids. Repeat Steps 2 and 3 until the centroids no longer move. This produces a separation of the objects into groups from which the metric to be minimized can be calculated.

Support Vector Support Vector An algorithm that implements classification, is known as a classifier. Some classification algorithms like SVM, uses pre-processing to find best discriminant hyper-planes between classes and one of these pre-processing is finding Support vector samples. Support vectors are marginal samples between classes which have the most closeness to other classes and closest to the separating hyper-plane.

01 02 03 SOME OF PREVIOUS WORKS Support Vector Machine (SVM) In 1963 was invented and uses Karush–Kuhn–Tucker conditions to finding support vectors. 02 Schölkopf, Bernhard in 2000 they proposed a new class of support vector algorithms for regression and classification, their main ideas was to eliminate the unnecessary parameters to increase the classification process 03 Hao, Pei-Yi In 2010, they proposed a modification of v-support vector machines (v-SVM) for regression and classification and the use of a parametric insensitive/margin model with an arbitrary shape.

PROBLEMS AND CHALLENGE noisy data outlier data

PROPOSED METHOD Select boundary sample by k-means Reduce sample number Delete outlier data n clusters in each class Find clusters center Calculate distances Eliminate unfit clusters

PROPOSED METHOD η ζ calculate three angles Select three points to make triangular calculate triangle area 𝑇𝑟𝑖𝑎𝑛𝑔𝑙𝑒 𝐴𝑟𝑒𝑎= 1 2 𝑏∗ℎ Finds support vectors based on triangular calculations, like calculating triangle angles, area and defining threshold for them. Angle A =cos 𝐴 = 𝑏 2 + 𝑐 2 − 𝑎 2 2(𝑏∗𝑐 η ζ

EXPERIMENTAL RESULTS proposed method on random data ζ=4 η=150 Experiment Databases Fisheriris Wine Using K-means before main process on random data 7 cluster ζ=4 η=150 Dataset Fisherir is Wine Attribute Types Real Integer, Real Number of Instances 150 178 Number of Attributes 4 13 Number of Classses 3 Year 1988 1991 Using K-means after main process on random data 7 cluster ζ=4 η=150

Calculating area for every three vertexes Start Calculating area for every three vertexes Selecting samples based on area threshold(ζ) Calculating angle for every corners of triangles Filtering samples based on, angle threshold(η) Classification (Method one) || Classification (Method two) End

CONCLUSION Proposed method can find proper support vectors It could also be used for data reduction process Combines with K-means clustering method

Thanks ؟