Mixed Factors Analysis

Option Dialog


Clicking "Mixed Factors Analysis" in menu, run the input parameter wizard. User is then required to specify the following parameters:

• Range of factor dimensions (number of module transcriptional) taken into considerations:
  For example, if user sets the factor dimensions ranging from Max=8 to Min=5, the ArrayCluster compute the corresponding BIC scores, and then select an optimal factor dimension, say Factor Dimension = 7, that attains the minimum BIC. The following results, e.g. clustering, module identification and so on, corresponds to those given by an optimal model, i.e. Factor Dimension=7. If user takes into consideration just uni-model, e.g. Factor Dimension=4, input "Factor Dimensions" equal to Max=4 and Min=4. Note that user must not enter any inconsistent values such as Max < Min, Max=0 and Min=0. The current version 1.0 places a 20 upper-limit on the maximum factor dimension.
  
  
• Range of the number of clusters taken into considerations:
  As in the case of the determination of factor dimension, the ArrayCluster searches an optimal number of clusters based on the BIC scores. For a specified candidate ranging Min <=#.Cluster <=Max and Min <=Factor Dimension<=Max, the program finds a most suitable combination, then return some outputs corresponding to the selected combination. Operation procedures and notandums are same with those of Factor Dimension.
  
  
• Initialization options:
  For the mixed factors model, the likelihood equations to be solved have multiple roots. Hence, the computation of EM algorithm should be repeated several times with a wide range of the initial parameters. The current version implements the randomized initialization for the determination of starting paramters with several times user specifies.
  
  
• Common Covariance Matrix Options:
  Mixed factors model assumes that the q-dimensional factor vector is distributed according to the mixture of the Gaussian distributions having the diagonal covariance matrices, V_g=diag(v_1g,····, v_qg), for g=1,····,G. ArrayCluster 1.0 equips the option for the use of isotopic covariance matrices, i.e. V_g=vI for all g.
  
  
• Number of Relevant Genes:
  As was already mentioned, the mixed factors analysis identifies total 2×(Factor Dimension) gene modules that are relevant to group structure of the gene expression signatures. In ArrayCluster, user can select the number of genes selected as members in one module through this option dialog.

Implementation


After specifying all parameters and pressing the "Finish" button, the Mixed_Factors_Analysis.exe runs on. If the process is completed, the messages shown in below appear on the DOS-windows.

At first, experimental parameters specified by user are notified, for example, Max and Min factor dimension, number of relevant genes to be selected.

Going a layer than that, user can view the process of EM algorithm for a combination of each factor dimension and number of clusters and initial parameters. The statements such as "* -C" or "* -OF" represent states of the convergence for the EM algorithm, "in convergence" or "occurrence of over-fitting", respectively.

Furthermore, a most suitable combination of factor dimension and the number of clusters are also shown, in this example, the optimal factor dimension and the number of clusters are equal to 7 and 5.

Subsequently, the calibrated clusters are shown. Each cluster is separated with the blank lines. Note that all samples in one clusters are ordered according to the degree of the belongings that are measured by the magnitude of Maharanobis distance between the sample points and the corresponding group centeroid.

Finally, the created six files that summarize some results of the mixed factors analysis and the folder locations are notified.. Description of the six files are in turn given through this tutorial, e.g. Model Selection, Clustering, Data Compression and Relevant Module Detection.

