Interrelated Two-way Clustering: An Unsupervised Approach for Gene Expression Data Analysis

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1 BIBE2001: 2nd IEEE International Symposim on Bioinformatics and Bioengineering Interrelated Two-way Clstering: An Unspervised Approach for Gene Expression Data Analysis Chn Tang, Li Zhang and Aidong Zhang Department of Compter Science and Engineering State University of New York at Bffalo Bffalo, NY chntang, lizhang, Mrali Ramanathan Department of Pharmacetical Sciences State University of New York at Bffalo Bffalo, NY Abstract DNA arrays can be sed to measre the expression levels of thosands of genes simltaneosly. Crrently most research focses on the interpretation of the meaning of the data. However, majority methods are spervised-based, less attention has been paid on nspervised approaches which is important when domain knowledge is incomplete or hard to obtain. In this paper, we present a new framework for nspervised analysis of gene expression data which applies an interrelated two-way clstering approach on the gene expression matrices. The goal of clstering is to find important gene patterns and perform clster discovery on samples. The advantage of this approach is that we can dynamically se the relationships between the grops of the genes and samples while iteratively clstering throgh both gene-dimension and sample-dimension. We illstrate the method on gene expression data from a stdy of mltiple sclerosis patients. The experiments demonstrate the effectiveness of this approach. 1 Introdction DNA microarray technology permits rapid, large-scale screening for patterns of gene expression and gives a simltaneos, semi-qantitative readots on the level of expression of thosands of genes [18, 15, 24, 27, 36, 20, 21, 8, 30]. This new technology also gives rise to a challenge: to interpret the meaning of this immense amont of biological information sally formatted in nmerical matrices. To meet the challenge, varios methods have been developed sing both traditional and innovative techniqes to extract, analyze and visalize gene expression data generated from DNA microarrays. A key step in the analysis of gene expression data is to detect grops that manifest similar expression patterns. Besides, clstering gene expression will redce complexity, facilitate interpretation, avoid redndancy and crb the noise. Information in gene expression matrices is special in that it can be stdied in two dimensions [2]: analyzing expression profiles of genes by comparing rows in the expression matrix [25, 23, 22, 3, 33, 10, 6, 26] and analyzing expression profiles of samples by comparing colmns in the matrix [11, 32, 9]. While most researchers focs on either gene dimension or sample dimension, in a few occasions, sample clstering has been combined with gene clstering. Alon et al. [34] have applied a partitioning-based clstering algorithm to stdy 6500 genes of 40 tmor and 22 normal colon tisses for clstering both genes and samples. Getz et al. [12] present a method applied on colon cancer and lekemia data set. By identifying sbsets of the genes and samples sch that when one of these is sed to clster the other, stable and significant partitions emerge. They call it copled two-way clstering. Althogh many different methods for data clstering have been proposed, two major paradigms can be identified: spervised clstering and nspervised clstering. The spervised approach assmes that for some (or all) profiles there is additional information attached, sch as fnctional classes for the genes, or diseased/normal attribtes for the samples. Having this information, a typical task is to bild a classifier to predict the labels from the expression profile. Brown et al. [23] have applied varios spervised learning algorithms on six fnctional classes of yeast genes sing gene expression matrices from 79 samples. Golb et al. [32] sed neighborhood analysis to constrct class predictors for samples. They bilt a weighted vote classifier based on 38 training samples and applied it on a collection of 34 new samples. Hastie et al. [33] proposed a tree harvesting method for spervised learning from gene expression data to discover genes that have strong effects on their own as well as genes that interact with others. r grop has developed a maximm entropy approach to classify gene array data sets [29]. We sed part of pre-known classes of sam-

