Steps Toward Large-scale Solar Image Data Analysis to Differentiate Solar Phenomena

Transcription

1 Sep Toward Large-cale Solar Image Daa Analyi o Differeniae Solar Phenomena J.M. Banda 1 R. A. Angryk 1 P.C.H. Maren 2,3 Abrac We deail he inveigaion of he fir applicaion of everal diimilariy meaure for large-cale olar image daa analyi. Uing a olar-domain-pecific benchmark daae ha conain muliple ype of phenomena, we analyzed combinaion of image parameer wih differen diimilariy meaure in order o deermine which combinaion will allow u o differeniae among he muliple olar phenomena from boh inra-cla and iner-cla perpecive, where by cla we refer o ame ype of olar phenomena. We alo inveigae he iue of reducing daa dimenionaliy by applying mulidimenional caling o he diimilariy marice we produced uing he previouly menioned combinaion. A an early inveigaion ino dimenionaliy reducion, by applying mulidimenional caling (MDS) we will inveigae how many MDS componen are needed in order o mainain a good repreenaion of our daa (in a new arificial daa pace) and how many can be dicarded in order o enhance our querying performance. Finally, we preen a comparaive analyi among everal claifier in order o deermine he qualiy of he dimenionaliy reducion achieved wih he aforemenioned combinaion of image parameer, imilariy meaure, and mulidimenional caling (MDS). Keyword: Solar image daa analyi, conen-baed image rerieval (CBIR), diimilariy meaure 1. Inroducion In hi aricle we preen ome of our preliminary ep oward he ambiiou goal of building a Conen Baed Image Rerieval (CBIR) yem for he Solar Dynamic Obervaory miion (SDO: do.gfc.naa.gov/). Our work i moivaed by he recogniion ha he maive amoun of daa ha he SDO miion i ranmiing preen a hereofore eldom-addreed problem in erm of image analyi for cienific purpoe. Wih SDO Amopheric Imaging Aembly (AIA) alone, he miion will generae eigh 4096 pixel 4096 pixel image every en econd, leading o a daa ranmiion rae of approximaely 700 gigabye per day (he enire miion i expeced o end abou 1.5 erabye of daa per day, for a minimum of five year). Hand labeling of hee image will be impoible and backracking o find imilar image wih new and currenly undicovered phenomena will be a nearly impoible ak wihou he aid of CBIR echnology. Such a CBIR yem will allow reearcher o query he indexed image of he SDO repoiory for image imilar o he one hey are currenly analyi. By uing differen imilariy meaure, reearcher will be preened wih differen e of reul ha migh aify heir querie beer han uing he andard Euclidean diance. Wih hi CBIR yem we will be able o provide he following advanage o he olar phyic communiy: i) A menioned earlier, once a new and unknown phenomenon i dicovered, our yem will allow uer o look for imilar occurrence of i in he SDO repoiory in a very fa and efficien manner wihou he need o develop a new feaure-finding module for hi paricular phenomena, ii) verificaion of exiing feaure-finding module in order o deermine heir real accuracy when deecing olar phenomena in a ricly image imilariy conex, iii) on a pracical level, baed on he raining wih curren known olar phenomena, our CBIR yem will allow reearcher o find image ha conain imilar-looking phenomena o he one preen in he 1 Monana Sae Univeriy, Deparmen of Compuer Science, Bozeman, MT USA {juan.banda,angryk}@c.monana.,edu 2 Deparmen of Phyic, Monana Sae Univeriy, 247 EPS, Bozeman, MT , USA maren@phyic.monana.edu 3 Harvard Smihonian Cener for Arophyic. 60 Garden Sree, Cambridge, MA. USA 1

2 image hey ue o query our yem ha are no rericed only o he SDO miion (e.g. Traniion Region and Coronal Explorer (TRACE) image). One of he main conribuion of our work i o deermine imilariy (or diimilariy), an iue ha in he lieraure ha alway been preened a a very domain-pecific problem ha need o be addreed in he conex of olar daa before we can coninue o build our CBIR yem. One can find preference for differen diimilariy meaure ued in differen informaion-rerieval (IR) yem, and we ried o cover mo of hem in hi work. For inance, he majoriy of ex-baed IR yem ue he coine diimilariy meaure (Tan, Seinbach, and Kumar, 2005), while CBIR yem for color image ofen ue he Kullback Leibler Divergence (KLD) meaure (Deelaer, Keyer, and Ney, 2008). CBIR communiy available ool like Lire (Lux and Savva, 2008), do no allow hi eing flexibiliy and are paricularly deigned for naural cene image, he bigge focu of he CBIR communiy, and modifying a ool like hi migh urn ou o be a bigger ak han creaing a cuom fied one for olar daa. Of all he ucceful non-proprieary CBIR yem ha we inveigaed in medical (Deelaer, Keyer, and Ney, 2008) and oher domain (Daa, Li, and Wang, 2005); none of hem have deal wih olar daa or he volume of daa ha he SDO miion generae. The only wo yem o our knowledge capable of dealing wih everal million of image are Google Similar Image and TinEye. Similar Image wa an experimenal yem ha in 2009 wa incorporaed ino he regular Google Image earch becoming propriearyechnology. The ame applie o TinEye, making boh yem (and deail) unavailable for reearch purpoe. While boh are freely available for ue, we doub ha NASA or any olar phyici will be willing o upload 1.5 Terabye of daa a day o heir erver in order o ry o make ue of hem, we alo doub ha hee companie will be willing o comply wih uch a dauning ak for a niche applicaion (olar image analyi v. general image analyi). 1.1 Thi Work in Conex of he Fuure SDO CBIR Syem In Figure 1 we preen how a radiional CBIR yem i deigned and queried by a uer. In hi figure we alo highligh in red he ecion of he yem and query mechanim ha hi work cover. While he complee yem i no fully available and deigned a of now, each of hee componen need o be properly analyzed before making final implemenaion deciion. Uing he image daae (Image Collecion on Figure 1) ha we have inroduced in Banda and Angryk (2010 a), we proceed o egmen our image (Image Segmenaion on Figure 1) and exrac our image parameer (Image Parameer Exracion on Figure 1). More deail of he parameer eleced and he egmenaion mehod are preened in Banda and Angryk (2010 a) however, on ecion we how how hee aiical image parameer are calculaed. Said parameer are hen ranformed ino feaure vecor (Feaure Vecor Creaion in Figure 1) for a more compac and reduced repreenaion, we ouline hi proce on ecion A hi age, we are now confroned wih he problem of deermining he mo informaive diimilariy meaure for our olar image ricly baed on he image parameer ha we have exraced. Thi work preen our experimenaion oward achieving ecion Feaure Vecor Indexing and Similariy Comparion and Rerieval in Figure 1. To achieve hi, we experimened wih 18 imilariy meaure ha are widely ued for cluering, claificaion, and rerieval of image (Ojala, Pieikainen, and Harwood, 1996; Lam e al., 2000; Aggarwal, 2

