ISSN: 2277 – 9043               International Journal of Advanced Research in Computer Science and Electronics Engineering...
ISSN: 2277 – 9043                    International Journal of Advanced Research in Computer Science and Electronics Engine...
ISSN: 2277 – 9043                International Journal of Advanced Research in Computer Science and Electronics Engineerin...
ISSN: 2277 – 9043               International Journal of Advanced Research in Computer Science and Electronics Engineering...
ISSN: 2277 – 9043               International Journal of Advanced Research in Computer Science and Electronics Engineering...
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  1. 1. ISSN: 2277 – 9043 International Journal of Advanced Research in Computer Science and Electronics Engineering (IJARCSEE) Volume 1, Issue 6, August 2012 CLASSIFICATION OF REMOTELY SENSED IMAGE USING RELEVANCE VECTOR MACHINE 1 A.Kalarani, 2G.viji, 2S.Ramprakash 1 Assistant Professor, P.S.R.Rengasamy college of engg for women, Sivakasi. 2 Assistant Professor, P.S.R.Rengasamy college of engg for women, Sivakasi. 2 Lecturer, M.Kumarasamy College of Engg, Karur.Abstract— This paper introduces a remotely sensed image classification of remotely sensed images. This featureclassification method based on relevance vector machines makes the RVM based classification approach more(RVMs). The features of the remotely sensed image are suitable for applications that require low complexity andextracted and the classification is done[4] with the help of possibly, real time classification.those features. It is shown that approximately the goodclassification accuracy is obtained using RVM-basedclassification, with a significantly smaller relevance vector II. PROPOSED METHODOLOGYrate and, therefore, much faster testing time. This featuremakes the RVM-based classification approach moresuitable for applications that require low complexity and, REMOTELY WAVELET FEATUREpossibly, real-time classification. SENSED TRANSFORM EXTRACTION IMAGEIndex Terms—Classification, remotely sensed image,Bayesian learning, relevance vector machines (RVMs). PERFORMANCE CLASSIFICATION MEASURES (RVM) I. INTRODUCTION In the recent years, relevance vector machines Fig 1.Proposed Method of RVM algorithm(RVMs) have been successfully used in many applicationdomains. In particular, the RVM constitutes a Bayesian The proposed methodology classifies the remoteapproximation for solving generalized linear classification and sensed image based on RVM algorithm. In the first stage theregression models[1]. This method not only provides accurate remote sensed image is transformed using DWT .Thepredictions but also force sparsity (simplicity) of the method, approximated image is then chosen. The features of theand can produce confidence intervals for the predictions. approximated image were extracted .The extracted featuresGood trade-offs between accuracy and sparseness of the were classified intosolution has been observed in many application domains. In i)statistical featuresthe field of remote sensing, the use of RVM has been recently ii)textural featuresintroduced for the prediction of biophysical parameters. The statistical features include i) mean ii) variance andBeing a kernel-based method, the key point for obtaining good iii) standard deviation. The textural features include i) energyRVM classifiers is the definition of a suitable kernel function ii) entropy iii) contrast and iv) homogeneity.The extractedthat can properly represent relations (similarities) among features were taken as training and testing samples. Thesamples (pixels). training and testing samples were classified using RVM algorithm and the performance were measured[12]. The advantages of the RVM are probabilistic predictions, automatic estimations of parameters, and the possibility of choosing arbitrary kernel functions. Most III. RVM CLASSIFICATION importantly, RVM classification results[9] in fewer relevance vectors (RVs), classification can be carried Supervised learning techniques make use of a out much faster with the RVM . For example, the training set that consists of a set of sample input vectors RVM has been used for the detection of micro calcification clusters in digital mammograms, and it has xn n1 together with the corresponding targets t n n1 . The N N been shown that the RVM classifier is much more suitable targets are basically real values in regression tasks or class for real-time processing and reduces the computational labels in classification problems. It is typically desired to learn complexity while maintaining similar detection accuracy. a model of the dependency of the targets on the inputs from It is proposed in this letter to utilize the RVM for the training set, so that accurate predictions of t can be made 88 All Rights Reserved © 2012 IJARCSEE