2 ples as training set and applied the maximm entropy model to generate an optimal pattern model which can be sed on new samples. Unspervised approaches assme little or no prior knowledge. The goal of sch approaches is to partition the set of samples or genes into statistically meaningfl classes [1]. A typical example of nspervised data analysis is to find grops of co-reglated genes or related samples. Crrently most of the research focses on the spervised analysis, relatively less attention has been paid to nspervised approaches in gene expression data analysis which is important when domain knowledge is incomplete or hard to obtain [31, 37]. The hierarchical [22, 16, 5] and K-means clstering algorithms [14, 28] as well as self-organizing maps [26] are major nspervised clstering methods which have applied to varios gene array datasets. In this paper, we present an interrelated two-way clstering approach for nspervised analysis of gene expression data. Unlike previos work mentioned above, in which genes and samples were clstered either independently or both dimensions being redced, or approach is to dynamically se the relationships between the grops of the genes and samples while iteratively clstering throgh both gene-dimension and sample-dimension to extract important genes and classify samples simltaneosly. We have applied the method to a data set on mltiple sclerosis patients collected by the Nerology and Pharmacetical Sciences departments in or niversity (Mltiple sclerosis (MS) is a chronic, relapsing, inflammatory disease and interferon- (IFN- ) has been the most important treatment for the MS disease for the last decade [35]). In particlar, we perform class discovery on the healthy control, MS and IFN-treated samples based on the data collected from the DNA microarray experiments. The gene expression levels are measred by the intensity levels of the corresponding array spots. The experiments demonstrate the effectiveness of this approach. This paper is organized as follows. Section 2 introdces or approach. Section 3 presents the experimental reslts on mltiple sclerosis data set. And finally, the conclsion is provided in Section 4. 2 Interrelated Two-way Clstering 2.1 Motivation Gene expression data are matrices where rows represent genes, colmns represent samples sch as tisses or experimental conditions, and nmbers in each cell characterizes the expression level of a particlar gene in a particlar sample. Let be the set of all genes, "!# be the set of all samples, and $ &% be the intensity vale associated with each gene and sample ' in the matrix. Ths the gene expression matrix () * $ &% +-,/ ,5.768.:9; has 3 rows (gene vectors) and 9 colmns (sample vectors). Based on the gene expression matrix ( which sally has thosands of rows and less than a hndred of colmns (3=<>9 ), a common problem is: can we effectively clster the samples with similar properties sing the genes atomatically? Note that for the nspervised analysis, the previos knowledge and the training data are not available. Also, becase the dimension of sample vectors is mch higher than the nmber of samples, it is very hard to get good reslt by directly sing traditional clstering algorithms [14, 13] for classifying samples on sch a high dimensional space. To achieve better class discovery on samples, we shold first try to lower the vector space into a relatively small one, which means redce the nmber of genes (eqals to the dimension of sample vectors) to a smaller dimension and then perform clstering. If the dimension of sample vectors is still too large, we contine to redce ntil it reaches a reasonable level on which clstering algorithms can work effectively and efficiently. However, the dimension redction is non-trivial. In recognizing the above problems, we propose a general framework for the nspervised gene expression data analysis. In this framework, an interrelated two-way clstering approach as well as a pre-processing procedre is applied on the gene expression matrix (, and the goal of clstering is to find important gene patterns and to perform class discovery on samples simltaneosly. To be more specific, we have two goals: (1) Find a sbset of genes, sally called important genes, which are highly related to the experiment conditions. This can also be considered