3 Hinneburg, and Keim, 2001; Guo e al., 2002; Francoi, Werz, and Verleyen, 2005) in order o deermine which one would provide a beer differeniaion of he olar phenomena preened on our image daae. In order o deermine which combinaion of image parameer and imilariy meaure work be, we inveigaed over 180 combinaion. Thee experimen were performed o help idenify he mo (and lea) informaive and ueful combinaion for our yem imilariy comparion, rerieval, and indexing need. Figure 1. Tradiional elemen of a CBIR yem. Highlighed componen are being addreed in hi work. Beide qualiaively deermining which combinaion of diimilariy meaure and image parameer work be via he viual analyi of diimilariy marice (uing caled image plo), we alo performed exenive quaniaive analye by applying mulidimenional caling (MDS) o our reuling diimilariy marice (aking advanage of he differen characeriic highlighed by each individual meaure) and hen compared he reuling reduced dimenional pace repreenaion of our feaure vecor wih hree differen claificaion algorihm in order o mimic our fuure rerieval componen o be ued on our CBIR yem. Thi MDS mehod ha widely been ued for viualizaion and dimenionaliy reducion by reearcher in differen area for image proceing and rerieval (Beay and Manjunah, 1997; Rubner, Guiba, and Tomai, 1997; Borg and Groenen, 2005; Daa, Li, and Wang, 2005). By applying MDS o our diimilariy marice, we: i) provide a mechanim for he conrucion of a 2D or 3D viualizaion of our daae diimilariie ha depic cla (differen ype of olar phenomena) eparaion in a convenien way, ii) eimae he amoun of dimenionaliy reducion ha we can achieve wih our daa poin mapped ino a new arificial dimenional pace generaed by MDS, and evaluae any performance co by preening a comparaive evaluaion uing everal claificaion algorihm. 3

4 In order o meaure he qualiy of our combinaion of diimilariy-meaure and image-parameer, and our dimenionaliy-reducion eimaion mehodology we e up wo differen way of limiing he number of MDS componen. We quaniaively evaluae our work uing comparaive analyi, where we compare he wo differen componen-elecion mehod by preening claificaion reul for hree differen claifier. Thi allowed u o deermine how o elec our MDS componen in order o achieve imilar (or even beer) claificaion reul han wih our original daa. In our paricular CBIR yem, wih he expeced growh of our repoiory, he applicabiliy of dimenionaliy reducion i very imporan in erm of allowing u o reduce our query performance. Baed on he propoed grid-baed repreenaion where we exrac image parameer from pixel cell from he olar image we would have o ore one dimenional vecor per image, reuling in a oal of 5.27 Gigabye of ex daa per day, which will be added o our CBIR yem daabae. Indexing and querying a daabae of hi ize and growh i a challenge on i own, and dimenionaliy reducion will grealy help u in providing an efficien and reponive CBIR yem for he communiy o ue. We preen hi work o he broader communiy of olar phyici and compuer cieni no only o conribue o he exiing knowledge on olar daa analyi (Banda and Angryk, 2009; 2010 a, b, c), bu alo o obain valuable feedback from he communiy. The poenial feedback from olar phyici uing image parameer differen han hoe preened in hi work will be epecially valuable. We look forward o building new collaboraion wih domain exper who are working on idenifying individual olar phenomenon, a we inend o proceed wih addiion o our previouly publihed benchmark daae ( Since he SDO miion ha been launched, he need o accuraely deec and claify differen ype of olar phenomena in an auomaed way i of vial imporance. We are open o dicuion and would grealy appreciae any feedback offered. Wih he ouline workflow preened here, oher olar phyici can grealy benefi from knowing which diimilariy-meaure image-parameer combinaion work well, and herefore can improve on heir own work in he domain of claificaion of pecific olar phenomenon. A we menioned in Banda and Angryk (2010 a), he reul are very pecific o he domain of individual olar phenomenon. They allow reearcher who are working on a paricular ype of olar even (e.g. flare) o ue a combinaion of diimilariy-meaure imageparameer meaure ha beer erve heir claificaion purpoe. Thi aricle i organized in he following way: We preen he neceary mehodology in Secion 2. In Secion 3 we preen our experimen and reul. Secion 4 conain our overall concluion baed on hee experimenal reul, and Secion 5 decribe fuure work. 2. Mehodology In hi ecion we idenify all of he componen ha are needed for our experimenal evaluaion. We fir characerize he benchmark daae of image ha we will be uing for our experimen. Afer he daae ha been inroduced, we will deail how we exrac numerical image parameer from he daae image and ranform hem ino feaure vecor for imilariy analyi by explaining our normalizaion and daa preproceing. We hen explain he diimilariy meaure ha we will be uing in our work a well a he principle 4

5 of Muli-Dimenional Scaling (MDS) and how we are uing hi mehod o viualize our daa relaionhip and make a preliminary eimae of dimenionaliy reducion in a very inroducory manner and i i no par of he acual yem. Laly, we explain he claificaion algorihm we uilized o provide a quaniaive comparion of he inricacie of our propoed experimenal evaluaion. 2.1 Benchmark Daae Ued Our daae, fir inroduced in Banda and Angryk (2010 a), coni of 1600 image obained in January of 2008 from he NASA TRACE (Handy e al., 1999) miion via he Heliophyic Even Knowledge Bae (HEK) ( Our daae i divided in eigh equally balanced clae repreening eigh ype of olar phenomena. Table 1 enumerae hee eigh ype of olar phenomena. Table 1. Characeriic of Our Benchmark Daae Phenomenon/Even Name # of image Wavelengh [Ångröm] Acive Region Coronal Je Emerging Flux Filamen Filamen Acivaion Filamen Erupion Flare Ocillaion The benchmark daae, boh in i original and pre-proceed forma, i freely available o he public via Monana Sae Univeriy erver ( All of our TRACE image in he daae have been annoaed for even and phenomenon by olar phyici who each have deailed knowledge of boh he TRACE obervaory and he ype of olar imagery involved, and repored heir finding in he HEK ( In hi work we aign one phenomenon label per image regardle of he even locaion in he image Feaure Vecor Generaion In order o build he feaure vecor repreenaion of our image, fir we need o exrac informaion abou heir conen. For hi ak we ue image parameer ha are deigned o calculae paricular ignaure baed on he image (or region) exure, gray-level diribuion, and produce differen numerical value o populae our feaure vecor repreenaion Image Parameer Exracion Baed on our lieraure review, we decided o ue ome of he mo popular image parameer ued in oher domain uch a: medical image analyi, ex recogniion, naural cene image analyi, and raffic image analyi (Penland, 1984; Chaudhuri and Nirupam, 1995; Cernada e al., 2005; Wen-lun, Zhong-ke, and Jian, 2005; Holalu and Arumugam, 2006; Deelaer, Keyer, and Ney, 2008; Devendran, Hemalaha, and Amiabh, 2009). Since he aforemenioned repecive image parameerizaion have hown o be very domain-pecific, we performed 5

