HYPERSPECTRAL IMAGE CLASSIFICATION USING A SELF-ORGANIZING MAP . (2)

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1 HYPERSPECTRAL IMAGE CLASSIFICATION USING A SELF-ORGANIZING MAP P. Martínez, 1 J.A. Gualter, 2 P.L. Agular, 1 R.M. Pérez, 1 M. Lnaje, 1 J.C. Precado, 1 A. Plaza 1 1. INTRODUCTION The use of hyperspectral data to determne the abundance of consttuents n a certan porton of the Earth s surface reles on the capablty of magng spectrometers to provde a large amount of nformaton at each pxel of a certan scene. Today, hyperspectral magng sensors are capable of generatng unprecedented volumes of radometrc data. The Arborne Vsble/Infrared Imagng Spectrometer (AVIRIS), for example, routnely produces mage cubes wth 224 spectral bands (Green, ). Ths undoubtedly opens a wde range of new possbltes, but the analyss of such a massve amount of nformaton s not an easy task. In fact, most of the exstng algorthms devoted to analyzng multspectral mages are not applcable n the hyperspectral doman, because of the sze and hgh dmensonalty of the mages. Hyperspectral unmxng or lnear pxel unmxng s becomng ncreasngly popular for the analyss and nterpretaton of hyperspectral mages (Martínez et al., 1999). The basc assumpton s that the sgnal receved from each pxel can be consdered as a smple lnear combnaton of the spectral contrbutons of all pxel components. The technque, therefore, decomposes the scene n such a way as to recover the fractonal contrbutons of the fundamental components or endmembers (as abundance or fracton mages). Ths provdes a means of extractng sub-pxel nformaton from the scenes, whch s partcularly advantageous when the sze of the nterestng ground elements s much smaller than the mage resoluton and there s domnance of mxed pxels. Unsupervsed clusterng s a challengng problem n many areas of data analyss (Antonlle & Gualter, 2000). It can be stated as follows: gven a set of N data ponts n a feature space of D dmensons, D { x, x,..., x } R, x = (x, x,..., x ), 1,..., N, (1) 1 2 N 1 2 D = we wsh to characterze K clusters for the data, where K s obtaned from statstcal nformaton about the data usng some dstance metrc, d j = d(x, x j). (2) The prncpal characterstc of unsupervsed clusterng s that t does not ncorporate any prevous knowledge about the data. Snce ground truth data n remote sensng s expensve and hard to obtan, the use of unsupervsed procedures has become more relevant n ths feld durng recent years. In partcular, several unsupervsed procedures to process hyperspectral data are avalable n well-known commercal software systems as Research Systems ENVI TM. The applcaton of neural networks to perform unsupervsed classfcaton of hyperspectral data has been tested by several authors (Jménez et al., 1999) and also by us n some prevous work (Agular et al., 1998; Martínez et al., 1999; Agular et al., 2000a, Agular et al., 2000b). We have also focused on analyzng the ntrnsc capablty of neural networks to parallelze the whole hyperspectral unmxng process (Pérez et al., 1999). The results shown n ths work ndcate that neural network models are able to fnd clusters of closely related hyperspectral sgnatures, and thus can be used as a powerful tool to acheve the desred classfcaton. 1 Departamento de Informátca, Unversdad de Extremadura, Avda. de la Unversdad s/n, Cáceres, SPAIN E-mal: pablomar@unex.es 2 Global Scence and Technology at Appled Informaton Scences Branch, NASA/GSFC, Greenbelt, Maryland 20771, U.S.A. E-mal: gualt@peep.gsfc.nasa.gov

2 One of the most wdely used unsupervsed neural network algorthms s the Self-Organzng Map (SOM), proposed by Kohonen, Ths approach has been successfully appled n many dfferent felds, ncludng mage analyss and computer vson, handwrtten text recognton, analyss and recognton of human voce and telecommuncatons. Some reasons for usng SOM to perform hyperspectral analyss have been descrbed by Bruske and Mereny, 1999, who hghlght the computatonal speed provded by ths method when mplemented by hardware n the form of a massvely parallel algorthm, surpassng the performance of conventonal classfcaton algorthms. Snce the Kohonen algorthm s smple and ntutve, hghly parallelzable (whch can lead to an easy VLSI mplementaton based on systolc arrays or FPGAs) and s easly extendable to a hgh number of dmensons, we