as the gene dimension redction. (2) Clster the samples into different grops. According to the most poplar experimental platforms, the nmber of different grops is sally two, for example, diseased samples and control samples. These two goals are actally two sides of one coin. If we can find important genes, then it is relatively easy to se traditional clstering algorithms to clster samples becase the sample vectors dimension is redced to a reasonable level (sally arond 100). n the other hand, if we can correctly clster the samples, important genes can be fond by sorting all genes sing similarity scores sch as correlation coefficient [32, 4] with patterns according to the clster reslts. ne of the advantages of or approach is that we can dynamically se the relationships between the grops of the genes and samples while iteratively clstering throgh both gene-dimension and sample-dimension. In doing iterative

3 \ i e R e \ clstering, redcing gene-dimension will improve the accracy of class discovery, which in trn will gide frther gene-dimension redction. 2.2 Pre-processing of Data In the gene expression matrix, different genes have different ranges of intensity vales. The intensity vales alone may not have significant meaning, bt the relative vales are more intrinsic. So we first normalize the original gene intensity vales into relative vales [19, 38]. r general formla is $2A B% $C&% EDGF F H$JILK"MK F N! P $ B% 9 Q $ &% A denotes normalized intensity vale for gene 0 of sample 6, $ B% represents the original intensity vale for gene 0 of sample 6, 9 (1) is the nmber of samples, and F is the mean of the intensity vales for gene 0 over all samples. Notice that among thosands of genes, not all of them have the same contribtion in distingishing the classes. Actally, some genes have little contribtion. We need to remove those genes which have little reaction to the experiment condition. We believe genes whose intensity vales keep invariant or change very little belong to this class (Figre 1 shows an example of gene distribtions). samples. We denote each gene vector (after normalization) as SR&$ A &% $ A B% T $ A &%!VU (2) where 0W X,YZ[ 3 for each gene. We se vector-cosine between each gene vector and a pre-defined stable pattern to test whether a gene intensity vale \ varies mch among samples. The pattern can be denoted as SR]KPKT^ K! U, where all K are eqal. _`a RBb U dcfe \hg N! e ikji \ i n P $ &%ml A K N! P $2o B% T n N! l P K T (3) where b is the angle between two vectors and e e in 9 - dimensional space. If the two vector patterns are more similar, the vector-cosine will be closer to,. The extreme case is that when two vectors are parallel, the vector-cosine vale is,. n the other hand, vector-cosine vale of two perpendiclar vectors is p. After calclating vector-cosine vales, we can \ choose a threshold to remove genes matching \ pattern (those genes vector-cosine vales with are higher than the threshold, which means these genes change little dring the experiment). Usally we can remove twenty to thirty percent of genes by this step, ths facilitating clstering in the next stage. 2.3 Interrelated Two-way Clstering Figre 1. Genes intensity vale distribtions after normalization. Horizontal axis represents samples. Each polygonal line indicates a gene changing level varies among samples. The red-solid lines represent gene intensity vales which vary little throgh all samples, and the ble-dash lines represent gene intensity vales which vary mch among samples. Let s assme we have 3 genes and 9 To perform two-way clstering, a distance measre to be sed dring the clstering procedre shold be careflly chosen. ne commonly sed distance is the Eclidean distance. Bt for gene data, patterns similarity seems more important than their spatial distance [32, 4]. So we choose correlation coefficient [17] which measres the strength of the linear relationship between two vectors. This measre has the advantage of calclating similarity depending only on the pattern bt not on the absolte magnitde of the spatial vector. The formla of correlation coefficient between two vectors qr srbt Pt T t U and vs srbw w T wy U is: xy{z tl l wy U D R t U Tƒ t T D R tl U l R w T D R w U w U Tƒ where is the length of vector q and v. Then we clster genes as well as samples. Dynamic relationship between gene clstering and sample clstering is sed to redce the vector space of samples into a reasonable level and perform class discovery. r approach, illstrated in Figre 3, is an iterative procedre based on with 3 (4)