6 our own inveigaion on he evaluaion of hee image parameer. All parameer where obained from Gonzalez and Wood (2006), wih he excepion of he fracal dimenion (Schroeder, 1991) and he Tamura exural parameer (Tamura, Mori, and Yamawaki, 1977). The en image parameer ha we ued for hi work are preened in Table 2. Noe ha hee image parameer are no exhauive, and here are many oher parameer ha we could have eed. In our previou work, we ared wih a larger li of parameer, bu we have ince dicarded ome baed compuaional expene, performance, and relevance (Banda and Angryk, 2009; and 2010 a). Table 2. Exraced image parameer. For he grey-cale image (cell) z, p(z i) denoe he hiogram coun value for he i h gray level in our image (cell) a decribed by Gonzalez and Wood (2006). In our cae we have 255 differen grey level. Correpondingly, z i will be he i h grey level for P1, P4, P5, and P10. For P3, P6, and P7, z j indicae he value of each pixel from he image (cell), aid j will cover all value in aid image (egmen) up unil K, where K i = number of pixel. The P2 i calculaed baed on he box-couning mehod where N(ε) i he number of boxe of ide lengh ε required o cover he image cell. In P6 we ued σ 2, which indicae he variance, a defined for P7. Label Image parameer Formula L 1 P1 Enropy E p z ) log p( ) (1) ( i 0 i 2 z i log N ( ) (2) D0 lim P2 Fracal Dimenion 0 1 log 1 K P3 Mean m j z (3) 1 j K L 1 3 z m p( z (4) P4 3 rd Momen (Skewne) 3 ) i 0 i i P5 4 h Momen (Kuroi) L z ( ) i0 i m p zi (5) P6 Relaive Smoohne R (6) P7 Sandard Deviaion 1 K 2 z j j m 1 K (7) P8 Tamura Conra * Tamura, Mori, and Yamawaki, 1977 P9 Tamura Direcionaliy * Tamura, Mori, and Yamawaki, 1977 P10 Uniformiy L 1 U p 2 ( z ) (8) i0 i Owing o he promiing reul obained during our preliminary inveigaion (Banda and Angryk, 2009) and ome earlier work (Lamb, 2008), we choe o egmen our image uing an eigh by eigh grid for our image parameer exracion and labeling. Thi proce i illuraed in Figure 2. Figure 2. Example of he converion beween olar image cell o numerical image-parameer repreenaion. 6

7 2.2.2 Tranformaion from Image Parameer o Feaure Vecor Once he en image parameer have been exraced from our image daae, we choe o rea each image parameer eparaely ince we wan o deermine he uefulne and behavior of each parameer wih he differen diimilariy meaure individually. Each image i ranformed ino en (one per image parameer from Table 2) 64-elemen (one cell equal one elemen) vecor, wih each elemen repreening he value of he each image parameer exraced from each grid cell. Each one of hee vecor i reaed a a hiogram in he ene ha each elemen poiion (1 o 64) become a bin and he value of each elemen become he value aociaed wih he bin, no an acual coun of hem. Here he bin are repreening he cell locaion in he image and heir value repreen he aiical parameer value. In order o ue hee vecor correcly when calculaing ome of he meaure (he KLD and Jenen Shannon divergence (JSD) meaure in paricular a defined in Secion 2.3) we need o make ure he um of he bin add o one. To achieve hi, we normalized every ingle parameer per image in he following way: Am Normalize( A) for m 1o n (9) n A m1 m where n = 64, ince we have a oal of 64 bin (dimenion in our feaure vecor), and A i ju he parameer value a aid bin. Thi allow u o cale our vecor and preerve heir hape, and rea hem a hiogram. For bin equaling zero, we add a very mall quaniy ( ) in order o avoid diviion by zero on he KLD meaure. Each of he en image parameer wa normalized in he ame way, allowing our value range o be conien and be he ame for all 18 differen meric eed. 2.3 Diimilariy Meaure Ued A diimilariy meaure (in hi conex) i a formula ha calculae how diimilar wo image are. We eleced 18 diimilariy meaure for comparaive analyi. Baed on our lieraure review we find ha he majoriy of he meaure ha we eleced are widely ued in image analyi and repored good reul when applied o image in oher domain (Penland, 1984; Chaudhuri and Nirupam, 1995; Cernada e al., 2005; Wen-lun, Zhong-ke, and Jian, 2005; Holalu and Arumugam, 2006; Deelaer, Keyer, and Ney, 2008; Devendran, Hemalaha, and Amiabh, 2009; Banda and Angryk, 2010 b, c). We inveigae hee differen meaure in order o verify how well hey differeniae our clae of olar phenomena a well a deermine peculiariie wihin he clae hemelve. We will addre hi laer in our experimen ecion, where we preen plo of diimilariy marice. The claical definiion of hee meric are provided in Appendix 1. Table 3 li hem and he range where hey are found in he lied figure. 7