Figure 1: Output files creadted by the mixed factros analysis






Messages appeared in DOS window (Mixed_Factors_Analysis.exe)

• --- SELECTED OPTIONS FOR MIXED FACTORS ANALYSIS ---
  * Max_Factor 8
  * Min_Factor 6
  * Max_Num_Clusters 6
  * Min_Num_Clusters 4
  * Num_Iterations_EM 3
  * Common_Covariance N
  * Num_Relevant_Feature 20
  
  -----------------------------
  PROCESS VIEW OF EM ALGORITHM
  FACTOR DIM. 6 NUM.CLUSTERS 4
  * -C
  * -OF
  * -C
  FACTOR DIM. 7 NUM.CLUSTERS 4
  * -OF
  * -OF
  * -OF
  * -C
  * -C
  * -C
  FACTOR DIM. 8 NUM.CLUSTERS 4
  * -C
  * -C
  * -C
  FACTOR DIM. 6 NUM.CLUSTERS 5
  * -C
  * -C
  * -C
  FACTOR DIM. 7 NUM.CLUSTERS 5
  * -C
  * -OF
  * -OF
  FACTOR DIM. 8 NUM.CLUSTERS 5
  * -C
  * -OF
  * -C
  FACTOR DIM. 6 NUM.CLUSTERS 6
  * -OF
  * -OF
  * -C
  FACTOR DIM. 7 NUM.CLUSTERS 6
  * -OF
  * -OF
  * -OF
  * -C
  * -OF
  * -OF
  FACTOR DIM. 8 NUM.CLUSTERS 6
  * -OF
  * -C
  * -OF
  -----------------------------
  
  --- SELECTED MODEL ---
  FACTOR DIM. 6 NUM.CLUSTERS 4
  MIN. BIC -173757.9536
  
  --- CLUSTERING ---
  
  ex2 2.5143
  ex56 3.0997
  ex53 3.3880
  ex17 3.6238
  ex54 3.6811
  ex61 3.7153
  ex32 4.0781
  ex21 4.3215
  ex15 5.0945
  ex16 5.4574
  ex51 5.5414
  ex55 6.4377
  ex4 6.4684
  ex1 7.3439
  
  ex34 2.6977
  ex26 2.8049
  ex27 3.3646
  ex28 3.4936
  ex30 4.3155
  ex40 4.5669
  ex31 5.3043
  ex25 5.9297
  ex33 6.1687
  ex29 8.3128
  ex24 10.7974
  
  ex58 2.7702
  ex6 2.8320
  ex60 2.9380
  ex5 3.4753
  ex45 3.7771
  ex11 3.8016
  ex13 4.0272
  ex8 4.3992
  ex12 4.5219
  ex9 4.6122
  ex57 4.7551
  ex7 4.7553
  ex59 5.2079
  ex10 5.8650
  ex3 6.6773
  ex44 8.2157
  ex62 8.8822
  ex63 16.1418
  
  ex52 1.0337
  ex20 3.1033
  ex50 3.5920
  ex22 3.6395
  ex43 3.8607
  ex37 3.8875
  ex39 3.9114
  ex36 4.1459
  ex48 4.2865
  ex41 5.2053
  ex23 5.6382
  ex47 5.7172
  ex46 6.0053
  ex18 6.9978
  ex19 7.0149
  ex49 7.0154
  ex35 7.3917
  ex38 8.6547
  ex42 8.6757
  ex14 9.2254
  
  OUTPUT FILE DESCRIPTION
  -----------------------------------------------------------
  * BIC Scores --->
  C:\ArrayCluster\extents\lunamacplugin\data\model_selection.txt
  * Clustering --->
  C:\ArrayCluster\extents\lunamacplugin\data\clustering.txt
  * Factor Scores --->
  C:\ArrayCluster\extents\lunamacplugin\data\mixed_factors.txt
  * Relevant Positive Gene Sets --->
  C:\ArrayCluster\extents\lunamacplugin\data\relvant_set_+.txt
  * Relevant Negative Gene Sets --->
  C:\ArrayCluster\extents\lunamacplugin\data\relvant_set_-txt
  * Estimated Parmeters --->
  C:\ArrayCluster\extents\lunamacplugin\data\parameters.txt
  * Missing Imputation --->
  C:\ArrayCluster\extents\lunamacplugin\data\.missing_imputation.txt
  -----------------------------------------------------------
  Fortran Pause - Enter command<CR> or <CR> to continue.