4 genes after pre-processing. Within each iteration there are five main steps: Step 1: clstering in the gene dimension. The task of this step is to clster 3 genes into grops, denoted as (,V.?0. ), each of which is an exclsive sbset of. The clstering method can be any method for which we can give the clster nmber, sch as K-means or SM [13, 14]. Step 2: clstering in the sample dimension. Based on each grop m (,. 0. ), we independently clster samples into two clsters (according to the most poplar experimental conditions [2]), represented by ˆB% and {B% Š. Step 3: clstering reslts combination. This step combines the clstering reslts of the step 1 and step 2. Withot loss of the generality, let Z. Then the samples can be divided into for grops: ŒŽ (all samples clstered into % based on and clstered into {T% based on mt ); ŒŽ T (all samples clstered into % based on and clstered into {T% Š based on mt ); ŒŽ k (all samples clstered into '% Š based on and clstered into {T% based on mt ); ŒŽ (all samples clstered into '% Š based on and clstered into T% Š based on T ). Figre 2 illstrates the reslts of this combination. If, there will be possible sample grops. In general, the nmber of possible sample grops eqals Z. Usally is set to be Z to redce the comptational complexity. Step 4: finding heterogeneos grops. Among the sample grops ^ T^ k, we choose two distinct grops k and (,/. YP š.œ ) which satisfy the following condition: for Ÿž C Ÿ = where ž and are samples, if ž?? &% P P G? &% then M sm T ( M PM T ª "«" ) for all 0 (,G. 0. ). We call (, ) heterogeneos grop. For example, (, ) is sch a heterogeneos grop (when Z ) becase all samples in grop are clstered into B% (,8.s0m. ), while all samples in grop are clstered into &% Š (,5.:02. ). For the same reason, ( T, ) is another heterogeneos grop. Step 5: sorting and redcing. For each heterogeneos grop, for example, (, ), two patterns R&p[p[ p,y,, U and R,,,YPp Pp[ p U are introdced. The pattern R&p Pp p[,,y, U incldes + + (nmber of samples in grop ) zeros followed by + + (nmber of samples in grop ) one s. Similarly, R,Y,Y,p[Pp p U incldes + ^+ one s followed by + + zeros. For each pattern, we se it to calclate vector-cosine defined in Eqation (3) with each gene vector, then sort all genes according to the similarity vales in descending order, and keep the first one third of the sorted gene seqence by ctting off the other two thirds of the gene seqence. By merging the Figre 2. Clstering reslts combination when ²±. ³ ³µ ³" in the first line represent samples. The second and third lines show clster reslts on samples based on gene grops or 8T independently. In each case, samples are clstered into two grops, which are marked as a or b. We se green color (second line) to represent clster reslts based on and ble color (third line) for reslts based on 8T. By combination, for possible sample grops are generated: ¹ incldes samples marked as a based on and marked as a based on T ; ¹ T incldes samples marked as a based on and marked as b based on T ; ¹ incldes samples marked as b based on and marked as a based on T ; ¹ incldes samples marked as b based on and marked as b based on 8T. remaining sorted gene seqences from two patterns, we obtain the redced gene seqence A where at least one third of the genes in are ct off. Similarly, for the other heterogeneos grop ( T, ), another redced gene seqence A A is generated. Now the problem is which gene sbset shold be chosen for the next The semantic meaning behind it is iteration, A or A A? to select a heterogeneos grop which is a better representation for the original distribtion of samples becase A and A A are generated based on the corresponding heterogeneos grops. Here we se the cross-validation method [32] to evalate each grop. In each heterogeneos grop, first choose one sample, then se the remaining samples of this grop to select important genes, and predict the class of the withheld samples. The process is repeated for each sample, and the cmlative error rate is calclated. When the heterogeneos grop which has lower error rate is fond, its corresponding redced gene seqence is selected as º with 3 T genes for the next iteration.

