Sequential Classification Algorithms

Transcription

1 Prde University Prde e-pbs LARS Symposia Laboratory for Applications of Remote Sensing Seqential Classification Algorithms R. Krishnan K. R. Rao Follow this and additional works at: Krishnan, R. and Rao, K. R "Seqential Classification Algorithms" (1981). LARS Symposia. Paper This docment has been made available throgh Prde e-pbs, a service of the Prde University Libraries. Please contact epbs@prde.ed for additional information.

2 Reprinted from Seventh International Symposim Machine Processing of Remotely Sensed Data with special emphasis on Range, Forest and Wetlands Assessment Jne 23-26, 1981 Proceedings Prde University The Laboratory for Applications of Remote Sensing West Lafayette, Indiana USA Copyright 1981 by Prde Research Fondation, West Lafayette, Indiana All Rights Reserved. This paper is provided for personal edcational se only, nder permission from Prde Research Fondation. Prde Research Fondation

3 SQUNTIAL CLASSIFICATION ALGORITHMS R. KRISHNAN) K.R. RAO National Remote Sensing Agency Secnderabad, India 1. ABSTRACT In this paper, for versions of the seqential maximm likelihood algorithm have been employed to classify LANDSAT data & their performance is compared with that of the maximm likelihood classifie~ The seqentiel maximm likelihood algorithm is a faster, bt slightly less accrate version of the conventional maximm likelihood algorithm. In the seqentiel case, the nmber of featres (MSS bands) sed to classify a given pixel depends pon the particlar band vales of that pixel, since on the average, the nmber of bands sed will be less than the maximm there will be a seving in comptational time. II. INTRODUCTION The seqential maximm likelihood algorithm (1) is a faster bt slightly less accrate version of the conventional maximm likelihood algorithm. In the seqential case, the nmber of bands sed to classify a given pixel depends pon the particlar reflectance vales of that pixel, whereas, in the conventional method all the bands are aed for all the pixels. Becase of the redction in the average nmber of hands sad, the comptational load is also redced and there is a saving in compter time. III. MTHOD In this stdy, for different versions of the seqential maximm likelihood algorithms are compared with each other as well as with the conventional maximm likelihood algorithm. A LANDSAT tape data was displayed and training samolss belonging to five different categories were chosen. from the training sets, the statistics for each class, namely, the mean reflectances in the 4 bands as well as the covariance matrices were calclated The training set itself was sed for classification. This enabled the classification to be calculated. In the following, the for versions of the algorithm are described and this is follow~d by a discssion of the reslts. A. ALGOR ITHM-1 IV. I\LGURITHI"S Let n be the totsl nmber of classes. Let m be the total nmber of bands. Let Pk(X/U i ), k.1,,m; i-1,,n, be the conditional density of the ith class sing the first k bands. N is the nmber of classes nder consideration at each instant. G' is the prespecified threshold. step 0: ~=1, N_n. Calclate Pi(X/U i ), ~=1,,N. Step 1: Calclate loge (Uk(X/U i '» 10ge(Pk(X/W i )/.* Pk(X/lJ j ') 11/N J c\ for i 1,, N. Step 2: If, for any i, loge(uk(x/wj~ 10ge(G'(1-k/m~ then drop that class from frther considerati~n. If all classes bt one are dropoed, then assign X to that class and stop. If all the classes satisfy the above ineqality then assign X to the class for which loge [Uk (X/IJ i')] is maximm among all the class.s nder consideration and stop. If the nmber of classes dro~ped dring the present exection of step 2 is s then change N to N-s. Go to step 3. Step 3: Change k to K+1. If k-m, go to step 4. Otherwise go to step

4 Step 4: Calclate loge Um{X/W i ' for i belonging to the set of classes nder consideration. Assign X to the class for which log w U (x/w.1 m 1 is a maximm. Stop. Note: B. ALGOIHTHM-2 G' shold be greater than zero. Algorithm-2 is 90t from algorithm-, by replacing loge G f l1-k/m) by G'{1-k/m). C. ALGOR ITHM-3 Step 0: k~', N.n. Calclate p,{x/w i ), i~',, N. step 1: Calclate 10ge[k(x/wi'B ~ 10ge[Pk(X/Wi)(;~ Pk(X/W j)j 1/N for i=1,,n. Step 2: If, for any i, loge Uk{X/Wi'L. loge G'(1-k/m) then drop that class from frther consideration. If all classes bt one are dropped then assign X to that class and stop. If all the classes satisfy the ineqality then assign X to that class for which loge Uk(X/W i ') is maximm among all the classes dropped dring the present exection of step 2. If the nmber of class2s drooped dring the present exection of step 2 is s, then change N to N-s. If sao, go to steo 3. lse go to step 1~ Step 3: Step 4: Note: Increment k. If k~m, go to step4. Otherwise, go to step 1. Calclate log U (X/W ) for i belonging to '0 rhe s~t of classes nder consideration. Assign X to the class for which log U (X/w.) is a maximm. e m G' shold satisfy 0 {. G t "- 1. V. CHOIC or G' To determine the vale of G' to be sed for any of the above al~orithms that particlar algorithm shold be aopli~d to the training set. The accracy of classification for ~arios vales of G' is determined and depending pon the accracy reqired a vale of G' is chosen. VI. RSULTS or COMOAAATIV STUDY One hndren and ninety-six training samples belonging to five different classes were classified sing all the abova algorithms and also the conventional maximm likelihood algorithm. Using diffprent vales of G'~ gra~hs connecting the accracy of classification and the time reqired for classification have been plotted. It can be seen th~t algorithms 2 and 4 perform better than the maximm likelihood algorithm. Among the two algorithms, 4 seems to be better. V II. ACK NOWLDGMNT The athors are thankfl to Mr. G. Rajaraman for neatly typing the manscript of this paper. RrRNCS r, K.$ 'Seqential Methods in Pattern Recognition and Machine Learning'. Academic Press, New York. D. ALGOR ITHM-4 Algorithm-4 is 90t from algorithm-3 by replacing loge G'l1-k/m') by Gf(1-k/m~. Note: G'~ 1. 1 j

5 I UIOO;-'- I leoo Seqential Algorithms I to III 1300 III : 1000 Q ID!!! :: '" c ! I n Ok RROR IN CLASSIFICATION & S 80 -= No. of misclassifications ot of i96 samples. 329