Feature Extraction Workflow
This example shows a complete workflow for feature extraction. The example uses the humanactivity data set, which has 60 predictors and tens of thousands of data samples.
Load and Examine Data
Load the humanactivity data, which is available when you run this example.
load humanactivityView a description of the data.
Description
Description = 29×1 string
" === Human Activity Data === "
" "
" The humanactivity data set contains 24,075 observations of five different "
" physical human activities: Sitting, Standing, Walking, Running, and "
" Dancing. Each observation has 60 features extracted from acceleration "
" data measured by smartphone accelerometer sensors. The data set contains "
" the following variables: "
" "
" * actid - Response vector containing the activity IDs in integers: 1, 2, "
" 3, 4, and 5 representing Sitting, Standing, Walking, Running, and "
" Dancing, respectively "
" * actnames - Activity names corresponding to the integer activity IDs "
" * feat - Feature matrix of 60 features for 24,075 observations "
" * featlabels - Labels of the 60 features "
" "
" The Sensor HAR (human activity recognition) App [1] was used to create "
" the humanactivity data set. When measuring the raw acceleration data with "
" this app, a person placed a smartphone in a pocket so that the smartphone "
" was upside down and the screen faced toward the person. The software then "
" calibrated the measured raw data accordingly and extracted the 60 "
" features from the calibrated data. For details about the calibration and "
" feature extraction, see [2] and [3], respectively. "
" "
" [1] El Helou, A. Sensor HAR recognition App. bat365 File Exchange "
" http:/matlabcentral/fileexchange/54138-sensor-har-recognition-app "
" [2] STMicroelectronics, AN4508 Application note. “Parameters and "
" calibration of a low-g 3-axis accelerometer.” 2014. "
" [3] El Helou, A. Sensor Data Analytics. bat365 File Exchange "
" /matlabcentral/fileexchange/54139-sensor-data-analytics--french-webinar-code- "
The data set is organized by activity type. To better represent a random set of data, shuffle the rows.
n = numel(actid); % Number of data points rng(1) % For reproducibility idx = randsample(n,n); % Shuffle X = feat(idx,:); % The corresponding labels are in actid(idx) Labels = actid(idx);
View the activities and corresponding labels.
tbl = table(["1";"2";"3";"4";"5"],... ["Sitting";"Standing";"Walking";"Running";"Dancing"],... 'VariableNames',{'Label' 'Activity'}); disp(tbl)
Label Activity
_____ __________
"1" "Sitting"
"2" "Standing"
"3" "Walking"
"4" "Running"
"5" "Dancing"
Set up the data for cross-validation. Use cvpartition to create training and validation sets from the data.
c = cvpartition(n,"HoldOut",0.1);
idxtrain = training(c);
Xtrain = X(idxtrain,:);
LabelTrain = Labels(idxtrain);
idxtest = test(c);
Xtest = X(idxtest,:);
LabelTest = Labels(idxtest);Choose New Feature Dimensions
There are several considerations in choosing the number of features to extract:
More features use more memory and computational time.
Fewer features can produce a poor classifier.
To begin, choose 5 features. Later you will see the effects of using more features.
q = 5;
Extract Features
There are two feature extraction functions, sparsefilt and rica. Begin with the sparsefilt function. Set the number of iterations to 10 so that the extraction does not take too long.
Typically, you get good results by running the sparsefilt algorithm for a few iterations to a few hundred iterations. Running the algorithm for too many iterations can lead to decreased classification accuracy, a type of overfitting problem.
Use sparsefilt to obtain the sparse filtering model while using 10 iterations.
tic
Mdl = sparsefilt(Xtrain,q,'IterationLimit',10);Warning: Solver LBFGS was not able to converge to a solution.
toc
Elapsed time is 0.116473 seconds.
sparsefilt warns that the internal LBFGS optimizer did not converge. The optimizer did not converge, at least in part because you set the iteration limit to 10. Nevertheless, you can use the result to train a classifier.
Create Classifier
Transform the original data into the new feature representation.