have selected t as our startng pont to deal wth hyperspectral data. The present work dscusses the possblty of usng a Self Organzng neural network to perform unsupervsed classfcaton of hyperspectral mages. In sectons 3 and 4, the topology of the proposed neural network and the tranng algorthm are respectvely descrbed. Secton 5 provdes the results we have obtaned after applyng the proposed methodology to real hyperspectral data, descrbed n secton 2. Dfferent parameters n the learnng stage have been modfed n order to obtan a detaled descrpton of ther nfluence on the fnal results. Fnally, n secton 6 we provde the conclusons at whch we have arrved. 2. DATA The hyperspectral unmxng algorthms proposed n ths work have been tested usng the publc doman Indan Pnes hyperspectral dataset, whch has been prevously used n many dfferent studes. Ths mage was obtaned from the AVIRIS magng spectrometer at Northern Indana on June 12, 1992 from a NASA ER2 flght at hgh alttude wth ground pxel resoluton of 17 meters. The dataset comprses 145x145 pxels and 220 bands of sensor radance wthout atmospherc correcton. It contans two thrds of agrculture (some of the crops are n early stages of growth wth low coverage), and one thrd of forest, two hghways, a ral lane and some houses. Ground truth determnes sxteen dfferent classes (not mutually exclusve). Water absorpton bands ( , and 220) were removed (Tadjudn and Landgrebe, 1998), obtanng a 200 band spectrum at each pxel. In order to reduce the tme of tranng and testng, we have selected a subscene of the complete Indan Pnes dataset (depcted n Fgure 1) of sze 68 samples x 86 lnes at [27-94] x [31-116] n the orgnal mage, consderng left n the full scene s at (1,1). In the selected subscene there are four known ground truth classes. Corn-notll Soybean 1 Grass Soybean 2 Fgure 1. A subset of the Indan Pnes hyperspectral dataset wth ground truth. 3. TOPOLOGY OF THE PROPOSED NEURAL NETWORK The Self-Organzng Map (SOM) s based on compettve learnng that leads to the constructon of topologc maps representng class prototypes. In order to understand the topology of the proposed neural network, we frst need to defne some basc concepts. A neuron s an nformaton-processng unt. Neurons are connected

3 by synapses or connectng lnks, each of them characterzed by a weght. Specfcally, a sgnal x j at the nput of synapse j connected to neuron k s multpled by the synaptc weght w kj. A neural network s a set of neurons organzed n the form of layers. In the smplest form, an nput layer projects onto an output layer of neurons. If the nput layer has N unts and the output layer has M unts, each unt n the output layer owns N weghts assocated to the connectons whch come from the nput layer, so that the set of neural weghts s organzed n the form of a two-dmensonal lattce (W MxN ). Our proposed network archtecture s depcted n Fgure 2 (Agular et al., 2000b). In our case, N corresponds to the number of channels of the hyperspectral mage and M s the number of classes or prototypes to be extracted by the network. M must be carefully selected accordng to some metrc (we wll nsst on ths ssue later on n the paper). There are feedforward connectons from the nput layer to the output layer and selffeedback and lateral feedback connectons n the output layer. These two types of local connectons serve two dfferent purposes: a) In the classfcaton stage, the weghted sum x W (scalar product ) of the nput sgnals x at each neuron performs feature detecton: each neuron produces a selectve response to nput sgnals. b) In the learnng stage, lateral and self-feedback connectons produce exctatory or nhbtory effects dependng on the dstance from the correspondng output layer neuron to the wnnng neuron (Agular et al., 2000c). Ther assocated weghts are used to determne the W classfcaton prototype for each neuron. 1 SOM Characterstcs R M y N W Fgure 2. SOM neural network topology ncludng weght matrx W and self-feedback and lateral feedback connectons. S y c sy 4. TRAINING ALGORITHM There are fve basc steps nvolved n the tranng algorthm. These steps are repeated untl the topologcal map s completely formed: a) Intalzaton: choose random values for the ntal weght vectors, w (0), = 1,2,... M. It s desrable to keep the magntude of the weghts small. b) Samplng: choose an nput pattern x(n) belongng to a set of learnng patterns or references, R. The selecton s done randomly. c) Smlarty Matchng: fnd the best-matchng (wnnng) neuron * at tme t, usng the mnmum-dstance crteron as shown n the followng equaton, where dst s the eucldean dstance: * [ x(n) ] mn dst{ x(n), w (t)}, j = 1,2,..., M = (3) j j

