Class imaging of hyperspectral satellite remote sensing data using FLSOM

Transcription

1 Class imaging of hypespectal satellite emote sensing data using FLSOM T. Villmann 1,F.-M.Schleif 1, E. Meenyi,M.Sticket 3, and B. Hamme 4 1 Univesity Leipzig, Rice Univesity Houston, 3 IPK Gatesleben, 4 Univesity of Technology Clausthal thomas.villmann@medizin.uni-leipzig.de Keywods: SOM, fuzzy classification, visualization Abstact We popose an extension of the selfoganizing map fo supevised fuzzy classification leaning, wheeby uncetain fuzzy) class infomation is also allowed fo taining data. The method is able to detect class similaities, which can be used fo data vizualization. Applying a special functional metic, deived fom of the L p noms, we show the application of the method fo classification and visualization of hype-spectal data in satellite image emote sensing image analysis. 1 Intoduction The self-oganizing map SOM) intoduced by T. KOHO- NEN constitutes one of the most popula data mining and visualization methods fo pocessing of high-dimensional and complex data [1]. It is based on pinciples of pototype based unsupevised vecto quantization wheeby a topological gid stuctue with neighbohood coopeativeness is installed on the set of pototypes, usually chosen as a ectangula two-dimensional lattice. Howeve, othe aangements ae possible. Unde cetain conditions the SOM pototype adjustment leaning) geneates a model which allows a nonlinea mapping of the given data set onto a the low-dimensional egula lattice in a topologypeseving fashion [1] fo easy data analysis and intepetation [0]. Duing the last yeas, seveal extensions of the basic SOM have been established to make the appoach moe flexible and to assess the quality of the geneated model [3]. These ae elated to adaptive lattice stuctues, to the pocessing of stuctued data and to handling of labeled data by supevised leaning. Theeby, the handling of appopiate, poblem dependent data metics becomes also moe and moe impotant metic adaptation) [8]. Although the leaning scheme of the SOM is quite simple, its mathematical foundation is non-tivial. Most theoetical esults ae only valid fo special cases, wheeas moe geneal appoaches become intactable. In paticula, it is a blemish that the usual SOM does not follow a gadient descent on any cost function [5] such that the final state is not well defined. This poblem can be solved by a small modification of the oiginal leaning scheme, as it was shown by HESKES [11]. This modification offes new possibilities fo supevised leaning using SOMs, i.e. fo active utilization of data labels duing taining. Seveal extensions of the unsupevised SOM wee pesented fo pocessing supevised classification tasks anging fom simple post-labeling, the wellknown counte-popagation netwok to combine SOMs and multilaye peceptons o fuzzy decision schemes [10, 1]. Howeve, all these methods have in common that the pototype leaning of the undelying SOM is not influenced by the subsequent classification leaning, and, hence, the pototypes ae not adjusted in dependence of the classification task. The FuzzySOM poposed by P. VUORIMAA imposes a supevised leaning vecto quantization scheme fo the SOM-pototypes LVQ) on an unsupevised tained usual SOM to lean a classification task [4]. The subsequent LVQ leaning ule does not minimizes the classification eo. Thus both pats of FuzzySOM ae based on heuistics and, theefoe, have not well-detemined optimization goals. Moeove, the topogaphic mapping leaned duing the unsupevised SOM phase may be violated by the classification leaning, because neighbohood coopeativeness is not integated in LVQ. Hee we popose the utilization of the cost function accoding to HESKES in combination with a misclassification penalization tem as the new cost function fo supevised SOM. Theeby fuzzy class membeships of taining data ae allowed, i.e. uncetain class infomation is can be used. Minimizing of the