5 9 Ð 9 After Step 5, the gene nmber is redced from 3 to 3 T. The above steps can be repeated by clstering 3 T genes, and so on. The iteration will be terminated ntil the termination conditions are satisfied. 2.4 Termination Condition To explain the termination condition, we first define the occpancy ratio between samples in heterogeneos grops and all samples, let» denote all heterogeneos grops: ¼V½½ M«Y 0 ¾# 1 «tàrà + +Á*+ + U (5) where R U»ŽR,#. 0 Â6Ã. Z U, 9 is the total nmber of the samples, + + is the nmber of samples in. Ths if ²Z, the occpancy ratio will be: ¼V½½ + +YÁs+ + M«0ľ# ² «YtÀR + T +ÁS+ + 9 U (6) Becase the sm of the nmber of samples in all heterogeneos grops is eqal to 9, the minimm vale of ¼V½½ M«0ľ is p[æå. If the gene clstering reslts based on and T are the same, then either 2Ç È ( is the set of all samples) or TkÇ *, in this case º (the remaining genes) is good enogh for sample ¼V½½ clstering. Note that nder sch optimal condition, the M«0ľ vale will reach the maximm vale,. pre-porcessing clstering in the gene dimension sing each gene grop clstering in the sample dimension sing two clster reslts clstering reslts combination finding heterogenos grops define patterns sorting and redcing cross-validation termination condition Figre 3. The strctre of Interrelated Twoway Clstering. ¼V½½ M«Y 0 ¾ vale can be sed as ¼V½½ one of the termination conditions for the iteration. If the M«0 ¾ vale reaches,, we can stop the iteration. However, since the optimal condition is hard ¼V½½ to reach, sally the iteration can be stopped when the M«0 ¾ vale reaches a threshold sch as p Ñ, meaning samples clster reslt at step 2 based on and mt ¼V½½are qite similar. Sometimes after many iterations, the M«0 ¾ vale still cannot reach the threshold, bt the remaining gene nmber (3ˆT ) is very small (for example, 100). This also can be sed as termination condition. The whole procedre of interrelated two-way clstering is presented in Figre 3. 3 Experimental Reslts The experiments are based on two data sets on mltiple sclerosis patients: the MS IFN grop and the CN- TRL MS grop. The MS IFN grop contains 28 samples while the CNTRL MS grop contains 30 samples. Each sample consists 4132 genes. We perform the interrelated two-way clstering approach for nspervised classification separately on each grop. To test the performance of or approach, we choose these two datasets in which the grond-trth is already known, that is, in the MS IFN grop, there are 14 MS samples and 14 IFN samples, and in CNTRL MS grop, there are 15 control samples and 15 MS samples. We only se this grond-trth to evalate or experimental reslts. vector cosine gene Figre 4. Distribtion of genes vector-cosine calclated from Eqation (3). Horizontal axis represents samples, vertical axis means vector-cosine vale. Samples are sorted in an ascending order, where we choose threshold 0.89 to redce 4132 genes to Dring the data pre-processing procedre, by sorting genes sing vector-cosine calclated from Eqation (3), we choose threshold p[ Ñ (See Figre 4), then remove genes for which vector-cosine with pattern \ is higher than that 2682

6 1 Relationship between Gene nmber and ccratio vale MS IFN grop CNTRL MS grop ccratio Gene nmber Figre 5. Relationship between Gene nmber and Ò ÓÓÔÕ Ö Ø]Ù vale. threshold, which means the gene intensity vales vary little among the samples genes are removed from As the reslt, 2682 genes are left. K-means clstering method is sed dring the interrelated two-way process, and correlation coefficient (Eqation (4)) is sed as the distance measre. Dring the iterative process, after each iteration the remaining genes are traced together with the occpancy ratio for the heterogeneos grops of the two dataset (See Figre 5). ne observation is