NewX = transform(Mdl,Xtrain);
Train a linear classifier based on the transformed data and the correct classification labels in LabelTrain. The accuracy of the learned model is sensitive to the fitcecoc regularization parameter Lambda. Try to find the best value for Lambda by using the OptimizeHyperparameters name-value pair. Be aware that this optimization takes time. If you have a Parallel Computing Toolbox™ license, use parallel computing for faster execution. If you don't have a parallel license, remove the UseParallel calls before running this script.
t = templateLinear('Solver','lbfgs'); options = struct('UseParallel',true); tic Cmdl = fitcecoc(NewX,LabelTrain,Learners=t, ... OptimizeHyperparameters="auto",... HyperparameterOptimizationOptions=options);
Copying objective function to workers... Done copying objective function to workers. |==============================================================================================================================| | Iter | Active | Eval | Objective | Objective | BestSoFar | BestSoFar | Coding | Lambda | Learner | | | workers | result | | runtime | (observed) | (estim.) | | | | |==============================================================================================================================| | 1 | 6 | Best | 0.24372 | 4.6976 | 0.24372 | 0.24372 | onevsall | 3.9324 | svm | | 2 | 6 | Accept | 0.56743 | 6.3649 | 0.24372 | 0.40007 | onevsone | 0.12409 | logistic | | 3 | 6 | Best | 0.047905 | 5.6082 | 0.047905 | 0.18708 | onevsall | 3.0428e-08 | svm | | 4 | 5 | Best | 0.044259 | 5.9896 | 0.044259 | 0.044417 | onevsone | 2.3997e-09 | svm | | 5 | 5 | Accept | 0.27949 | 5.8778 | 0.044259 | 0.044417 | onevsall | 0.0026915 | logistic | | 6 | 6 | Accept | 0.27072 | 1.4726 | 0.044259 | 0.046079 | onevsall | 4.6009 | svm | | 7 | 6 | Accept | 0.044951 | 2.6811 | 0.044259 | 0.045078 | onevsone | 8.4641e-07 | svm | | 8 | 6 | Accept | 0.047074 | 2.4291 | 0.044259 | 0.043721 | onevsall | 4.6737e-10 | svm | | 9 | 5 | Accept | 0.048782 | 2.2619 | 0.044259 | 0.045714 | onevsall | 4.188e-07 | svm | | 10 | 5 | Accept | 0.74128 | 1.3176 | 0.044259 | 0.045714 | onevsone | 4.6111 | svm | | 11 | 4 | Accept | 0.047951 | 9.4874 | 0.044259 | 0.039012 | onevsall | 2.5237e-09 | logistic | | 12 | 4 | Accept | 0.044259 | 2.4651 | 0.044259 | 0.039012 | onevsone | 4.639e-10 | svm | | 13 | 6 | Accept | 0.047305 | 2.1181 | 0.044259 | 0.04016 | onevsall | 4.6238e-10 | svm | | 14 | 6 | Accept | 0.13762 | 1.563 | 0.044259 | 0.039295 | onevsall | 0.000197 | svm | | 15 | 6 | Best | 0.044213 | 2.2286 | 0.044213 | 0.040603 | onevsone | 3.2212e-07 | svm | | 16 | 6 | Best | 0.044028 | 2.1986 | 0.044028 | 0.042724 | onevsone | 3.3084e-08 | svm | | 17 | 6 | Accept | 0.047397 | 2.2898 | 0.044028 | 0.042701 | onevsall | 7.0046e-09 | svm | | 18 | 6 | Best | 0.043982 | 2.2335 | 0.043982 | 0.04234 | onevsone | 4.8906e-08 | svm | | 19 | 6 | Accept | 0.044074 | 4.8905 | 0.043982 | 0.0426 | onevsone | 4.618e-10 | logistic | | 20 | 5 | Accept | 0.049889 | 4.6319 | 0.043982 | 0.042666 | onevsall | 1.5731e-07 | logistic | |==============================================================================================================================| | Iter | Active | Eval | Objective | Objective | BestSoFar | BestSoFar | Coding | Lambda | Learner | | | workers | result | | runtime | (observed) | (estim.) | | | | |==============================================================================================================================| | 21 | 5 | Accept | 0.044074 | 2.3749 | 0.043982 | 0.042666 | onevsone | 9.2673e-08 | svm | | 22 | 6 | Accept | 0.047397 | 5.9207 | 0.043982 | 0.042595 | onevsall | 4.6968e-10 | logistic | | 23 | 6 | Accept | 0.044074 | 2.0958 | 0.043982 | 0.042706 | onevsone | 4.7064e-10 | svm | | 24 | 6 | Accept | 0.74128 | 1.3176 | 0.043982 | 0.042866 | onevsall | 4.6104 | logistic | | 25 | 5 | Accept | 0.044074 | 2.3518 | 0.043982 | 0.043111 | onevsone | 1.6131e-07 | svm | | 26 | 5 | Accept | 0.04412 | 2.2526 | 0.043982 | 0.043111 | onevsone | 4.951e-09 | svm | | 27 | 6 | Accept | 0.044397 | 4.4049 | 0.043982 | 0.04312 | onevsone | 1.9221e-08 | logistic | | 28 | 6 | Accept | 0.33889 | 1.6083 | 0.043982 | 0.043246 | onevsone | 0.0057941 | svm | | 29 | 6 | Accept | 0.048689 | 5.0386 | 0.043982 | 0.043249 | onevsall | 1.8172e-08 | logistic | | 30 | 5 | Accept | 0.047397 | 6.426 | 0.043982 | 0.043243 | onevsall | 4.6642e-10 | logistic | | 31 | 5 | Accept | 0.1882 | 1.4843 | 0.043982 | 0.043243 | onevsall | 0.031302 | svm |
__________________________________________________________
Optimization completed.