8 Table 3. Diimilariy Meaure Label Ued in Our Claificaion Accuracy Figure Label Diance Ued in Figure D1 Euclidean 10, 12, 13, and 14 D2 Sandarized Euclidean 10 and 12 D3 Mahalanobi 10 and 12 D4 Ciy Block 10, 12, 13, and 14 D5 Chebychev 10, 12, 13, and 14 D6 Coine 10 and 12 D7 Correlaion 10 and 12 D8 Spearman 10 and 12 D9 Haudorff 10 and 12 D10 Jenen-Shannon divergence (JSD) 10 and 12 D11 χ2 10 and 12 D12 Kullback Leibler divergence (KLD) A-B 10 and 12 D13 Kullback Leibler divergence (KLD) B-A 10 and 12 D14 Fracional Minkowki p = and 14 D15 Fracional Minkowki p = and 14 D16 Fracional Minkowki p = and 14 D17 Fracional Minkowki p = and 14 D18 Fracional Minkowki p = and 14 Pleae noe ha he fir eigh and he la five meaure are given for an m-by-n daa marix [X] (in our cae i conain m = 1600 image and n = 64 image parameer value), which i reaed a m (1-by-n) row vecor [x 1, x 2,..., x m ]. Meaure 9 o 14 are preened for hiogram. In order o repreen our feaure vecor a a hiogram, we reaed each elemen of n a a bin (n = 64). For example, we conver x o he hiogram A, he value in each bin [A j ] (for j = 1 o n) i equal o each x j (for j = 1 o n) Tranformaion of Diimilariy Marice via Mulidimenional Scaling (MDS) Since we waned o expand our qualiaive analyi of he diimilariy marice achieved by looking a heir viualizaion via he caled image plo, we applied MDS o hee diimilariy marice in order o verify he degree of dimenionaliy reducion ha can be achieved wih hee diimilariy meaure - image parameer combinaion. MDS i a e of aiical echnique ued for he exploraion of diimilariie in daa, and i i popular in he field of informaion viualizaion. By uing he fir wo mo ignifican reuling componen, we ge he andard 2D MDS plo; if we ue he fir hree mo ignifican componen we ge he 3D MDS plo. Thee componen are he ored eigen-value whoe relaive magniude indicae how many dimenion we can afely ue. MDS i alo commonly ued a 8

9 a mehod for dimenionaliy reducion for large diimilariy marice (Beay and Manjunah, 1997; Rubner, Guiba, and Tomai, 1997; Borg and Groenen, 2005; Daa, Li, and Wang, 2005;). We ue he claical MDS approach, ince we have inpu marice giving diimilariie beween pair of iem (produced by our diimilariy meaure). Thi proce will oupu a coordinae marix whoe configuraion minimize a lo funcion called rain. Wih he reuling MDS marice, we have a new re-arranged dimenional pace, baed on he diimilariy marice of he original daa (imilar o Principal Componen Analyi (PCA) or Singular Value Decompoiion (SVD)). However, one of he main iue behind MDS i ha doe no provide an explici mapping funcion governing he relaionhip beween paern in he inpu pace and in he projeced pace (Naud, 2001). Thi iue ignificanly limi he populariy of MDS a a dimenionaliy-reducion echnique, ince you need he full diimilariy marix of he oal daa o generae he new dimenional pace Claificaion Algorihm a a Tool for Quaniaive Evaluaion In general erm, a claificaion algorihm i a procedure for elecing a hypohei from a e of alernaive ha be fi a e of obervaion. In our conex, a claificaion algorihm will build a model baed on labeled-raining daa ha will help wih he proper labeling of new daa (e e). In hi aricle, we eleced he Naïve Baye Claifier and Suppor Vecor Machine (SVM) wih a linear kernel funcion a our linear claifier, and C4.5 a a deciion ree claifier. Linear claifier creae grouping of iem ha have imilar feaure value by making claificaion deciion baed on he value of a linear combinaion of he feaure. C4.5 ue an enropy-baed informaion gain meaure o pli ample ino clae. In erm of how o meaure hee claificaion experimen, we eleced he radiional claificaion accuracy meaure o deermine heir effecivene. rue poiive rue negaive accuracy (10) rue poiive fale poiive fale negaive rue negaive The accuracy of claificaion meaure derive from a confuion marix. In hi marix, each column repreen he inance in a claified cla, while each row repreen he inance in he acual cla a hown in Figure 3. Figure 3. Confuion marix example Noe ha we ue hee claifier in order o preen a comparaive and quaniaive analyi of our experimen, and we are no rying o find he be claificaion reul or adju he claifier o perform a heir be. We are rying o deermine wo hing: i) he winning combinaion of diimilariy meaure / image parameer, and ii) an eimae of how many componen of our new arificial MDS daa pace can be omied wihou a ignifican decreae in he claificaion accuracy. 9

10 3. Experimenal Evaluaion and Reul In hi ecion, we will provide he deail of our experimenal evaluaion and he reul we obained Preliminarie All experimen were performed uing Malab R2009b. For he exponenial curve fiing we ued he Ezyfi Toolbox ( The claificaion experimen were performed uing WEKA (Hall e al. 2009). Thee program were run on a PC wih an AMD Ahlon II X GHz Quad Core proceor wih 8 GB of RAM and Window XP 64-bi Ediion. Afer all our daa wa normalized, we calculaed he pairwie diance beween he hiogram uing Malab pdi funcion. A hi funcion i highly opimized for performance, he compuaion ime for our fir eigh (and la five) meaure wa le han a few minue. The Haudorff, KLD, JSD and χ 2 diance were implemened from crach and yielded a higher compuaional expene due o he naure of he algorihm. In oal we produced 180 diimilariy marice (18 meaure, couning KLD A- B and B-A eparaely, ime a oal of en differen image parameer). All hee diimilariy marice are ymmeric, real and poiive valued, and have zerovalued diagonal. Thu hey fi he claical MDS requiremen Diimilariy Marix Calculaion Figure 4 preen hee diimilariy marice ha help u o qualiaively idenify which image parameer and meaure provide informaive differeniaion for our image beween he eigh differen clae of our daae. In hi aricle, we how hree of he mo inereing parameer-meaure combinaion generaed (good and bad). We refer reader who wan o learn abou pecific combinaion o our preenaion online a ( where all 180 combinaion are preened. Here he clae of our benchmark are eparaed on he axe. Blue mean low diimilariy, and red mean high diimilariy. Pleae noe ha each diimilariy marix ha been normalized uing min-max normalizaion in order o have all figure cale o he ame range, allowing u o compare all differen diimilariy meric in he ame conex and all figure o be conien. 10