poposed cost function by gadient descent leads to the fuzzy labeled SOM FLSOM). Like the usual SOM, the FLSOM geneates a topology peseving data mapping onto the SOM gid fo faithful taining conditions and pope data. Moeove, each pototype is equipped with a fuzzy label vecto descibing its pobabilistic o possibilistic class membeship. Using the topology pesevation popety of the SOM one can deive class similaities by investigation of the spatial distibution of the class membeship within the lattice envionment, which finally allows similaity peseving visualization of the classification by multi-dimensional scaling MDS) of the label vectos. The powe of the FLSOM is demonstated fo hypespectal image analysis of satellite emote sensing spectal data. In this context a special data similaity mea-

2 sue is used based on the Minkowski-nom. This so-called paametic) functional nom takes the spatial coelations within each spectum into account. We futhe integate the idea of metic adaptation into the above FLSOM scheme which impoves classification and gives a task dependent filteing of the specta. This is done by optimizing of the functional nom as a gadient descent with espect to the nom paametes. Fuzzy-Labeled SOM.1 Basic SOM with cost function Oiginally, the SOM is an unsupevised leaning of topogaphic vecto quantization such that data ae mapped onto a egula gid of nodes neuons). Assume data v V R DV ae given distibuted accoding to an undelying distibution P V). A SOM is detemined by a set A of neuons equipped with weight vectos/pototypes w R D V and aanged on a lattice stuctue which detemines the neighbohood o topological elation N, 0 ), the discete gid distance, between neuons and 0. Denote the set of pototypes by W = {w } A.IntheSOMvaiantaccoding to HESKES [11], the mapping desciption of a tained SOM defines a function Ψ V A : v 7 s v) = agmin de v, ). 1) A with local data) eos de v, ) = X 0 A h σ, 0 )ξ v, w 0) ) and µ h σ, 0 )=exp N, 0 ) 3) σ detemines the neighbohood coopeation with ange σ> 0. ξ v, w) is an appopiate distance measue, usually the standad Euclidean nom ξ v, w )=kv w k =v w ). 4) Howeve, hee we assume ξ v, w) to be abitay supposing that it is a diffeentiable and symmetic function which measues some data similaity. In this fomulation, an input stimulus is mapped onto that position of the SOM, whee the distance ξ v, w ) is minimum, wheeby the aveage ove all neuons accoding to the neighbohood is taken. We efe to this neuon sv) as the winne. Duing the adaptation pocess a sequence of data points v V is pesented to the map epesentative fo the data distibution P V). Each time the cuently most poximate neuon sv) accoding to 1) is detemined. All weights within the neighbohood of this neuon ae adapted by 4w = h σ,sv)) ξ v, w ) w 5) with leaning ate >0. This adaptation follows the stochastic gadient descent of the cost function E SOM = 1 Z P v) X δ sv) de v, ) dv 6) Cσ) wee C σ) is a constant which we will dop in the following, and δ 0 is the usual Konecke symbol checking the identity of and 0. One main aspect of SOMs is the visualization ability of the esulting map due to its topological stuctue. Unde cetain conditions the esulting non-linea pojection Ψ V A geneates a continuous mapping fom the data space V onto the gid stuctue A [1]. This mapping can mathematically be intepeted as an appoximation of the pincipal cuve o its highe-dimensional equivalents [9]. Thus, as pointed out above, simila data points ae pojected on pototypes which ae neighboed in the gid space A. Futhe, pototypes neighboed in the lattice space should code simila data popeties, i.e. thei weight vectos should be close togethe in the data space accoding to the metic ξ. This popety of SOMs is called topology peseving o topogaphic) mapping ealizing the mathematical concept of continuity. Fo a detailed consideation of this topic we efe to [1].. Integating fuzzy classification into SOM We now integate