that ¼V½½ in or experiment, while gene-dimension is redced, the M«0 ¾ vale increases, the samples clster reslts based on and mt become more similar. ¼V½½ n the MS IFN grop, after nine iterations, the M«0ľ vale reaches p ÑZ. We redce 2682 genes to 100 genes and clster samples into two grop: 11 samples in grop one, which are all correctly classified to samples having MS disease. Another 17 samples are in grop two, in which 14 of them is IFN treated, bt another 3 were in the wrong grop. In Figre 6, we se a liner mapping fnction [7] which maps the 3 -dimension vectors into two dimensions to show the samples distribtion before and after or approach for the MS IFN grop. Similarly, for the CNTRL MS grop, we redce 1474 genes with the same threshold as the MS IFN grop in the pre-processing step, and se the remaining 2658 genes to perform the interrelated two-way clster. The reslt is 8 samples being incorrectly classified ot of 30 samples. For the prpose of comparison, we also directly perform K-means clstering method and self-organizing maps on both the MS IFN and CNTRL MS grop data after normalization bt withot any gene-dimension dedction. Figre 7 lists the sample clstering accracy rate achieved Figre 6. Approach applying on the MS IFN grop. (A) Shows the original 28 samples distribtion, Each point represents a sample, which is a mapping from the sample s 4132 genes intensity vectors. There is no obvios clster border as we see. (B) Shows the same 28 samples distribtion after sing or approach. We redce 4132 genes to 100 genes. So each sample is a 100-dimension vector. The green and red colors show the clster reslt sing or approach, while two dash circles indicate the real sample clster and three arrows point ot the incorrectly classified samples. by these methods. From this figre, we can see that sing or approach, the accracy of class discovery is higher than those of traditional methods, which illstrates the effectiveness of the interrelated two-way clstering method on sch high dimensional gene data. 4 Conclsion In this paper, we have presented a new framework for the nspervised analysis of gene expression data. In this framework, an interrelated two-way clstering method is developed and applied on the gene expression matrices transformed from the raw microarray data. We were able to find important gene patterns and to perform class discovery on samples simltaneosly. It has the advantage of dynamically sing the relationships between the grops of the genes and samples while iteratively clstering throgh both gene-dimension and sample-dimension. In doing iterative clstering, redcing gene-dimension will benefit the accracy improvement of class discovery, which in trn will gide frther gene-dimension redction. In particlar, we sed the above approach to distingish the healthy control, MS and IFN-treated samples based on the data collected from DNA microarray experiments. From

7 Figre 7. Comparison of accracy rate achieved by interrelated two-way clstering (ITC), self-organizing maps (SM) and K- means clstering methods. (A) Shows clstering reslts on the MS IFN grop which inclde 28 samples. (B) Shows clstering reslts on the CNTRL MS grop which inclde 30 samples. or experiments, we demonstrated that this approach is a promising approach to be sed for nspervised analysis of gene array data sets. References [1] A. Ben-Dor, N. Friedman, and Z. Yakhini. Class discovery in gene expression data. In Proc. Fifth Annal Inter. Conf. on Comptational Moleclar Biology (RECMB 2001), [2] Alvis Brazma and Jaak Vilo. Minireview: Gene expression data analysis. Federation of Eropean Biochemical societies, 480:17 24, Jne [3] Amir Ben-Dor, Ron Shamir and Zohar Yakhini. Clstering gene expression patterns. Jornal of Comptational Biology, 