11 Figure 4. Scaled diimilariy marix for (a) Correlaion (D7) meaure wih image parameer mean (P3), (b) JSD (D10) meaure wih image parameer mean (P3), (c) Chebychev (D5) meaure wih image parameer relaive moohne (P6). The color bar nex o (c) repreen he diimilariy range for all Figure wih hee kind of plo. A we can ee from figure 4(a), hi combinaion of imilariy meaure D7 (correlaion) and image parameer P3 (mean) produce an example of poor eparaion beween all clae ince we have very divere coloring hroughou he figure. Figure 4(b) how ha he D10 (JSD) meaure produce an enirely differen diimilariy marix for he ame image parameer P3 (mean), which highligh differen diimilariie han he correlaion meaure (Figure 4(a)). Figure 4(c) i a clear example of a combinaion of a diimilariy meaure D5 (Chebychev) and an image parameer P6 (relaive moohne) ha highligh diimilariie wihin only one cla of he benchmark, bu recognize ha everyhing ele i highly imilar for he re of he clae. In hee plo we are looking for clear block ha eparae one cla from he oher, a found in Figure 4(c). Thi validae our idea of eing every pair of diimilariy meaure and image parameer individually, ince here are combinaion ha will allow u o noice differen relaionhip beween he clae of olar image Tranformaion of Diimilariy Marice via Mulidimenional Scaling (MDS) Afer generaing 180 diimilariy marice, we performed claical mulidimenional caling uing Malab cmdcale funcion. MDS ha been widely 11

12 uilized in image-rerieval reearch o reduce dimenionaliy (Beay and Manjunah, 1997; Rubner, Guiba, and Tomai, 1997), and o aid in he viual depicion of image diimilariy in a convenien wo and hree dimenional plo (Borg and Groenen, 2005). However, hee aricle preen reul on a coniderably maller number of image and ue a coniderably maller number of dimenion. The mo commonly ued MDS plo involve uing he fir wo or hree componen of he calculaed coordinae marix. In Figure 5 we how boh 2D and 3D plo of hee componen. Figure 5. MDS map for he correlaion meaure D7 wih image parameer mean (P3) (a) op 2 and (b) op 3 componen. Each image in each cla i repreened by a number and each cla i decribed in differen color a indicaed on he legend. A we expeced, in Figure 5 we canno eaily idenify a clear eparaion beween our eigh differen clae on wo or hree dimenion of he reuling MDS dimenional pace. However, elecing he correc combinaion migh yield inereing 3D map for cerain diimilariy meaure and image parameer pair. In Figure 6 we how he 3D MDS componen plo for he diimilariy marice of Figure 4. Here we how ha, while for Figure 6 (a) and (b) he map do no really highligh any cluer, in (c) we have a clear cluer for cla Acive Region (color red). Thi i exacly wha i indicaed in Figure 4 (c). Thee 3D MDS componen plo omeime how very clear cluering, and oher ime hey can be ued o aid in he inerpreaion of he caled image plo of he diimilariy marice. (We will alk abou hi when we dicu he fracional Minkowki meric reul) 12

13 Figure 6. 3D MDS componen plo for (a) Correlaion (D7) meaure wih image parameer mean (P3), (b) JSD (D10) meaure wih image parameer mean (P3), (c) Chebychev (D5) meaure wih image parameer relaive moohne (P6). Each image in each cla i repreened by a number and each cla i decribed in differen color a indicaed on he legend Fracional Minkowki Meric We inveigae he behavior of Minkowki-baed fracional meric on our domain pecific daae, becaue hey have provided very inereing reul in oher domain (Aggarwal, Hinneburg, and Keim, 2001; Francoi, Werz, and Verleyen, 2005), and are mahemaically proven o be beer han oher more radiional nonfracional Minkowki meric (Aggarwal, Hinneburg, and Keim, 2001). In hi ecion, uing Figure 7 and 8, we preen a comparion beween he caled image plo and he 3D MDS componen plo for wo differen fracional meric of he ame image parameer. In hee wo figure we illurae how he fracional meric improve in performance when p ge cloer o one (Ciy Block diimilariy meaure (D4)). 13

14 Figure 7. Fracional Minkowki meric wih p = 0.25 (D14) and he fracal dimenion image parameer (P2): (a) Scaled Image Plo, (b) 3D MDS componen plo. The color legend only applie o (b). From Figure 7, we can oberve a relaively clean eparaion of wo clae (Acive Region and Emerging Flux), when i come o he caled image plo of he diimilariy marix (a). However, in erm of he 3D MDS componen plo (b) he cluer correponding o Acive Region (red color) and Emerging Flux (blue color) eem omewha fuzzy and mixed in wih he re of he clae. According o our lieraure review (Aggarwal, Hinneburg, and Keim, 2001; Francoi, Werz, and Verleyen, 2005) hee fracional meric end o improve when p approache one. In Figure 8 we ry o verify hee claim for our own domain-pecific daae. Figure 8. Fracional Minkowki meric wih p = 0.95 (D18) and he fracal dimenion image parameer (P2): (a) Scaled Image Plo, (b) 3D MDS componen plo. The color legend only applie o (b). A he lieraure menion (Aggarwal, Hinneburg, and Keim, 2001; Francoi, Werz, and Verleyen, 2005), once p i approache one we ee ha on boh he caled image plo of he diimilariy marix (Figure 8 (a)) and he 3D MDS componen plo (Figure 8 (b)), he clae Acive Region and Emerging Flux are more eparable and hence have beer cluering. I i alo very inereing ha he re of he clae end o ge dragged away from hee wo clae, making he 14

15 Acive Region and Emerging Flux clae even more diinguihable. Noe however, hi increae he eparaion of he oher clae. Thi only how ha each combinaion of diimilariy meaure and image parameer i unique, and ha heir behavior need o be analyzed individually o gain he mo informaion Componen Threholding Baed on he magniude of each of he reuling MDS componen, we decided o ue exponenial curve fiing in order o apply a hrehold o he opimal number of componen needed o reduce dimenionaliy and ill reain valuable componen o produce good claificaion reul. For comparaive purpoe, we alo inveigaed a far impler approach of elecing only he op en componen and dicarding he re. Thee wo approache allow u o verify how much a few (or many) exra componen will increae or decreae he accuracy of our claificaion reul, or in oher word how many componen we need in order o mainain a good repreenaion of our daa in he new dimenional pace, and how many componen we can dicard in order o opimize our querying reponivene. Noe ha hi MDS dimenionaliy-reducion analyi i of exploraory naure, and i i only ued for eimaion of poenial dimenionaliy reducion. We preen a more comprehenive and exenive analyi uing beer fied mehod in Banda, Angryk, and Maren, In order o deermine he aforemenioned number of componen, we ploed he magniude of each componen. Since he MDS marix oupu i ordered by imporance, he magniude hould be decreaing a he number of componen increae. Afer empirical analyi of he magniude of he reuling MDS componen, we oberved ha afer en componen he decreae of heir magniude moderae (in mo of he cae), o herefore we iniially decided o ake a omewha naïve approach and applied a hrehold of en componen per imilariy meaure/image parameer combinaion. In our econd approach, we uilized exponenial curve fiing (Shepard, 1980) o find a funcion ha model hi behavior. Our inen wa o locae a hrehold for he number of neceary componen. We uilize a 135-degree angle of he angen line o hi funcion o deermine he hrehold and dicard he componen whoe magniude are no providing ignifican improvemen over he previou one. Thi angen line i indicaed a he red line in Figure 9; he red do indicae he inerecion poin, which equal he number of componen ha we will ue. Figure 9. The e of ored (decending) eigenvalue whoe relaive magniude indicae how many componen (dimenion) one can afely ue. Each eigenvalue i indicaed by he y-axi, and he number of componen i indicaed by he x-axi (from 1 o 63). Top i he exponenial curve fiing for: (a) correlaion meaure (D7) wih image parameer mean (P3), (b) JSD meaure (D10) 15