the label class) infomation into the leaning scheme of SOM to allow supevised leaning. This is done in such a way that the pototype adjustment is depending on both the data distibution as well as the label infomation. Assume taining point v is equipped with a label vecto x [0, 1] C descibing the class infomation of C classes, wheeby the component x i of x detemines the pobabilistic/possibilistic assignment of v to class i fo i =1,...,C. Hence, we can intepet the label vecto as pobabilistic o possibilistic fuzzy class membeships. In case of pobabilistic labeled data we have the constaint P C i=1 x i =1and fo cisp labeled data the additional condition x i {0, 1} holds. Accodingly, we add to each pototype vecto w of the map a label vecto y [0, 1] C which detemines the amount of neuon assigned to the espective classes. The new cost function to be minimized contains two tems: the unsupevised pat E SOM and a new one E FL descibing the classification accuacy E FLSOM =1 β) E SOM + βe FL 7) whee β [0, 1] is a balance facto to detemine the influence of the goal of clusteing the data set and the goal of achieving a coect labeling. One can simply choose β = 0.5, fo example. Fo classification accuacy we choose E FL = 1 Z P v) X ce v, ) dv 8)

3 3 with local, weighted classification eos ce v, ) =g γ v, w )x y ) 9) and g γ v, w ) is a Gaussian kenel descibing a neighbohood ange in the data space: µ g γ v, w )=exp ξ v, w ) γ. 10) This choice is based on the assumption that data points close to the pototype detemine the coesponding label if the undelying classification is sufficiently smooth. Note that g γ v, w ) depends on the pototype locations, such that E FL is influenced by both w and y, and, hence, E FL w contibutes to the usual SOM-leaning by Z E FL w = 1 4γ P v) ce v, ) ξ v, w ) w dv 11) The label update is independent fom the fist tem E SOM such that it simply becomes Z E FL = P v) g γ v, w y ) x y ) dv 1) It can be intepeted as a weighted aveage of the data fuzzy labels of those data close to the associated pototypes. As mentioned above, unsupevised SOMs geneate a topogaphic mapping fom the data space onto the pototype gid unde specific conditions. If the classes ae consistently detemined with espect to the vaying data, one can expect fo supevised topogaphic FLSOMs that the labels become odeed within the gid stuctue of the pototype lattice. In this case the topological ode of the pototypes should be tansfeed to the topological ode of pototype labels such that we have a smooth change of the fuzzy class label vectos between neighboed gid positions. This is the consequence of following fact: the neighbohood function h σ, s) of the usual SOM leaning 5) foces the topological odeing of the pototypes. In FL- SOM, this odeing is futhe influenced by the weighted classification eo ce v, ), which contains the data space neighbohood g γ v, w ), eq. 11). Hence, the pototype odeing contains infomation of both data density and class distibution, wheeby fo high value β the latte tem becomes dominant. Othewise, the data space neighbohood g γ v, w ) also tigges the label leaning 1), which is, of couse, also dependent on the undelying leaned pototype distibution and odeing. Thus, a consistent odeing of the labels is obtained in FLSOM. Hence, the evaluation of the similaities between the pototype label vectos yields suggestions fo the similaity of classes, i.e. simila classes ae epesented by pototypes in a local spatial aea of the SOM lattice. In case of ovelapping class distibutions the topogaphic pocessing leads to pototypes with unclea decision, located between pototypes with clea vote. Futhe, if classes ae not distinguish-able, thee will exist pototypes esponsive to those data which have class label vectos containing appoximately the same degee of class membeship fo the espective classes..3 Functional nom and metic adaptation In usual SOMs the data similaity measue ξ v, w ) is usually