Patent Application: US-80047807-A

Abstract:
process and apparatus for combining multiple processes for choosing features such as biomarkers in statistical data using consensus voting among the multiple processes and their chosen features .

Description:
fig1 illustrates a flow chart of a method of reliable feature selection . the observed data from 1 are fed into multiple feature selection methods in parallel . in 2 , a set of feature selection methods are chosen typically based on their merits and the specific data set at hand . such a method can be anova test [ 8 ], b - max [ 9 ], b - min [ 9 ], b - scatter [ 9 ], boosting flexible learning ensembles with dynamic feature selection [ 10 ], brown forsythe statistic [ 8 ], cart [ 11 ], chi squared [ 9 ], comb [ 9 ], correlation based [ 11 ], fisher score [ 12 ], fold change [ 13 ], forward substitution and backward elimination [ 14 ], gene shaving [ 15 ], gini impurity [ 16 ], goodness - of - fit [ 11 ], information gain [ 16 ], kolmogorov - smirnov test [ 17 ], kruskal - wallis test ( h test ) [ 8 ], margin based [ 18 ], minmax [ 9 ], nearest shrunken centroid [ 19 ], partial least square [ 20 ], random forest [ 21 ], signal to noise ratio [ 22 ], significance analysis of microarray ( sam ) [ 23 ], support vector machine based [ 24 ], [ 26 ], t test [ 26 ], transductive support vector machine [ 27 ], wavelet - based [ 28 ], welch t [ 29 ], wilcoxon rank sum [ 30 ], and the like . ( references are given below .) more than one method should be used in order to take the advantage offered by this invention . the underlying assumption is that the more different methods agree on a feature , the more reliable the feature is . the selected features from each method are then integrated using the consensus voting and ranking module 3 . optionally , the observations are pre - processed by 102 before passing into the feature selection module 2 , as shown in fig2 . the data pre - processing step 102 is typically required when significant noise is presented in the data set . common types of pre - processing include calibration , normalization , spatial and / or temporal alignment , background adjustments , and other noise filtering techniques . note that , as used herein , the terms “ samples ” and “ observations ” are used interchangeably , referring to related data from the inputs , which can be either pre - processed or not . fig2 also shows an optional resampling module 202 . when the size of the observations is limited , the feature selection result may be biased to sample variation . resampling is a method to assess the variance associated with the small sample size by perturbing the inputs . depending on the problem at hand , the resampling can employ a bootstrap method , a bagging method , a jackknife method , a permutation test , or a cross validation method . in one embodiment , each feature selection method employs a resampling step independently , when limited sample size is presented . fig3 details the process flow for reliable feature selection when the integration of results from different feature selection methods is used . in 203 , each of the k feature selection methods m 1 , m 2 , . . . m k , . . . , and m k selects j features along with associated ranks , either using the optional resampling method or not , and sends them to 301 . the numbers k and j can be user assigned or recommended by a software implementation . in a diagnostic context focusing on particular features such as biomarkers , j may be small , such 1 or 2 . in a discovery context , j may be up to 100 or more . current research suggests that 10 - 40 may be optimal for drug development . in some embodiments , j may be selected as a multiple , such as 2 or 3 , of the number of features user is interested . these k sets of feature lists with length j will form a combined feature list . in one embodiment as an example , a union feature set can be obtained from the k feature sets , which is consisted of l (& gt ;= j ) unique features in these k sets . for each feature in the union set , we obtain its rank , rank , in each of the k sets . if a feature does not appear in one of the k sets , its rank is j + 1 in that set . for each feature in the union set , we obtain its frequency of occurrence , freq (& lt ;= k ), in all the k sets . the final feature list is obtained using these ranks and frequencies . the consensus method , which can also be considered “ voting ” for features by each feature selection method , uses a reliability assessment or a weight to each feature selection method . the rationale is that the more a method agrees with the other methods , the more reliable it is . therefore , in 302 , each method k is given a weight . wk which is related to the ranks of the j features in set m k and the frequency of occurrence of these features across the k sets . for each feature in any of the k feature sets , we define a reverse rank as below . if a feature is not present in a particular list , its reverse rank is 0 . the top ranked feature in a list , rank = 1 , will have reverse rank j . thus , the higher the reverse rank value , the more important of this feature in the list . we then define method score and feature score . method score is calculated for each method that will be used to compute the weights of all methods in consensus voting . feature score