16 wih image parameer mean (P3). The red angen line i ued o elec he number of componen o analyze a he inerecing poin (red do). A can be een from Figure 9, he magniude of he componen (y-axi) decreae up o a cerain poin, and afer hi poin he change i minimal and hu no oo imporan for he new dimenional pace. Baed on hee curve-fiing reul and he hrehold oupu, we deermined a pecific number of componen per combinaion of diimilariy-meaure image-parameer. We can now deermine how well hi reduced dimenionaliy perform in our claificaion ak in Secion Quaniaive Evaluaion via Comparaive Analyi of Claifier We have decribed how we applied he diimilariy meaure o our image parameer and produced diimilariy marice. We alo analyzed how MDS ranformed hee diimilariy marice ino a differen dimenional pace, one ha will require, hopefully, fewer dimenion in order o diinguih differen ype of olar phenomena. We now decribe he claificaion experimen we performed on he naïve en-componen hrehold and he angen hreholded componen compared o our original daa. All claificaion experimen ued enfold cro-validaion. We ran a oal of 180 differen daae hrough he hree claifier decribed in Secion 2.5. In he following figure we preen he overall reul of hee claificaion experimen and offer a more deailed explanaion of he mo inereing reul. Figure 10 how he claificaion accuracy of our eleced claifier on our en componen per diimilariy-meaure image-parameer combinaion. The fir en column indicae our original normalized daae value wih no meaure or dimenionaliy reducion applied o hem. The re of he column indicae our diimilariy-meaure image-parameer combinaion in he. Each ick in each group repreen one parameer from Table 2. Each group conain en parameer and hen i move on o he nex diimilariy meaure a indicaed in he figure. 16

17 Figure 10. Percenage of correcly claified inance for he en-componen hrehold: (op) for he Naïve Baye claifier, (middle) for he deciion-ree (C4.5) claifier, and (boom) for he SVM claifier, for he original daa and our 180 experimen (D1 o D18). A hown in Figure 10(a) and 10(b), our en-componen-only approach produce very imilar claificaion reul o our original daa for mo combinaion of meaure and image parameer. We alo noice ha he wor performing diimilariy-meaure image-parameer combinaion i D9, correponding o he Haudorff diimilariy meaure. In figure 11 we how he reuling number of componen o be ued baed on he angen hreholding. The column repreen he 180 differen image parameer/meaure combinaion (wih he omiion of he fir en, which are he original daae). In hi figure, a high number of componen indicae ha he componen do no eem o decreae eadily in magniude. 17

18 Figure 11. Number of componen o ue indicaed by he angen-hreholding mehod for each diance meaure-image parameer combinaion. In Figure 12 we how he angen-hreholded claificaion reul. The number of componen eleced varie beween 1 and 63 depending on he combinaion of meaure/image parameer. For direc comparion he experimen were ordered he ame way a in Figure 10. Figure 12. Percenage of correcly claified inance for he angen-baed componen hrehold: (op) for he Naïve Baye claifier, (middle) for he deciion-ree (C4.5) claifier, and (boom) for he SVM claifier, for he original daa and our 180 experimen (D1 o D18). 18

19 In hee hreholded componen claificaion reul we ge very imilar reul compared o claificaion reul ha ued only en componen for NB and C4.5, and in ome cae we ge coniderable drop like for he Chebychev meaure (D5). Thi i due o he fac ha he angen baed hreholding elec fewer han en componen per combinaion of meaure/image parameer and in ome inance even only one componen (ee Figure 11). An inereing hing o noice i ha he overall claificaion percenage increae conienly for he KLD A-B and KLD B-A (D12 and D13) combinaion, alhough hi migh be due o he fac ha he angen hreholding eleced 63 componen for everal of he image parameer combinaion. We alo oberve ha providing large number of componen o greedy claifier (NB and C4.5), making he locally opimal choice a each age, doe no help hem improve much, wherea SVM ake clear advanage of more daa. In he reul for boh he angen hreholding and he en-componen limiing, we oberve ha wih only en componen we can achieve good accuracy reul (around 80 o 90 %) for he eleced claifier. Thi ranlae o an eimaed average of 70 % dimenionaliy reducion from our original number of dimenion. We can alo ee which image parameer perform he be wih which meaure, which wa one of our objecive wih hi reearch Quaniaive Evaluaion via Comparaive Analyi of Claifier for he Fracional Minkowki Meric In Figure 13 and 14, we ake an in-deph look a he claificaion reul for he Fracional Minkowki diimilariy meaure (D14 o D18) paired wih our oher hree diimilariy meaure baed on he Minkowki meric. Thee diimilariy meaure are: Ciy Block diance (p = 1) (D4), Euclidean diance (p = 2) (D1), and Chebychev meaure (p = ) (D5). Figure 13. Percenage of claificaion accuracy for he en-componen Minkowki baed fracional meric wih p = 0.25 o p = (D14 18, D4, D1, D5), ordered by image parameer. 19