chosen to be the squaed Euclidean metic. Howeve, depending on task, this choice may be not optimum. Theefoe, othe measue ae also of inteest, fo example TAN- IMOTO s distance o coelation measues in taxonomy o medicine/biology. Now we conside a paametized diffeentiable distance measue ξ λ v, w) with a paamete vecto P λ =λ 1,...,λ M ) with λ i 0 and nomalization i λ i = 1. The idea of metic adaptation o elevance leaning is to optimize the paametes λ i with espect to the classification task using a gadient descent [7]. Fomal deivation yields We obtain with and E FLSOM E SOM = 1 Z =1 β) E SOM P v) X + β E FL 13) δ sv) dev, ) dv 14) dev, ) = X 0 h σ, 0 ) ξλ v, w ) 15) E FL = 1 4γ Z P v) X ce v, ) ξλ v, w ) dv 16) fo the espective paamete adaptation. In case of ξ λ v, w) being the scaled Euclidean metic ξ λ v, w) = X i λ i v i w i ), 17) elevance leaning anks the input dimensions i accoding to thei elevance fo the classification task at hand. Thus, the coesponding leaning ule fo the elevance paametes becomes 1 β X 4λ l = λ h σ sv), ) v l w ) l ) 18) β X + λ 4γ g γ v, w )v l w ) l ) x y ) subscipt l denoting the component l of a vecto) with leaning ate λ > 0. This update is followed by nomalization to ensue λ i 0 and P i λ i =1. The Euclidean metic takes the input dimensions as independent. Howeve, fo functional data like specta o

4 4 time seies, the data dimensions coespond to fequencies o time points, espectively, and, theefoe, they ae spatially coelated. LEE&VERLEYSEN poposed a functional nom which takes these coelations implicitly into account [13]. Fo a vectoial epesentation v of a function we assume that between neighboed data dimensions thee is a constant fequency o time diffeence. Then, the functional p-nom is defined as Futhe, the deivative of δ λ v, w ) with espect to the metic paametes λ k, which have to be plugged into the gadient fomulae 14) and 16) fo metic adaptation, ae δ λ v, w ) λ k = ½ c k v k z k, k 1) v k ½ c + k v k z k, k +1) v k if 0 v k 1 v k if 0 >v k 1 v k if 0 v k+1 v k if 0 >v k+1 v k L fc p v) = with the tems and A k v) = B k v) = τ τ Ã D X τ k=1 A k v)+b k v)) p! 1 p 19) v k if 0 v k v k 1 vk 0) v k + v k 1 if 0 >v k v k 1 τ v k if 0 v k v k+1 vk 1) v k + v k+1 if 0 >v k v k+1 Fo p = it induces the quadatic functional metic ³ δ v, w )= L fc v w ). In analogy to the scaled Euclidean metic we intoduce the scaled quadatic functional metic ³ δ λ v, w )= L fc Λ v w )) ) with c j = A j λv)+b j λv) and. z k, j) = λ kc k v k c jv j λ j +λ k c k v k v j λ j λ k v k + v j λ j ) 3 HiT-MDS- fo class label visualization Now we tun to use the leaned class elations fo visualization. As descibed in Sec.., the fuzzy label vectos y of the FLSOM eflect class similaities. Fo visualization of class membeship of data we suggest a colo epesentation. Theeby, we make use of the leaned class similaities. Thus we look fo a similaity based epesentation. Fo this pupose, we map the pototype label vectos y onto colo vectos c hee chosen as RGB-vectos epesenting the colo intensities fo the colos ed, geen and blue. Yet, othe colo space epesentations ae possible. Similaity peseving mapping can be obtained by seveal appoaches, fo example by thee-dimensional SOM, with Λ being a diagonal matix with enties Λ ii = λ i and λ i 0 and P i λ i =1. The deivative δ λv,w ) w detemines the leaning ules and is obtained fo the of the kth MDS o local linea embedding. Hee we apply an advanced MDS scheme called HiT-MDS-, which is moe o- dimension as: µ bust than usual MDS [19]. We biefly explain this method δλ v, w ) = U k 1 U k+1 )V k 1 + V k+1 ) 4 k in the following. w k Geneally, MDS 3) ³ efes to the optimization of N point with locations t i = t 1 i,...,tďi RĎ in a taget space in such a way that thei distance elationships faithfully eflect those of the associated oiginal data vectos o 0 if 0 4 k 4 k 1 U k 1 = ³ i λ k 1 4 k 1 λ k 4 k +λ k 1 4 k 1 if 0 > 4 k 4 k 1 O R D [3]. Obviously, in