  2. 2. ISSN: 2277 – 9043 International Journal of Advanced Research in Computer Science and Electronics Engineering (IJARCSEE) Volume 1, Issue 6, August 2012for previously unseen values of x[8]. Commonly, these N   w2  pw /     ipredications can be based on some function y(x) defined over 2 exp   i i    (3)the input space in the form of i 1  2    1 ,  2 ,...., N T M y x; w   wi x   wT x  (1) where shows the hyper parameters i 1 introduced to control the strength of the prior over its associated weight[3]. Hence, the prior is Gaussian, but conditioned on  .For a certain  value, the posterior weightas a linearly weighted sum of M (generally nonlinear and distribution conditioned on the data can be obtained usingfixed) basis functions Bayes‘ rule, i.e.,x   (1 x ,  2 x ,..., M x ) T . pt / w pw /  Although this model is linear in the parameters (or pw / t ,    (4)weights), w  w w ..., wM  it can still be highly flexible T pt /   1, 2,as the size of the basis set M can be effectively large. Learning where p(t/w) is the likelihood, p(w/α) is the prior, and p(t)isis basically the process of inferring the function or, referred to as evidence. The weights cannot be analyticallyequivalently, the parameters of the function y(x). In this obtained, and therefore, a Laplacian approximation procedurecontext, it is desired to estimate reasonable values for the is used.1) Since p(w/t,α) is linearly proportional to p(t/w) ×parameters (or weights), w  w w1, 2, ..., wM  . Given a set T p(w|α), it is possible to aim to find the maximum ofof N corresponding training pairs x n , t n n 1 , the objective is logpt / w pw /    Nto find values for the weights w  w w ..., wM  , such T N  t log y n  1  t n  log 1  y n   1, 2, 1 T (5) n w Awthat y(x) generalizes well enough to new data, yet only a few n 1 2elements of w are nonzero[5]. Having only a few nonzeroweights facilitates a sparse representation with the advantageof providing fast implementation. for the most probable weights WMP, with yn = σ{y(xn;w)} and A = diag(α0, α1, . . . , αN) being composed of the current The RVM introduces a prior over the model weights values of α. This is a penalized logistic log-likelihood functiongoverned by a set of hyper parameters , in a probabilistic and requires iterative maximization. The iteratively reweighedframework. One hyper parameter is associated with each least-squares algorithm] can be used to find WMP[6]. Theweight, and the most probable values are iteratively estimated logistic log-likelihood function can be differentiated twice tofrom the training data[1]. The most compelling feature of the obtain the Hessian in the form ofRVM is that it typically utilizes significantly fewer kernelfunctions , while providing a good performance. For two-class classification, any target can be classified into two ww log pw / t ,   | wMP    T B  A   (6)classes such that t n   ,1 . A Bernoulli distribution can 0  where B = diag(β1, β2, . . . , βN) is a diagonal matrix with βnbe adopted for p(t|x) in the probabilistic framework because = σ{y(xn;w)}[1 − σ{y(xn;wMP)}], and Φ is the ‗design‘ matrixonly two values (0 and 1) are possible. The logistic sigmoid with Φnm = K(xn, xm−1) and Φn1 = 1. This result is thenlink function σ(y) = 1/(1 + e−y) is applied to y(x) to link negated and inverted to give the covariance Σ, as shown asrandom and systematic components, and generalize the linear follows[12], for a Gaussian approximation to the posteriormodel. over weights centered at WMP.Following the definition of the Bernoulli distribution , thelikelihood is written as Σ = (ΦT BΦ + A)−1. (7) Npt / w    y ( x n ; w) n 1   y ( x n ; w) t 1t n In this way, the classification problem is locally linearized (2) around WMP. in an effective way with n 1 WMP =ΣΦTBˆt (8)for the targets tn Є {0, 1}.The likelihood is complemented bya prior over the parameters(weights) in the form of t=ΦwMP + B−1(t − y). (9) These equations are basically equivalent to the solution of a generalized least-squares problem. After obtaining WMP, the 89 All Rights Reserved © 2012 IJARCSEE