20 A we can ee in Figure 9 and 11 (D14-D18) and in Figure 12, he fracional meric end o perform in a very able manner, dropping for he ame image parameer (Fracal Dimenion (P2) and Tamura Direcionaliy (P9)) for all of he differen p value we inveigaed. An inereing hing in hi figure i ha a p ge cloer o one, he experimen do no how a clear endency of increaing claificaion accuracy. Alo, while we have differen reul for inra-cla eparaion for ome cla behavior, a we how in Secion 3.4, he iner-cla eparaion of he remaining clae eem o balance ou he claificaion reul. We alo have bigger drop a p approache infiniy for he Chebychev diimilariy meaure (D5), indicaing ha Minkowki meric wih a p cloer o 2, perform beer (and more ably) han hi diimilariy meaure. A final obervaion from Figure 12 i ha wih he en-componen hrehold he reebaed claifier (C4.5) achieve he be claificaion reul, while SVM eem o ay almo 10 % behind. Figure 14. Percenage of claificaion accuracy for he Tangen hreholded Minkowki baed fracional meric wih p= 0.25 o p= (D14 18, D4, D1, D5), ordered by image parameer. In Figure 14, we ee wo very inereing difference beween he angen hrehold and our en-componen hrehold. The fir i ha SVM ake a definie lead in erm of claificaion, wih accuracy approaching 90 % for he majoriy of diimilariy meaure/image parameer pair and reaching our overall be reul of 94.4 % for he mahalanobi diimilariy meaure (D3) combined wih he mean image parameer (P2). The ree-baed claifier C4.5 keep almo he ame claificaion accuracy a wih en-componen, cauing u o believe ha high dimenionaliy doe no benefi hi claificaion model. The improvemen of he SVM accuracy hown in Figure 14, i due o he fac ha we eleced a coniderably larger amoun of componen wih he angen hrehold, beween 46 and 63, wih he majoriy being 63 (ee Figure 9). Thi grealy improve he performance of he SVM claifier in he majoriy of our experimen. The elecion of hi large number of componen i due o he fac ha he decreae in magniude of he componen i very mall, making curve fiing ineffecive. The econd hing o noice i ha our claificaion accuracy drop coniderably for p 20

21 value greaer and equal o one, over % for ome image parameer, and for he majoriy of he Chebychev meaure (D5) reul. Thi could be parly due o he fac ha he number of componen eleced i le han 30 for mo inance (ee Figure 14, experimen for p = 1 (D4), p = 2 (D1), and for p = (D5)), a well a he acual diimiliude found for he combinaion of meaure/image parameer in queion. In Table 4 we preen he op en claificaion reul for boh he angen hreholded and he en componen limied daae. Thi will help u o quaniaively evaluae he difference beween hee wo mehod. Table 4. Top en claificaion accuracy reul for en componen hreholded dimenionaliy reducion experimen. DM indicae diimilariy meaure and IP indicae image parameer. NB C45 SVM DM-KLD B-A-IP-FracDim DM-correlaion-IP-Mean DM-pearman-IP-Mean DM-KLD A-B-IP-FracDim DM-KLD A-B-IP-Mean DM-correlaion-IP-Mean DM-KLD A-B-IP-Mean DM-pearman-IP-Mean DM-correlaion-IP-Enropy DM-correlaion-IP-Mean DM-Euclidean-IP-Mean DM-pearman-IP-RelSm DM-pearman-IP-Mean DM-JSD-IP-Mean DM-pearman-IP-Uniformiy DM-KLD B-A-IP-Mean DM-SandEuclidean-IP-Mean DM-correlaion-IP-RelSm DM-KLD A-B-IP-Enropy DM-Min p=0.95-ip-mean DM-correlaion-IP-Momen DM-Euclidean-IP-Mean DM-Euclidean-IP-Enropy DM-correlaion-IP-Uniformiy DM-correlaion-IP-Enropy DM-correlaion-IP-Enropy DM-ciyblock-IP-Mean DM-Min p=0.95-ip-mean DM-ciyblock-IP-Mean DM-pearman-IP-Enropy Table 5. Top en claificaion accuracy reul for angen hreholded dimenionaliy reducion experimen. DM indicae diimilariy meaure, IP indicae image parameer, and C= indicae number of componen. NB C45 SVM C=63-DM-KLD A-B-IP-FracDim C=21-DM-KLD A-B-IP-Mean C=63-DM-mahalanobi-IP-Mean C=32-DM-correlaion-IP-Enropy C=27-DM-pearman-IP-Mean C=59-DM-SandEuclidean-IP-Mean C=29-DM-correlaion-IP-Mean C=12-DM-euclidean-IP-Mean C=63-DM-mahalanobi-IP-Enropy C=59-DM-STDEuclidean-IP-Mean C=59-DM-STDEuclidean-IP-Mean C=63-DM-KLD A-B-IP-FracDim C=27-DM-pearman-IP-Mean C=14-DM-KLD B-A-IP-Mean C=63-DM-KLD B-A-IP-FracDim C=63-DM-KLD B-A-IP-FracDim C=29-DM-correlaion-IP-Mean C=63-DM-KLD A-B-IP-TamCon C=35-DM-pearman-IP-RelSm C=15-DM-JSD-IP-Mean C=63-DM-mahalanobi-IP-Momen C=35-DM-pearman-IP-Uniformiy C=27-DM-ciyblock-IP-Mean C=63-DM-mahalanobi-IP-RelSm C=63-DM-mahalanobi-IP-RelSm C=32-DM-correlaion-IP-Enropy C=63-DM-KLD B-A-IP-TamCon C=35-DM-ciyblock-IP-Uniformiy C=25-DM-KLD B-A-IP-Uniformiy C=63-DM-mahalanobi-IP-Momen In Table 4 (he en-componen hrehold) we have very differen meaure performing he be for he differen claifier. In erm of our image parameer, Mean manage o appear in our op en almo 50 % of he ime, nex o fracal dimenion (P2), and enropy (P1). I i inereing o noe ha he KLD meaure (D12-13) eem o perform very well for our Naïve Baye claifier, filling five ou of 10 po in hi able. KLD alo ake he fir wo po when combined wih he fracal dimenion parameer (P2), and boh direcion of hi KLD meaure (A-B and B-A, D12 and D13) eem o appear cloe o each oher, indicaing ha we migh be able o only ue one of he direcion and coniderably reduce i compuaional expene. We noiced ha for he remaining wo claifier (C4.5 and SVM) we have differen combinaion of he mean parameer (P3) and very differen ype of meaure (correlaion (D7), KLD (D12-13) and Spearman (D8)) aking he fir few place. However, he mo inereing reul for u, wa ha he fracional meric only appear wice in hi able, howing ha 21