case of dimension eduction with D>Ď such optimization will need to find a compomise solution. Let δ i,k = δ o i, o k ) be the similaity 0 if 0 4 k 4 k+1 distance) measue in the oiginal data space O. Futhe, let U k+1 = ³ λ k+1 4 k+1 d i,k = d t i, t k ) be the distance in the lowe-dimensional λ k 4 k +λ k+1 4 k+1 if 0 > 4 k 4 k+1 taget space RĎ. If distances ae Euclidean then the minimum of the canonical point-embedding stess function J = P i<k 1λ k if 0 4 k 4 d i,k δ i,k ) =minyields taget configuations which ae equivalent to the linea pojections of pin- k 1 V k 1 = λ k 4 k λ k 4 k +λ k 1 4 k 1 if 0 > 4 k 4 k 1 cipal component analysis PCA). Although the benefit ove PCA is moe flexibility in the choice of distance measues, like many othe metic MDS appoaches, minimization of 1λ k if 0 4 k 4 k+1 the espective stess function suffes fom the pesence of V k+1 = λ k 4 k λ k 4 k +λ k+1 4 k+1 if 0 > 4 k 4 k+1 local minima. One avoidable eason fo local minima is a too stingent fomulation of the stess function. In most and 4 k = v k w k. metic appoaches, econstucted distances ae foced onto

5 5 a pe-defined line, such as the one with unit slope fo the canonical stess, in the coesponding δ i,k -vs.-d i,k Shepad plot. In contast to that, HiT-MDS- maximizes the Peason coelation [ 1; 1] P q<k = δ q,k μ δ ) d q,k μ d ) q P q<k δ q,k μ δ ) P q<k d q,k μ d ) B = C D between enties of the souce distances and the coesponding taget space distances by minimizing negative Fishe s Z 0 : J Z 0 = 1 log µ a + a! =min, a =1+ 4) Theeby, μ δ and μ d ae the aveaged distances in the data and taget space, espectively. Locations of points t i in taget space ae obtained by iteative gadient descent 4t k i = ε J Z 0 t k i of step size ε on the stess function J Z 0 using the chain ule: J Z 0 = a a 5) = δ i,j μ δ ) D d i,j μ d ) B 6) d i,j D C D d i,j t k = t k i tk j fo Euclidean taget space) 7) i d i,j These equations yield a substantially impoved convegence ove the old fomulation of HiT-MDS poposed ealie [19]. HiT-MDS- makes use of two non-citical paametes, the leaning ate ε =0.1 and the exta Z 0 infinitypevente = 0.001, which in Fishe s oiginal fomula would be zeo. While, fo plotting puposes, taget distances ae usually Euclidean, howeve, input distances can be mee dissimilaities such as coelation. A futhe emak is due to optimized computation of MDS embedding in case of incemental adaptation: The computational cost can be damatically educed using the fact that fo each iteation only a few distances ae eally changed [19]. 4 Application We applied the FLSOM fo classification of hype spectal images in satellite emote sensing image analysis. Aibone and satellite-bone emote sensing spectal images consist of an aay of multi-dimensional vectos specta) assigned to paticula spatial egions pixel locations) eflecting the esponse of a spectal senso at vaious wavelengths. A spectum povides a clue to the suface mateial within the espective suface element. The utilization of these specta includes aeas such as mineal exploation, land use, foesty, ecosystem management, assessment of natual hazads, wate esouces, envionmental contamination, biomass and poductivity; and many othe activities of economic significance. The numbe of applications has damatically inceased in the past yeas with the advent of imaging spectometes such as AVIRIS of NASA/JPL. [] Imaging spectometes sample a spectal window contiguously with vey naow, 10 0 nm bandpasses [18]. Depending on the wavelength esolution and the width of the wavelength window the dimensionality of the specta can as high as seveal hunded [6]. Spectal images can be fomally descibed as a matix S = v x,y),wheev x,y) R D V is the vecto of spectal infomation associated with pixel location x, y). The elements v x,y) i, i =1...D V of spectum v x,y) eflect the esponses of a spectal senso at a suite of wavelengths [4]. The spectum is a chaacteistic fingepint patten that identifies