6(3/4): , [4] Anna Jorgensen. Clstering excipient near infrared spectra sing different chemometric methods. Technical report, Dept. of Pharmacy, University of Helsinki, [5] Ash A. Alizadeh, Michael B. Eisen, R. Eric Davis, Chi Ma, Izidore S. Lossos, Adreas RosenWald, Jennifer C. Boldrick, Hajeer Sabet, Trc Tran, Xin Y, John I. Powell, Liming Yang, Gerald E. Marti et al. Distinct types of diffse large b- cell lymphoma identified by gene expression profiling. Natre, Vol.403: , Febrary [6] Charles M. Pero, Stefanie S. Jeffrey, Matt Van De Rijn, Christia A. Rees, Michael B. Eisen, Doglas T. Ross, Alexander Pergamenschikov, Cheryl F. Williams, Shirley X. Zh, Jeffrey C. F. Lee, Deval Lashkari, Dari Shalon, Pat rick. Brown, and David Bostein. Distinctive gene expression patterns in hman mammary epithelial cells and breast cancers. Proc. Natl. Acad. Sci. USA, Vol. 96(16): , Agst [7] D. Bhadra and A. Garg. An interactive visal framework for detecting clsters of a mltidimensional dataset. Technical Report , Dept. of Compter Science and Engineering, University at Bffalo, NY., [8] D. Shalon, S.J. Smith, P.. Brown. A DNA microarray system for analyzing complex DNA samples sing two-color florescent probe hybridization. Genome Research, 6: , [9] Donna K. Slonim, Pablo Tamayo, Jill P. Mesirov, Todd R. Golb, and Eric S. Lander. Class Prediction and Discovery Using Gene Expression Data. In RECMB 2000: Proceedings of the Fifth Annal International Conference on Comptational Biology. ACM Press, [10] Elisabetta Mandchi, Gregory R. Grant, Steven E. McKenzie, G. Christian verton, Sal Srrey and Christian J. Stoeckert Jr. Generation of patterns form gene expression data by assigning confidence to differentially expressed genes. Bioinformatics, Vol. 16(8): , [11] Francisco Azaje Department. Making genome expression data meaningfl: Prediction and discovery of classes of cancer throgh a connectionist learning approach, [12] Gad Getz, Erel Levine and Eytan Domany. Copled twoway clstering analysis of gene microarray data. Proc. Natl. Acad. Sci. USA, Vol. 97(22): , ctober [13] J. Hartigan and M. Wong. Algorithm AS136: a k-means clstering algorithms. Applied Statistics, 28: , [14] Hartigan J.A. Clstering Algorithm. John Wiley and Sons, New York., [15] J. DeRisi, L. Penland, P.. Brown, M.L. Bittner, P.S. Meltzer, M. Ray, Y. Chen, Y.A. S, J.M. Trent. Use of a cdna microarray to analyse gene expression patterns in hman cancer. Natre Genetics, 14: , [16] Javier Herrero, Alfonso Valencia, and Joaqin Dopazo. A hierarchical nspervised growing neral network for clstering gene expression patterns. Bioinformatics, 17: , [17] Jay L. Devore. Probability and Statistics for Engineering and Sciences. Brook/Cole Pblishing Company, [18] J.J. Chen, R. W, P.C. Yang, J.Y. Hang, Y.P. Sher, M.H. Han, W.C. Kao, P.J. Lee, T.F. Chi, F. Chang, Y.W. Ch, C.W. W, K. Peck. Profiling expression patterns and isolating differentially expressed genes by cdna microarray system with colorimetry detection. Genomics, 51: , [19] Johannes Schchhardt, Dieter Bele, Arif Malik, Eryc Wolski, Holger Eickhoff, Hans Lehrach and Hanspeter Herzel. Normalization strategies for cdna microarrays. Ncleic Acids Research, Vol. 28(10), [20] M. Schena, D. Shalon, R.W. Davis, P.. Brown. Qantitative monitoring of gene expression patterns with a complementary DNA microarray. Science, 270: , [21] Mark Schena, Dari Shalon, Ren Heller, Andrew Chai, Patrick. Brown, and Ronald W. Davis. Parallel hman genome analysis: Microarray-based expression monitoring of 1000 genes. Proc. Natl. Acad. Sci. USA, Vol. 93(20): , ctober [22] Michael B. Eisen, Pal T. Spellman, Patrick. Brown and David Botstein. Clster analysis and display of genomewide expression patterns. Proc. Natl. Acad. Sci. USA, Vol. 95: , 1998.