  3. 3. ISSN: 2277 – 9043 International Journal of Advanced Research in Computer Science and Electronics Engineering (IJARCSEE) Volume 1, Issue 6, August 2012 i are updated using  , K xi , x j   xi .x j  dhyper parameters i  i / wi where wi is the ith posterior mean weight, new 2and i is defined as i  1   i  i i , where Σii is the ith RBF kerneldiagonal element of the covariance, and can be regarded as ameasure of how well determined each parameter wi is by the  K ( xi , x j )  exp   || xi  x j || 2 data[15]. During the optimization process, many i will havelarge values, and thus, the corresponding model weights are The accuracy and the relevance vector for the extractedpruned out, realizing sparsity. The optimization process features (homogeneity and contrast) are tabulated astypically continues until the maximum change in  i valuesis below a certain threshold or the maximum number of Table 1. Extracted features:iterations is reached. MODEL FEATURES AC RV III. EXPERIMENTAL RESULTS RVM homogeneity 96 5 In this section, the proposed RVM classifier istested on an urban image of the area of pavia, italy. RVM contrast 97 11 The RV plots for the two class problem{0,1} for the features homogeneity and contrast are shown in Figures1and 2 respectively. RVM Classification Fig (a) Fig (b) 1.2 Class 1 Class 2Fig.(a) RGB composition of Pavia image, and b) groundtruth. 1.1 Decision boundary p=0.25/0.75This image was acquired by the DAIS 7915 airbone imaging 1 RVsspectrometer of DLR . This is a challenging urban 0.9classification problem dominated by directional features and 0.8relatively high spatial resolution.Different values of the width 0.7for the kernel were tried exponentially . 0.6 The most popular kernels used in RVM are the 0.5linear, polynomial, and radial basis function (RBF) kernels. 0.4The RBF kernel typically shows a performance and istherefore employed in the provided results. Note that  0.3 0.2serves as an inner product coefficient for the polynomial 0.2 0.4 0.6 0.8 1 1.2kernel, whereas it determines the RBF width in the case of theRBF kernel. Fig. 2. Classification maps obtained for a two-class problem for the feature homogeneity. Red and blue dots indicate theLinear kernel classes {0,1}, red dots point out the relevant vectors (RVs), the K xi , x j   xi .x j red line represents the classification boundary, and the grey lines are the confidence intervals at p = 0.25 and p = 0.75.Polynomial kernel 90 All Rights Reserved © 2012 IJARCSEE
  4. 4. ISSN: 2277 – 9043 International Journal of Advanced Research in Computer Science and Electronics Engineering (IJARCSEE) Volume 1, Issue 6, August 2012 RVM Classification Class 1 Class 2 Decision boundary [6] D. J. C. MacKay, ―The evidence framework applied to 2 p=0.25/0.75 Classification networks,‖ Neural Comput., vol. 4, no. 5, pp. RVs 720– 736, 1992. 1.5 [7] I.T.Nabney, ―Efficient training of RBF networks for classification,‖ inProc. 9th ICANN, 1999, vol. 1, pp. 210–215. 1 [8] R.Johansson and P.Nugues, ―Sparse Bayesian classification of Predicate arguments,‖ in Proc. 9th Conf. 0.5 Comput. Natural Language Learn.,43rd Annu. Meeting Assoc. Comput. Linguistics, Ann Arbor, MI, 2005,pp. 177–200. 0.5 1 1.5 2 2.5 3 [9] G.Camps-Valls, L.Gomez-Chova, J. Vila-Franc´es, J. Amor´os-L´opez,J. Mu˜noz-Mar´ı, and J. Calpe-Maravilla,Fig. 3. Classification maps obtained for a two-class problem ―Retrieval of oceanic chlorophyll concentration withfor the feature contrast. Red and blue dots indicate the classes relevance vector machines,‖ Remote Sensingof Environment,{0,1}, red dots point out the relevant vectors (RVs), the red vol. 105, no. 1, pp. 23–33, Nov 2006.line represents the classification boundary, and the grey linesare the confidence intervals at p = 0.25 and p = 0.75. [10] B. E. Boser, I.M. Guyon, and V. Vapnik, ―A training algorithm for optimal margin classifiers,‖ in Proc. 5th Annu. IV. CONCLUSION ACM Workshop Comput. Learn.Theory, 1992, pp. 144–152. RVM-based image classification provide good [11] C. Burges, ―A tutorial on support vector machines forclassification accuracy, with a significantly smaller RV rate pattern recognition,‖in Proc. Data Miningand Knowl.and therefore , much faster testing time.The most evident and Discovery,compelling results are its accuracy and sparseness .RVM- U.Fayyad, Ed., 1998, pp. 1–43.based classification approach is more suitable for applicationsthat require low complexity and, possibly, real-time [12] F. Melgani and L. Bruzzone, ―Classification of hyperclassification. spectral remote sensing images with support vector machines,‖ IEEE Transactions on Geoscience and Remote REFERENCES Sensing, vol. 42, no. 8, pp. 1778-1790,Aug 2004.