is calculated for each feature in the union set that will be used to rank all l features . in one embodiment , a method score for method k can be calculated as the sum of the products of frequency and the square root of reverse rank ( or other mathematical functions of reverse rank ) for each of the features in the feature list generated using method k : in another embodiment , a method score for method k can be calculated as the sum of the quotients of frequency and the square root of rank ( or other mathematical functions of rank ) for each of the features in the feature list generated using method k : in one implementation , the weight for method k is calculated as in another implementation , the weights are assigned by users according to their understanding or investigation of the samples and features . in yet another implementation , the weights are assigned of equal weights . in one embodiment , a feature score for feature 1 can be calculated as the sum of the products of weight for the kth method and the square root of reverse rank ( or other mathematical functions of reverse rank ) in the kth list for feature 1 in the union feature list over all k methods selected : in another embodiment , a feature score for feature 1 can be calculated as the sum of the products of weight for the kth method and the square root of rank ( or other mathematical functions of reverse rank ) in the kth list for feature 1 in the union feature list over all k feature methods selected : the f features ( f =& lt ; j ) that have the highest feature score values are chosen as the final selected features , and are outputted to the next step . f is typically an integer assigned by user or some pre - determined criterion . the ranks of the f selected features are determined by the feature score values . the rank of the features provides information about the importance of the features been selected . in biomarker discovery , focus should be directed to the top ranked features . the ranked result also reduces the chance of repeating the data analysis due to a change in investigation objectives . if a particular application needs to narrow down the number of selected features from f to f ′, simply order the features by rank , and choose the f ′ top ranked features . a computer - software implementation of the aforementioned method is deployed and illustrated in fig4 . such a system includes an input module 1 which consists of an observation input sub - module 101 and an optional pre - processing sub - module 102 , feature selection using individual methods module 2 , consensus voting and ranking module 3 , quality measure module 4 , and feature output module 5 . the observation input sub - module 101 can receive data directly from outside input and cache the data into computer memory or files . alternatively , data can be saved first to a database , and be retrieved at a later time . the database facility can also store outputs from the feature output module 5 . sub - module 201 enables users to select specific feature selection methods which they see fit , or to use a set of default feature selection methods . optional cross validation resampling technique can be applied by sub - module 202 . sub - module 203 applies the selected multiple feature selection methods and obtain multiple feature lists after the optional step 202 . the consensus voting and ranking module 3 consists of a union set of features sub - module 301 , a consensus method voting sub - module 302 and a feature ranking sub - module 303 . final selected features are then sent to quality measure module 4 to evaluate their quality , such as by reproducibility or prediction accuracy . ( reproducibility may be measured by the percentage of occurrence of the feature when each of the n samples is taken out of the data set . prediction accuracy may be measured by taking one sample out of the data set , forming a training set of n − 1 samples , and using it to predict the label of the removed sample , repeated n times .) the selected features are sent to output module 5 which directs the features to either outside applications or storage in the database facility for future use . while there have been described what are presently believed to be the preferred embodiments of the invention , those skilled in the art will realize that various changes and modifications can be made to the invention without departing from the spirit of the invention , and it is intended to claim all such changes and modifications as fall within the scope of the invention . fig5 shows two screenshots for an implementation of the method in a software product , topbiomarkers ™. fig5 a is a data / parameter input sheet of the implementation using the invention for the reliable feature section from dataset with multiple classes . there are six sections in this input interface . section 1 specifies the input data file that contains the feature expression values of multiple classes and indicates whether this dataset has been log - transformed . this relates to the pre - processing in block 102 of fig2 and sub - module 102 of fig4 . section 2 specifies the location of output file and the file format . section 3 is a list of pre - processing steps that filter out the obviously unwanted features . this list includes range cut - off , p - value cutoff , fold change cutoff , and