4 d) Learnng: adjust the synaptc weght vectors of all neurons, usng the update formula (4), where η(t) s a ( ) * learnng-rate parameter, and t,, [ x(n) ] γ s a Gaussan neghborhood functon centered around the wnnng neuron. The sze of the neghborhood s determned by the reference dstance σ (t) (see equaton 5). * ( t,, [ x(n) ])( x(n) w (t)) w (t + 1) = w (t) + η(t) γ (4) From the dfferent optons to select the prevously mentoned parameters, takng nto account the studes done n Agular, 2000, we have selected the followng ones: 1 ( t) = t ( ) e γ =, σ(t) * η, t,, [ x(n) ] dst( * ) 2, σ 0 σ (t) =. (5) t e) Contnue from step b) untl no notceable changes n the weght space are observed, or untl the maxmum convergence tme s acheved. In order to analyze a hyperspectral mage usng ths algorthm, the network must be traned wth hyperspectral sgnatures obtaned drectly from the mage. The weghts ntally assocated wth each output layer neuron contan the hyperspectral sgnatures of some carefully selected pxels on the mage (accordng wth ther spatal dstrbuton). 5. RESULTS AND DISCUSSION We have appled our proposed neural network to real hyperspectral data, descrbed n secton 2. Snce there are several parameters nvolved n the tranng algorthm (descrbed n the prevous secton) n ths secton we analyze the nfluence of those parameters n the process of class prototype extracton. In partcular, the parameters that we consder n the present study are the number of teratons untl convergence of the neural network s reached, the sze of neghborhood functon γ centered around the wnnng neuron, whch s determned by σ (t), and the number of neurons n the output layer of the neural network. The experment s performed as follows. We tran the network wth all the hyperspectral sgnatures of the mage. Durng the learnng stage, we go through all the pxels of the mage startng from a random pxel whch s dfferent n each of the teratons. Once class prototypes have been extracted, each pxel s classfed and the confuson matrx (Chuveco, 2000) s obtaned. Ths matrx allows us to vsualze wnnng neuron densty for each class. The characterstcs of the confuson matrx provdes us wth a comprehensve vsualzaton of dstrbuton n N-dmensonal space, and may ndcate the accuracy of the classfcaton. Snce each column corresponds to an output neuron, f one column presents hgh values for dfferent classes, the overall accuracy of the classfcaton should be low. In order to measure the degree of accuracy of the classfcaton, we propose the followng metrc based on the topology of the confuson matrx: Xm E =, Xm Max(X j) Xs =, Xs = X j. (6) Xm s the maxmum value for a column of the confuson matrx and Xs s the sum of all the values n that column. E provdes nformaton about the capacty of each neuron to dscrmnate between the classes, and can be averaged for all the neurons n the network, provdng a general measure about the accuracy of the classfcaton. The performance of the SOM Neural Network depends on a lot of adjustng parameters: 1. Number of output neurons: the deal numbers of output neurons must be equal to the number of ground truth classes, assocatng exactly one neuron wth one class. Usually ths fact s not possble f we have a larger number of output neurons that ground truth classes. In ths way, one correct classfcaton j

5 uses several neurons for each ground truth class. In the Indan Pnes ground-truth mage there are 16 classes (plus one class of unclassfed pxels). 2. Wegth ntalzaton: the weghts w j ntally assocated wth each neuron contan random values. 3. Order to scan the mage: a random ntal pont of the mage s selected at each teraton. 4. Neghborhood functon: as mentoned before, our choce for the neghborhood functon s the Gaussan functon. 