8 [23] Michael P. S. Brown, William Noble Grndy, David Lin, Nello Cristianini, Charles Sgnet, Terrence S. Frey, Manel Ares and Jr.David Hassler. Knowledge-based analysis of microarray gene expression data sing spport vector machines. Proc. Natl. Acad. Sci., 97(1): , Janary [24]. Ermolaeva, M. Rastogi, K.D. Pritt, G.D. Schler, M.L. Bittner, Y. Chen, R. Simon, P. Meltzer, J.M. Trent, M.S. Bogski. Data management and analysis for gene expression arrays. Natre Genetics, 20:19 23, [25] rly Alter, Patrick. Brown and David Bostein. Singlar vale decomposition for genome-wide expression data processing and modeling. Proc. Natl. Acad. Sci. USA, Vol. 97(18): , Agest [26] Pablo Tamayo, Donna Solni,m Jill Mesirov, Qing Zh, Stisak Kitareewan, Ethan Dmitrovsky, Eric S. Lander and Todd R. Golb. Interpreting patterns of gene expression with selforganizing maps: Methods and application to hematopoietic differentiation. Proc. Natl. Acad. Sci. USA, Vol. 96(6): , March [27] R.A. Heller, M. Schena, A. Chai, D. Shalon, T. Bedilion, J. Gilmore, D.E. Woolley, R.W. Davis. Discovery and analysis of inflammatory disease-related genes sing cdna microarrays. Proc. Natl. Acad. Sci. USA, 94: , [28] S. Tavazoie, D. Hghes, M.J. Campbell, R.J. Cho and G.M. Chrch. Systematic determination of genetic network architectre. Natre Genet, pages , [29] Shmei Jiang, Chn Tang, Li Zhang and Aidong Zhang, Mrali Ramanathan. A maximm entropy approach to classifying gene array data sets. In Proc. of Workshop on Data mining for genomics, First SIAM International Conference on Data Mining, [30] S.M. Welford, J. Gregg, E. Chen, D. Garrison, P.H. Sorensen, C.T. Denny, S.F. Nelson. Detection of differentially expressed genes in primary tmor tisses sing representational differences analysis copled to microarray hybridization. Ncleic Acids Research, 26: , [31] Spellman P.T., Sherlock G., Zhang M.Q., Iyer V.R., Anders K., Eisen M.B., Brown P.., Botstein D., Ftcher B.. Exploring the metabolic and genetic control of gene expression on a genomic scale. Mol. Biol. Cell, page 3273, [32] T.R. Golb, D.K. Slonim, P. Tamayo, C. Hard, M. Gassenbeek, J.P. Mesirov, H. Coller, M.L. Loh, J.R. Downing, M.A. Caligiri, D.D. Bloomfield and E.S. Lander. Moleclar classification of cancer: Class discovery and class prediction by gene expression monitoring. Science, Vol. 286(15): , ctober [33] Trevor Hastie, Robert Tibshirani, David Boststein and Patrick Brown. Spervised harvesting of expression trees. Genome Biology, Vol. 2(1): , Janary [34] U. Alon, N. Barkai, D.A. Notterman, K.Gish, S. Ybarra, D. Mack and A.J. Levine. Broad patterns of gene expression revealed by clstering analysis of tmor and normal colon tisses probed by oligoncleotide array. Proc. Natl. Acad. Sci. USA, Vol. 96(12): , Jne [35] V. Yong, S. Chabot, Q. Stve and G. Williams. Interferon beta in the treatment of mltiple sclerosis: mechanisms of action. Nerology, 51: , [36] V.R. Iyer, M.B. Eisen, D.T. Ross, G. Schler, T. Moore, J.C.F. Lee, J.M. Trent, L.M. Stadt, Jr. J. Hdson, M.S. Bogski, D. Lashkari, D. Shalon, D. Botstein, P.. Brown. The transcriptional program in the response of hman fibroblasts to serm. Science, 283:83 87, [37] Y Barash and N Friedman. Context-specific bayesian clstering for gene expression data. Bioinformatics, RECM01, [38] Yang Y.H., Ddoit S., L P. and Speed T. P. Normalization for cdna Microarray Data. In Proceedings of SPIE BiS 2001, San Jose, California, Janary 2001.

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