the suface mateial within the aea defined bypixelx, y). The individual -dimensional image S i = v x,y) i at wavelength i is called the ith image band. The data space V spanned by Visible-Nea Infaed eflectance specta is [0 noise, U + noise] DV R DV whee U > 0 epesents an uppe limit of the measued scaled eflectivity and noise is the maximum value of noise acoss all spectal channels and image pixels. The data density P V) may vay stongly within this space. Sections of the data space can be vey densely populated while othe pats may be extemely spase, depending on the mateials in the scene and on the spectal bandpasses of the senso [16]. In addition to dimensionality and volume, othe factos, specific to emote sensing, can make the analyses of hypespectal images even hade. Fo example, given the ichness of data stuctues, the goal is to sepaate many cove classes, howeve, suface mateials that ae significantly diffeent fo an application may be distinguished by vey subtle diffeences in thei spectal pattens. The pixels can be mixed, which means that seveal diffeent mateials may contibute to the spectal signatue associated with one pixel. Taining data may be scace fo some classes, and classes may be epesented vey unevenly. All the above difficulties motivate eseach into advanced and novel appoaches. A Visible-Nea Infaed μm), 4-band, 0 m/pixel AVIRIS image of the Luna Cate Volcanic Field LCVF), Nevada, U.S.A., was analyzed in ode to study FLSOM pefomance fo high-dimensional emote sensing spectal imagey. AVIRIS is the Aibone Visible-Nea Infaed Imaging Spectomete, developed at NASA/Jet Populsion Laboatoy. Figue 1 shows a natual colo composite of the LCVF with labels making the locations of 3 diffeent suface cove types of inteest. This 10 1 km aea contains, among othe mateials, volcanic cinde cones class A, eddest peaks) and weatheed deivatives theeof such as feic oxide ich soils L, M, W), basalt flows of vaious

6 6 ages F, G, I), a dy lake divided into two halves of sandy D) and clayey composition E); a small hyolitic outcop B); and some vegetation at the lowe left cone J), and along washes C). Alluvial mateial H), dy N,O,P,U) and wet Q,R,S,T) playa outwash with sediments of vaious clay contents as well as othe sediments V) in depessions of the mountain slopes, and basalt cobble stones stewn aound the playa K) fom a challenging seies of spectal signatues fo patten ecognition see in [16]). A long, NW-SE tending scap, staddled by the label G, bodes the vegetated aea. Since this colo composite only contains infomation fom thee selected image bands one Red, one Geen, and one Blue), many of the cove type vaiations emain undistinguished. Afte atmospheic coection and emoval of excessively noisy bands satuated wate bands and ovelapping detecto channels), 194 image bands emained fom the oiginal 4, i.e.d V = 194. The 3 geologically elevant classes indicated in Figue 1 epesent a geat vaiety of suface coves in tems of spatial extent, the similaity of spectal signatues [16], and the numbe of available taining samples N = 931. Figue 1, middle panel, visualizes the best classification, with 9% oveall image accuacy, poduced by an SOM- MLP-hybid netwok [15]. This netwok fist leans in an unsupevised mode the hidden SOM laye. Afte the SOM convegence, the output laye is allowed to lean class labels via a Widow-Hoff leaning ule. Taining samples fo the supevised classifications wee selected based on field knowledge. In a second study a genealized leaning vecto quantization scheme GRLVQ, [7]) was applied [14]. The oveall numbe of pototypes was chosen as 115, i.e. 5 pototypes fo each class. The achieved accuacy fo the available taining samples is 97.0%, wheeby a scaled Euclidean metic was applied togehte with elevance leaning fo inpoved pefomance. To be compaable to the latte appoach, the FLSOM lattice stuctue was chosen as 11 pototypes in a 16 7 gid. The gid edge length atio was detemined using