5. Reference dstance σ(t): when the algorthm starts (t=1), the neural lattce s n a random state, the neghborhood functon n these frst teratons of the algorthm must have smlar values for to nclude a large number of neurons and obtan some average values (hgh σ(0) values). When t ncreases, γ(t,, * [x(n)] ) needs to be adjusted to reduce the number of neghbor neurons. Care must be taken nto account to avod a quckly reducton of the number of neghborhood neurons, ths reducton can be accomplshed by changng the reference dstance σ (t). Our choce for the reference dstance evoluton s σ (t)=(1/t) 2 The parameters that we analyze n the present study are the number of neurons n the output layer, the number of teratons of the neural network and the neghborhood startng value σ 0. Next, some results obtaned for the hyperspectral data descrbed n secton 2 are provded. In our frst experment, we have consdered 16 neurons n the output layer, 100 teratons and σ 0 = 2. Table 1 shows the resultng confuson matrx and Fgure 3 shows the the resultng classfcaton provded by the neural network usng the prevously mentoned parameters along wth a greyscale representaton of the confuson matrx shown n Table 1. A favorable result would be obtaned f neurons actvate exclusvely for a partcular class, dscrmnatng ths class from the others. In the confuson matrx, ths can be graphcally expressed as a row for whch several columns present hgh values. In Fgure 3 we can apprecate ths stuaton at four dfferent rows (2,6,10,11 and 17). The fact that column values overlap ndcates an naccurate classfcaton. Another ndcator of the qualty of the classfcaton s the contnuty of hgh values n the rows of the confuson matrx (ths fact should produce brght contguous rows n the confuson matrx mage). In ths experment, the topology of the resultng classes s not preserved snce we can apprecate several dscontnutes n the learnt classes. The overall accuracy of the classfcaton obtaned n ths experment was 60% accordng to the measure provded n equaton 6. Nevertheless, we have to take nto account that class 17 n the confuson matrx (see Table 1) corresponds to pxels whch have not been classfed durng the process, and we are consderng these pxels when calculatng the overall accuracy (f we do not consder these pxels, accuracy ncreases to 80%). Classes Neurons n the output layer CORN-NOTILL GRASS SOYBEAN SOYBEAN UNCLASS Table 1. Resultng confuson matrx for the Indan Pnes dataset consderng 100 teratons, 16 neurons n the output layer and σ 0 = 2. Non-zero cells n the matrx are hghlghted.

6 In our second experment, we consder a smaller number of neurons n the output layer (5), 80 teratons and σ = 4 0. Fgure 4 shows the resultng classfcaton and the assocated confuson matrx. We can apprecate an mprovement n the topology of the confuson matrx (horzontal lnes are more contguous). In ths case, the overall accuracy s 60%, wthout consderng the unclassfed pxels. Fgure 3. Resultng classfcaton and greyscale representaton of the confuson matrx for the Indan Pnes dataset consderng 100 teratons, 16 neurons n the output layer and σ 0 = 2. The tme used for ths computaton was approxmately 60 mnutes n an AMD K MHz Processor wth 128 Mb of SDRAM memory and IDL 5.4. Fgure 4. Resultng classfcaton and assocated confuson matrx for the Indan Pnes dataset consderng 80 teratons, 5 neurons n the output layer and σ = 0 4. The tme used for ths computaton was 20 mnutes n an AMD K MHz Processor wth 128 Mb of SDRAM memory and IDL 5.4. Fnally, n our last experment we ncrease the number of neurons n the output layer (16), we decrease the number of teratons (20) and consder σ = The results are addressed n Fgure 5. A general mprovement n the topology s acheved n ths experment, and the overall accuracy n ths case s 72%, due to the fact that we compensate the ncrease n the number of neurons wth a subsequent ncrease n the number of neurons that are consdered n the compettve step ( σ = 0 12 ). Table 2 shows other experments we have performed over the Indan Pnes hyperspectral dataset. As we can apprecate n Fgure 5, the ncrease n the number of neurons produces some dscontnutes n the topology, but the overall performance ncreases due to the reducton n the overlappng percentage between brght zones (hgh values) n the confuson matrx. These facts can be reduced ncreasng σ 0. From the prevously addressed results, we can conclude: 1. The number of teratons needed to obtan an acceptable accuracy s low compared to other SOM applcatons. Ths fact s probably related to the hgh dmensonalty of hyperspectral sgnatures.