22 hey are no very good for our daae. They are alo eaily beaen by he euclidean diance (P1) on boh occaion, howing a differen rend han in he arificial daae comparion preened in by Aggarwal, Hinneburg, and Keim, (2001) and Francoi, Werz, and Verleyen, (2005) in erm of claificaion accuracy. The angen hreholded claificaion reul in Table 5, how differen rend in he op en claificaion reul. The combinaion preened for he Naïve Baye claificaion reul only bea he en-componen one by 3-4 % and have almo hree ime a many componen (from 29 o 63), howing ha he encomponen hrehold perform well when i come o hi claifier. We alo have urpriing reul for he C4.5 claifier. Here, for he op reul, we acually have a drop in accuracy of 1 % when uing hree ime a many componen (fir wo), howing he behavior we menioned abou ree keeping imilar claificaion reul for boh hreholding mehod (bu wih a coniderable increae in he number of daa poin). The combinaion of diimilariymeaure image-parameer eem o hold for hee wo claifier when i come o achieving he highe accuracy. One hing o noe i ha none of he fracional meric (D14 18) make any difference when i come o hi hreholding mehod. Thi reinforce he claim ha hey are very able (hence heir claificaion accuracy i no increaing for a higher number of componen eleced by he angen hreholding mehod). 4. Concluion Wih he ambiiou ak of analyzing all of he combinaion beween image parameer and diimilariy meaure compleed, we managed o creae a olid foundaion ha will allow u o deermine wha work be for quick and accurae recogniion of differen olar phenomenon. The reul of hee experimen alo how ha we can reduce our dimenionaliy coniderably and ill achieve good claificaion reul. Some diimilariy meaure, uch a correlaion (D7), euclidean (D1), KLD (D12-13), and JSD (D10), allow u o find he diimilariie beween he image in our daae and provided differen level of relevance for differen image parameer. A every applied reearcher know, no everyhing alway work, and wih hi reearch we can acually diinguih wha work well and when in erm of olar image. The fracional diimilariy meaure perform very well for ome daae according o he lieraure (Aggarwal, Hinneburg, and Keim, 2001; Francoi, Werz, and Verleyen, 2005), bu in our pecific domain hey do no eem o ignificanly make any ignifican impac o enable u o improve our reul over he radiional Minkowki-baed meaure (ciy block (D4), euclidean (D1)). While no all diimilariy meaure performed equally well, we now know which one o omi due o heir compuaional expene for fuure experimen (i.e. Haudorff meaure (D9)). In erm of dimenionaliy reducion, we managed o achieve very imilar claificaion reul o hoe obained wih he original daa. A imilar machine learning approach o claify by individual phenomenon can benefi from our approach on how o elec he number of componen and implemen i in order o peed up query rerieval ime. Wih he maive number of experimen performed, we lack he proper pace in hi medium o diplay all he reul we produced. All he diimilariy marice, 22

23 MDS map, exponenial curve fiing plo, and claificaion reul are available ( for reearcher inereed in all hee reul. We alo included all Malab and WEKA file produced in order for reearcher o replicae hee reul eaily. 5. Fuure Work We are currenly working wih dimenionaliy-reducion mehod oher han MDS, uch a Principal Componen Analyi and Singular Value Decompoiion. Thee wo mehod have he advanage of producing mapping funcion in order o ranform new daa ino he arificial dimenional pace creaed by hem. Thi will enable u o ue a paricular raining daae and a new e daae in order o creae more accurae claificaion predicion. A menioned above, all of he claifier ued in hi aricle were creaed uing heir defaul WEKA eing. The claificaion reul are for comparaive purpoe and in no way hey reflec he reul ha can be obained afer fine uning he eing of hee claifier. We are currenly working on hi, and we expec o publih oon reul of fine-uned claifier. We alo expec o increae he number of claifier ued o have a more comprehenive evaluaion of hem. Laly, we coninue working oward he goal of creaing a fully working CBIR yem for he SDO miion, and wih hi work a well a our previou aricle, we are geing cloer o hi goal. Acknowledgemen: Thi work wa uppored in par by he NASA Gran Award No. 08-SDOSC , funded from NNH08ZDA001N-SDOSC: Solar Dynamic Obervaory Science Cener oliciaion. We would alo like o hank our inernal reviewer Michael Schuh and Richard McAllier. Appendix 1 Claical definiion of diimilariy meaure ued in hi work: 1) Euclidean diance: A found in Yang and Trewn (2004) i i defined a he diance beween wo poin given by he Pyhagorean Theorem: D ( x x )( x x )' (10) 1 2) Sandardized Euclidean diance: A found in Yang and Trewn (2004) i i defined a he Euclidean diance calculaed on andardized daa by he andard deviaion: D2 ( x x ) V 1 ( x x )' (11) Where V i he n-by-n diagonal marix whoe j h diagonal elemen i S(j) 2, where S i he vecor of andard deviaion. 3) Mahalanobi diance: A found in Yang and Trewn (2004) hi i he Euclidean diance wih normalizaion baed on a covariance marix making i cale-invarian: D3 ( x x ) C 1 ( x x )' Where C i he covariance marix. (12) 23

24 4) Ciy block diance: A found in Yang and Trewn (2004) i repreen he diance beween poin in a grid by examining he abolue difference beween coordinae of a pair of objec: n D4 x j x j (13) j1 5) Chebychev diance: A found in Yang and Trewn (2004) i meaure diance by auming only he mo ignifican dimenion i relevan: j j j D5 max x x (14) 6) Coine diance: A defined in Tan, Seinbach, and Kumar (2005) i calculae he diimilariy beween wo vecor by deermining he coine of he angle beween hem: x x ' D6 1 (15) ( x x ')( x x ') 7) Correlaion diance: A defined in Tan, Seinbach, and Kumar (2005) i meaure he diimilariy of he ample correlaion beween poin a equence of value. ( x x )( x x )' D7 1, (16) ( x x )( x x )' ( x x )( x x )' where x 1 n x j n j 1 and 1 x n x j n j 1 8) Spearman diance: Originally defined by Spearman (1904) o meaure he diimilariy of he ample Spearman rank correlaion beween obervaion: ( r r )( r r )' D8 1 (17) ( r r )( r r )' ( r r )( r r )' Where r j i he rank of x j aken over x 1j, x 2j... x nj, r, and r are he coordinaewie rank vecor of x and x, i.e. r = (r 1,r 2,..,r m ) and m m 1 ( m 1) 1 ( m 1) r rj, r rj m 2 m j 1 j 1 2 In our lieraure review (Chaudhuri and Nirupam, 1995; Cernada e al., 2005; Holalu and Arumugam, 2006; Devendran, Hemalaha, and Amiabh, 2009), mo reearcher compare image feaure vecor a hiogram-like rucure. We preen he following meaure in erm of hiogram, a hey are widely ued for maller-cale image analyi in differen domain. In order o repreen our feaure vecor a a hiogram, we reaed each elemen of n a a bin (n = 64). For example, we conver x o he hiogram A, he value in each bin [A j ] (for j = 1 o n) i equal o each x j (for j = 1 o n). 24