the gowing SOM []. The final balancing paamete was β =0.85. The topogaphy of the FLSOM is quite good giving a topogaphic poduct value neaby zeo [1]. Small violations wee detected by the topogaphic function [1]. The FL- SOM accuacy fo taining samples majoity vote) is obtained as 95.3% fo the Euclidean metic and 95.7% fo the functional metic. The educed accuacy in compaison to GRLVQ is due to the β-value, which means a nonvanishing tem of unsupevised leaning in the cost function. Howeve, futhe inceasing of β would lead to lost of the neighbohood egulaization, which is needed fo detecting class similaities based on topogaphy popeties see Sec..). In fact, the esulted distibution of the label vectos on the gid shows a clea odeing and smooth tansitions, wheeby classes with simila meaning ae gouped togethe Figue ). This esult can be evaluated by validity measues assessing cluste patitions in fuzzy clusteing. Thee exist a boad ange of indices [17]. Roughly speaking, most of the measues take mainly the compactness and the sepaability of clustes fo judgement into account. Taking the class label distibution as cluste distibution, we can adapt them to the specific task of assessing the quality of the label distibution in the FLSOM-gid. Hee we used the validity index V m povided in [17]: with V m = J m A, Y) K m A, Y) 8) J m A, Y) = X A CX y i m da, c i ) 9) i=1 is the cost function of fuzzy-c-means assessing the compactness of the clustes. Theeby, y = y,...,y 1 C ae the label vectos of the pototypes, and c i is the cente location of class i. Itisdefined as the lattice location of the label with the highest class assignment c i =agmax y i 30) A d A is the Euclidean distance taken the gid indices as locations. The second tem S m A, Y) in 8) is the sepaation index S m A, Y) = 1 X C #A A i=1 CX y i m da, c) 31) judging the sepaability of clustes with c = 1 C P C i=1 c being hee the mean of all gid locations of class centes c i. The obtained label distibution in the application see Figue ) shows a clealy impoved validity V m index compaed to labeling achieved by usual SOM-leaning with subsequent post-labeling. Both tems J m and S m ae indepentently optimized such that both coveed featues, compactness and sepaability, show impoved pefomance fo FLSOM leading to bette intepetability. Compaing the SOM-MLP-hybid ANN visualization with the visualization obtained by FLSOM with subsequent HiT-MDS- colo mapping Figue 1, bottom), the fist obsevation is the stiking coespondence. Yet, the optimized coloing by class label mapping using HiT-MDS-, which takes the class similaities detected by FLSOM into account see Figue ), leads to a moe smoothed visualization, wheeby simila mateial ae epesented by simila colos. Fo example, pototypes esponsible fo simila mateials wet playa - classes Q, R, S, T; alluvium - classes C, H, M; dy wash - classes N, O, P) ae in small gid aeas and the espective class label show a continuous tansition, which geneates simila colo epesentation in visualization. Evaluation of futhe efinements ae left to futue wok.

7 7 5 Conclusion We popose an extension of SOMs fo fuzzy classification. The appoach allows the detection of class similaities. Fo this pupose, the neighbohood coopeativnes of SOMs is used and tansfeed also to the supevised pat of taining fo classification leaning. The achieved similaity infomation can be used fo bette visualization of classification esults. We demonstate the method fo hype-spectal data classification and visualization in satellite emote sensing image analysis. Acknowledgements EM has been patially suppoted by NASA AISRP gant NNG05GA94G. Refeences [1] H.-U. Baue, K. Pawelzik, and T. Geisel. A topogaphic poduct fo the optimization of selfoganizing featue maps. In J. E. Moody, S. J. Hanson, and R. P. Lippmann, editos, Advances in Neual Infomation Pocessing Systems 4, pages Mogan Kaufmann, San Mateo, CA, 199. [] H.