profile constrain . section 4 lists a number of feature selection methods . the user can select any combination of these methods and obtain the ranked feature list using each method and the final ranked list with the consensus voting method . this section also specifies the number of features of user &# 39 ; s interest . section 5 specifies the choice of weights to the selected feature selection methods for consensus voting . it has three options : equal weights , an implementation of the weights described above , and any set of weights provided by users . section 6 provides two quality measures of the selected features , namely , reproducibility of the features selected and the prediction accuracy when the set of features is used to develop a predictive classification model . fig5 b is a screenshot that shows the last part of the output file . the middle of the screenshot contains information on the ten features ( in this case , genes or probes ) obtained using the consensus method . the three columns on the left are the ranks , names , and indices ( locations of the genes or features in the input data file ) of the ten features selected . the eight columns on the right show the ranks of these ten features using each of the eight individual feature selection methods . in this case , these eights methods are : fold change , sam , t - test , fisher &# 39 ; s test , wilcoxon method , kolmogrov - smirnov test , support vector machines , and bscatter method . the bottom portion of the screenshot shows the calculated weights for the eight feature selection methods used in the consensus voting . the example below is used to illustrate the application of the consensus voting method for reliable feature selection . this example shows the consensus voting between the relative importance of using reproducibility and classification accuracy as criteria in selecting features . one method , the t test p - value method with a small fold change cutoff has been frequently used to select features which typically yields features with higher classification power , both sensitivity and specificity , usually preferred by statisticians . another method , the fold change method with small p - value cutoff has been proposed by maqc phase i ( 2006 ) [ 31 ] which typically yields high reproducibility of features selected across different sites and platforms , usually preferred by biologists . an implementation of the consensus voting feature selection method is used in this example to reliably select features with both reproducibility and classification accuracy . the effectiveness of the invention is illustrated using a dataset from golub et al [ 22 ]. this data set contains 47 acute lymphoblastic leukemia ( all ) samples and 25 acute myeloid leukemia ( aml ) samples . all those samples were measured using affymetrix genechip , which contain 6 , 817 human genes . the objective is to select features ( genes ) that have high fold change values ( strong reproducibility ) and low p - values ( strong differentiation between all and aml ). fig6 a shows a volcano plot using fold change as feature selection method with a p - value cut - off at p = 0 . 05 . the 20 solid points are the selected genes and the numbers are their corresponding ranks . this is a method proposed in maqc phase i study that can achieve higher reproducibility across different experiments . fig6 a indicates that the top genes are on the two extreme sides of the graph . the closer the genes to the middle at log2 ( fold change )= 0 , the lower their ranks . there are several genes with p - values very close to the cutoff value 0 . 05 in spite of that all the 20 selected genes have large fold changes . thus , the selected 20 genes may have high reproducibility , but their classification accuracy may be relatively low . fig6 b shows a volcano plot when t - test p - value method is used , with fold change cutoff fc = 2 , to select features . the higher the spots in fig6 b , the higher their ranks . the twenty selected features , represented by the solid spots , have very low p - value indicating of high classification accuracy . however , there are always several features very close to the two vertical lines fc = 2 and fc = 0 . 5 which indicating of relatively low reproducibility . there has been a continuing debate as to which of these two feature selection methods should be used . to resolve the debate , we developed an implementation of the consensus feature selection voting method , which takes into account both the reproducibility and classification accuracy and makes a good balance between them . fig6 c shows a volcano plot using the invention , the consensus voting feature selection method . the twenty selected genes are again marked in solid spots and the numbers are their corresponding ranks . no cutoff values are used . it is seen that the top features are located at the two top side - corners . the closer the spots to the origin , the lower their ranks . the selected twenty genes are both of high fold change values and low p - values , far away from the fold change cutoff lines and the p value cutoff line . this example indicates that the invention is effective at selecting reliable genes , which are of not only high reproducibility , but also classification accuracy . anderson et al . 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