7 2. It s more effcent, n terms of accuracy, to ncrease the number of neurons and decrease the number of teratons. As we ncrease the number of neurons, the overall accuracy ncreases, but the topology of the classes s poor. 3. When the SOM neural network has a large number of neurons n the output layer, the ntal reference dstance must be ncreased n order to mantan smlar performance values n the compettve process. In ths sense, σ(t) plays an mportant role. 4. Further work s stll needed n order to acheve a reasonable compromse between topology preservaton, σ(t) functon and overall accuracy. Fgure 5. Resultng classfcaton and greyscale representaton of the confuson matrx for the Indan Pnes dataset consderng 20 teratons, 16 neurons n the output layer and σ = The tme used for ths computaton was 7 mnutes n an AMD K MHhz Processor wth 128 Mb of SDRAM memory and IDL 5.4. Number of neurons Number of teratons Sze of neghborhood ( σ 0 ) Accuracy (%) Table 2. Other experments performed over the Indan Pnes dataset.

8 6. CONCLUSIONS We have presented a new approach to unsupervsed classfcaton of hyperspectral mages usng a Self Organzng Map. The overall performance of the method has been tested by ts applcaton to real hyperspectral data. The avalablty of ground truth allows us to ntroduce a new statstcal measure to quantfy the accuracy of the resultng classfcaton. Snce the tranng stage of the neural network ncorporates several parameters, we have studed the nfluence of some of these parameters on the fnal result. ACKNOWLEDGEMENTS Fundngs from Junta de Extremadura (PRI Program, IDUAP Grant) and European Communty (LFR Program, TEITORS Grant) are also gratefully acknowledged. REFERENCES Agular, P.L, Martínez, P., Pérez R.M., Hormgo, A., Abundance Extractons from AVIRIS Images Usng a Self Organzng Neural Network, Summares of the IX JPL Arborne Earth Scence Workshop, pp , JPL/NASA, 2000a. Agular, P.L., Cuantfcacón de Frmas Hperespectrales Usando Mapas Autoorganzatvos, PhD Thess, Escuela Poltecnca de Cáceres, Unversdad de Extremadura, 2000c. Agular, P.L., Pérez, R.M., Martínez, P., Bachller, P., Merchán, A., Spectra Evaluaton and Recognton n the Mxture Problem Usng SOFM Algorthm, Proc. Internatonal Symposum on Engneerng of Intellgent Systems, (EIS 98), 1998, Vol. 2, pp Agular, P.L., Plaza, A., Martínez, P., Pérez, R.M., Endmember Extracton by a Self-Organzng Neural Network on Hyperspectral Images, Proc. Internatonal Conference on Automaton, Robotcs and Computer Vson, Nanyang Technologcal Insttute, Sngapore, 2000b. Antonlle, S. and Gualter, J.A., Vsualzng Clusters n Hgh-Dmensonal Data wth a Kohonen Self Organzng Map, Techncal Report, Bruske, J. and Merény, E., 1999, Estmatng the Intrnsc Dmensonalty of Hyperspectral Images, Proc. European Symposum on Artfcal Neural Network, ESANN 99, Brussels, Belgum, Aprl, 1999, pp Chuveco, E., Fundamentos de Teledeteccón Espacal, Edcones Ralp, Span, Green, R.O., Edtor, AVIRIS Earth Scence Workshop Proceedngs, Avalable at Jmenez, L.O., Morales-Morell, A., Creus, A., Classfcaton of Hyperdmensonal Data Based on Feature and Decson Fuson Approaches Usng Projecton Pursut, Majorty Votng, and Neural Networks, IEEE Trans. Geoscence and Remote Sensng, Vol. 37, Issue 3, Part 1, May 1999, pp Kohonen, T., Self-Organzng Maps (2 nd ed.), Sprnger Seres n Informaton Scence Martínez, P., Pérez, R.M., Agular, P.L., Bachller, P. and Daz, P., A Neuronal Tool for AVIRIS Hyperspectral Unmxng, Summares of the IX JPL Arborne Earth Scence Workshop, pp , JPL/NASA, Pérez, R.M., Agular, P.L., Bachller, P. and Martínez, P., Neural Network Quantfer for Solvng the Mxture Problem and ts Implementaton by Systolc Array, Mcroelectroncs Journal, 30 (1), pp , Taudjn, S. and Landgrebe, D., Classfcaton of Hgh Dmensonal Data wth Lmted Tranng Samples, Doctoral Thess, School of Electrcal Engneerng and Computer Scence, Purdue Unversty, 1998.