-U. Baue and T. Villmann. Gowing a Hypecubical Output Space in a Self Oganizing Featue Map. IEEE Tansactions on Neual Netwoks, 8):18 6, [3] A. Buja, D. Swayne, M. Littman, N. Dean, and H. Hofmann. Inteactive Data Visualization with Multidimensional Scaling. Repot, Univesity of Pennsylvania, [4] J. Campbell. Intoduction to Remote Sensing. The Guilfod Pess, U.S.A., [5] E. Ewin, K. Obemaye, and K. Schulten. Selfoganizing maps: Odeing, convegence popeties and enegy functions. Biol. Cyb., 671):47 55, 199. [6] R. O. Geen. Summaies of the 6th Annual JPL Aibone Geoscience Wokshop. Pasadena, CA, Mach [7] B. Hamme, M. Sticket, and T. Villmann. Supevised neual gas with geneal similaity measue. Neual Pocessing Lettes, 11):1 44, 005. [8] B. Hamme and T. Villmann. Classification using non-standad metics. In M. Veleysen, edito, Poc. Of Euopean Symposium on Atificial Neual Netwoks ESANN 005), pages , Bussels, Belgium, 005. d-side publications. [9] T. Hastie and W. Stuetzle. Pincipal cuves. J. Am. Stat. Assn., 84:50 516, [10] R. Hecht-Nielsen. Countepogagation netwoks. Appl. Opt., 63): , Decembe [11] T. Heskes. Enegy functions fo self-oganizing maps. In E. Oja and S. Kaski, editos, Kohonen Maps, pages Elsevie, Amstedam, [1] T. Kohonen. Self-Oganizing Maps, volume 30 of Spinge Seies in Infomation Sciences. Spinge, Belin, Heidelbeg, Second Extended Edition 1997). [13] J. Lee and M. Veleysen. Genealization of the l p nom fo time seies and its application to selfoganizing maps. In M. Cottell, edito, Poc. of Wokshop on Self-Oganizing Maps WSOM) 005, pages , Pais, Sobonne, 005. [14] M. Mendenhall. A Neual Relevance Model fo Featue Extaction fom Hypespectal Images, and its Application in the Wavelet Domain. PhD thesis, Rice Univesity, Houston, TX, August 006. [15] E. Meenyi. pecision mining" of high-dimensional pattens with self-oganizing maps: Intepetation of hypespectal images. In P. Sincak and J. Vascak, editos, Quo Vadis Computational Intelligence? New Tends and Appoaches in Computational Intelligence Studies in Fuzziness and Soft Computing, Vol. 54. Physica-Velag,?, 000. [16] E. Meényi. Self-oganizing ANNs fo planetay suface composition eseach. In Poc. Of Euopean Symposium on Atificial Neual Netwoks ESANN 98), pages 197 0, Bussels, Belgium, D facto publications. [17] N. Pal and J. Bezdek. On the cluste validity fo the Fuzzy c-means model. IEEE Tansactions on Fuzzy Systems, 33): , [18] J. Richads and X. Jia. Remote Sensing Digital Image Analysis. Spinge-Velag, Belin, Heidelbeg, New Yok, thid, evised and enlaged edition edition, [19] M. Sticket, S. Teichmann, N. Seenivasulu, and U. Seiffet. High-Thoughput Multi-Dimensional Scaling HiT-MDS) fo cdna-aay expession data. In W. Duch et al., edito, Atificial Neual Netwoks: Biological Inspiations, Pat I, LNCS 3696, pages Spinge, [0] J. Vesanto. SOM-based data visualization methods. Intelligent Data Analysis, 37):13 456, [1] T. Villmann, R. De, M. Hemann, and T. Matinetz. Topology Pesevation in Self Oganizing Featue Maps: Exact Definition and Measuement. IEEE Tansactions on Neual Netwoks, 8):56 66, [] T. Villmann, E. Meényi, and B. Hamme. Neual maps in emote sensing image analysis. Neual Netwoks, 163-4): , 003. [3] T. Villmann, U. Seiffet, and A. Wismülle. Theoy and applications of neual maps. In M. Veleysen, edito, Euopean Symposium on Atificial Neual Netwoks 004, pages d-side publications, 004. [4] P. Vuoimaa. Fuzzy self-oganizing map. Fuzzy Sets and Systems, 66):3 31, Sept 1994.

8 8 Figue 1: top - natual colo composite of the LCVF with labels making the locations of 3 diffeent suface cove types see text); middle - colo epesentation of the classification esult of the SOM-MLP-hypid netwok; bottom - similaity based colo epesentation of the classification esult of the FLSOM appoach using HiT-MDS- mapping. Figue : Visualization of the class label distibution within the FLSOM lattice. A clea odeing can be obseved, which is the convegence of the class similaity leaning.