[1] Pijush Samui1, Venkata Ravibabu Mandla, Arun [14] G.Camps-Valls and L. Bruzzone, ―Kernel-basedKrishna and Tarun Teja ―Prediction of Rainfall Using Support methods for hyper spectral image classification,‖ IEEEVector Machine and Relevance Vector Machine‖, Open Transactions on Geoscience and Remote Sensing, vol. 43, no.access e-Journal Earth Science India, eISSN: 0974 – 8350 Vol. 6, June 2005.4(IV), October, 2011, pp. 188 – 200 [15] G. Camps-Valls, L. G´omez-Chova, J. Mu˜noz-Mar´ı, J.[2] A., Chua, L. H. C., and Quek, C. (2010) ―A novel Vila-Franc´es,and J. Calpe-Maravilla, ―Composite kernels forapplication of a neuro-fuzzy computational technique in hyper spectral image classification,‖ IEEE Geoscience andevent-based rainfall–runoff modeling. Expert Systems with Remote Sensing Letters, vol. 3,no. 1, pp. 93–97, Jan 2006.Applications,‖ v. 37(12), pp. 7456–7468. [16] Matthias Seeger, ―Gaussian processes for machine[3] M. E. Tipping, ―The relevance vector machine,‖ in learning,‖ International Journal of Neural Systems, vol. 14,Advances in Neural Information ProcessingSystems , vol. 12, no. 2, pp. 69–106, 2004.S. A. Solla, T. K. Leen, and K.-R. Müller, Eds. Cambridge,MA: MIT Press, 2000. [17] C. E. Rasmussen and C. K. I. Williams, Gaussian Processes for Machine Learning, The MIT Press, 2006.[4] M. E. Tipping, ―Sparse Bayesian learning and therelevance [18] N. Nikolaev and P. Tino, ―Sequential relevance vectorvector machine,‖ J. Mach. Learn. Res., vol. 1, pp. 211–244, machine earning from time series,‖ in Proceedings of2001. International Joint Conference on Neural Networks, Montreal, Canada, Aug 2005, pp. 468–473.[5] W. Liyang, Y. Yongyi, R. M. Nishikawa, M. N.Wernick,and A.Edwards,―Relevance vector machine for automaticdetection of clustered microcalcifications,‖IEEE Trans. Med.Imag., vol.24, no. 10, pp. 1278–1285,Oct. 2005. 91 All Rights Reserved © 2012 IJARCSEE
  5. 5. ISSN: 2277 – 9043 International Journal of Advanced Research in Computer Science and Electronics Engineering (IJARCSEE) Volume 1, Issue 6, August 2012[19] J. Qui˜nonero-Candela, Learning with Uncertainty – Ramprakash SubburamGaussian Processes and Relevance Vector Machines, Ph.D. received the B.Engg. degree inthesis, Technical University of Denmark, Informatics and Electronics and InstrumentationMathematical Modelling, Kongens Lyngby (Denmark), Engineering from AnnaNovember 2004. University, Chennai, in 2009 and doing Master of Engg. degree in[20] G. Camps-Valls, M. Mart´ınez-Ram´on, J. L. Rojo- Anna University, coimbatore. He´Alvarez, and J. Mu˜noz-Mar´ı, ―Nonlinear system has been worked as anidentification with composite relevance vector machines,‖ Instrumentation Site Engineer in Micotec EngineersIEEE Sign Processing Letters, vol. 14, no. 4, pp. 279–282, and contractors ( A sub contractor to Yokogawa indiaApril 2007. ltd) to Empee Cogen power plant, Edaikal, Tirunelveli District from may 2009. From June 2010[18] G. Camps-Valls, L. Gomez-Chova, J. Vila-Franc´es, J. to till now, he is working in M.Kumarasamy CollegeAmor´os-L´opez,J. Mu˜noz-Mar´ı, and J. Calpe-Maravilla, of Engg, Karur. His research area includes wireless―Relevance vector machines for sparse learning of biophysical communication, Bio-medical instrumentation,parameters,‖ in SPIE International Symposium Remote process control, Digital Image processing.Sensing, XI, Bruges, Belgium, Set 2005, vol. 5982.[19] G.Camps-Valls, L. Gomez-Chova, J. Vila-Franc´es,J.Amor´os- L´opez,J. Mu˜noz-Mar´ı, and J. Calpe-Maravilla,―Retrieval of oceanic chlorophyll lconcentration withrelevance vector machines,‖ Remote Sensing of Environment,vol. 105, no. 1, pp. 23–33, Nov 2006. Kalarani Athilingam completed her B.Engg. degree in Electronics and Communication Engineering from Anna University, Chennai, in 2008 and the Master of Engg. degree from Anna University, Tirunelveli, in 2010. From June 2010 to till now, She is working in P.S.R.Rengasamy College of Engg for women, Sivakasi. Her research area includes Digital Electronics, Digital Imageprocessing, Antenna. Communication theory.She has beenattended several workshops and conferences in various enggcolleges. Viji Gurusamy received the B.Engg. degree in Electronics and Communication Engineering from Anna University, Chennai, in 2008 and the Master of Engg. degree from Anna University, Thirunelveli, in 2010. From June 2010 to May 2012, She was worked in M.Kumarasamy College ofEngg, Karur. Now she is currently working inP.S.R.Rengasamy College of Engg for women, Sivakasi. Shehad attended four international conferences and one nationalconference in various colleges. Her research area includesDigital Signal processing, Digital Image processing, DigitalCommunication. 92 All Rights Reserved © 2012 IJARCSEE

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