MaxObjectiveEvaluations of 30 reached.
Total function evaluations: 31
Total elapsed time: 23.9334 seconds
Total objective function evaluation time: 108.0825
Best observed feasible point:
Coding Lambda Learner
________ __________ _______
onevsone 4.8906e-08 svm
Observed objective function value = 0.043982
Estimated objective function value = 0.043668
Function evaluation time = 2.2335
Best estimated feasible point (according to models):
Coding Lambda Learner
________ __________ _______
onevsone 1.6131e-07 svm
Estimated objective function value = 0.043243
Estimated function evaluation time = 2.4171
toc
Elapsed time is 25.690360 seconds.
Evaluate Classifier
Check the error of the classifier when applied to test data.
TestX = transform(Mdl,Xtest); Loss = loss(Cmdl,TestX,LabelTest)
Loss = 0.0489
Did this transformation result in a better classifier than one trained on the original data? Create a classifier based on the original training data and evaluate its loss.
tic Omdl = fitcecoc(Xtrain,LabelTrain,Learners=t, ... OptimizeHyperparameters="auto",... HyperparameterOptimizationOptions=options);
Copying objective function to workers...
Warning: Files that have already been attached are being ignored. To see which files are attached see the 'AttachedFiles' property of the parallel pool.
Done copying objective function to workers. |==============================================================================================================================| | Iter | Active | Eval | Objective | Objective | BestSoFar | BestSoFar | Coding | Lambda | Learner | | | workers | result | | runtime | (observed) | (estim.) | | | | |==============================================================================================================================| | 1 | 6 | Best | 0.035259 | 5.5107 | 0.035259 | 0.035259 | onevsone | 0.77518 | svm | | 2 | 6 | Best | 0.021829 | 8.7406 | 0.021829 | 0.022507 | onevsone | 1.4423e-09 | svm | | 3 | 6 | Accept | 0.03729 | 13.605 | 0.021829 | 0.021838 | onevsall | 0.6103 | svm | | 4 | 6 | Accept | 0.022383 | 8.5819 | 0.021829 | 0.021836 | onevsone | 4.1356e-09 | svm | | 5 | 6 | Accept | 0.024045 | 7.7692 | 0.021829 | 0.02255 | onevsone | 4.6679e-10 | svm | | 6 | 6 | Accept | 0.040198 | 8.308 | 0.021829 | 0.022615 | onevsall | 4.6023 | logistic | | 7 | 6 | Best | 0.021553 | 7.829 | 0.021553 | 0.0221 | onevsone | 7.3067e-08 | svm | | 8 | 6 | Accept | 0.021829 | 7.6416 | 0.021553 | 0.021892 | onevsone | 5.8054e-09 | svm | | 9 | 6 | Best | 0.021506 | 9.0909 | 0.021506 | 0.021558 | onevsone | 8.1397e-08 | svm | | 10 | 6 | Best | 0.019937 | 33.993 | 0.019937 | 0.019992 | onevsone | 0.0001022 | logistic | | 11 | 6 | Accept | 0.021091 | 8.4908 | 0.019937 | 0.019984 | onevsone | 3.4715e-08 | svm | | 12 | 6 | Accept | 0.019937 | 46.814 | 0.019937 | 0.019961 | onevsone | 1.569e-05 | logistic | | 13 | 6 | Accept | 0.022152 | 6.9556 | 0.019937 | 0.019965 | onevsone | 3.7097e-08 | svm | | 14 | 6 | Accept | 0.039275 | 7.372 | 0.019937 | 0.019897 | onevsone | 1.0643 | logistic | | 15 | 6 | Best | 0.019799 | 53.215 | 0.019799 | 0.019695 | onevsone | 1.1332e-07 | logistic | | 16 | 6 | Accept | 0.022568 | 8.594 | 0.019799 | 0.019662 | onevsone | 2.0178e-05 | svm | | 17 | 6 | Accept | 0.020906 | 20.329 | 0.019799 | 0.019877 | onevsone | 0.00079115 | logistic | | 18 | 6 | Accept | 0.023814 | 43.531 | 0.019799 | 0.019875 | onevsall | 4.6349e-10 | svm | | 19 | 6 | Accept | 0.020353 | 45.355 | 0.019799 | 0.020057 | onevsone | 2.5069e-05 | logistic | | 20 | 6 | Accept | 0.020214 | 46.906 | 0.019799 | 0.020048 | onevsone | 4.64e-10 | logistic | |==============================================================================================================================| | Iter | Active | Eval | Objective | Objective | BestSoFar | BestSoFar | Coding | Lambda | Learner | | | workers | result | | runtime | (observed) | (estim.) | | | | |==============================================================================================================================| | 21 | 6 | Best | 0.019614 | 51.847 | 0.019614 | 0.02 | onevsone | 1.5863e-06 | logistic | | 22 | 6 | Accept | 0.020168 | 49.186 | 0.019614 | 0.01991 | onevsone | 3.644e-07 | logistic | | 23 | 6 | Accept | 0.022845 | 130.99 | 0.019614 | 0.019909 | onevsall | 3.2522e-09 | logistic | | 24 | 6 | Accept | 0.024691 | 45.677 | 0.019614 | 0.01991 | onevsall | 1.0458e-06 | svm | | 25 | 6 | Accept | 0.020629 | 46.99 | 0.019614 | 0.019901 | onevsone | 7.1125e-09 | logistic | | 26 | 6 | Accept | 0.02026 | 47.407 | 0.019614 | 0.019899 | onevsone | 3.5513e-08 | logistic | | 27 | 6 | Accept | 0.020168 | 48.879 | 0.019614 | 0.019912 | onevsone | 4.9086e-09 | logistic | | 28 | 6 | Accept | 0.02026 | 46.764 | 0.019614 | 0.019909 | onevsone | 1.3482e-08 | logistic | | 29 | 6 | Accept | 0.02003 | 46.455 | 0.019614 | 0.019916 | onevsone | 3.6929e-09 | logistic | | 30 | 6 | Accept | 0.024229 | 8.5617 | 0.019614 | 0.019905 | onevsone | 0.0091116 | svm |
__________________________________________________________
Optimization completed.
MaxObjectiveEvaluations of 30 reached.
Total function evaluations: 30
Total elapsed time: 190.1928 seconds
Total objective function evaluation time: 921.392
Best observed feasible point:
Coding Lambda Learner
________ __________ ________
onevsone 1.5863e-06 logistic
Observed objective function value = 0.019614
Estimated objective function value = 0.019832
Function evaluation time = 51.8468
Best estimated feasible point (according to models):
Coding Lambda Learner
________ _________ ________
onevsone 3.644e-07 logistic
Estimated objective function value = 0.019905
Estimated function evaluation time = 51.7579
toc
Elapsed time is 195.893143 seconds.
Losso = loss(Omdl,Xtest,LabelTest)
Losso = 0.0177
The classifier based on sparse filtering has a higher loss than the classifier based on the original data. However, the classifier uses only 5 features rather than the 60 features in the original data, and is much faster to create. Try to make a better sparse filtering classifier by increasing q from 5 to 20, which is still less than the 60 features in the original data.
q = 20;
Mdl2 = sparsefilt(Xtrain,q,'IterationLimit',10);Warning: Solver LBFGS was not able to converge to a solution.
NewX = transform(Mdl2,Xtrain); TestX = transform(Mdl2,Xtest); tic Cmdl = fitcecoc(NewX,LabelTrain,Learners=t, ... OptimizeHyperparameters="auto",... HyperparameterOptimizationOptions=options);
Copying objective function to workers...
Warning: Files that have already been attached are being ignored. To see which files are attached see the 'AttachedFiles' property of the parallel pool.
Done copying objective function to workers. |==============================================================================================================================| | Iter | Active | Eval | Objective | Objective | BestSoFar | BestSoFar | Coding | Lambda | Learner | | | workers | result | | runtime | (observed) | (estim.) | | | | |==============================================================================================================================| | 1 | 6 | Best | 0.12147 | 1.2383 | 0.12147 | 0.12147 | onevsall | 0.39835 | svm | | 2 | 6 | Accept | 0.74128 | 1.4354 | 0.12147 | 0.43121 | onevsall | 2.244 | logistic | | 3 | 6 | Accept | 0.74128 | 1.5455 | 0.12147 | 0.53465 | onevsone | 4.6046 | svm | | 4 | 6 | Best | 0.036136 | 3.915 | 0.036136 | 0.082195 | onevsall | 2.1658e-06 | svm | | 5 | 6 | Best | 0.032352 | 5.1021 | 0.032352 | 0.032396 | onevsone | 1.3434e-07 | svm | | 6 | 6 | Accept | 0.040151 | 3.7664 | 0.032352 | 0.032389 | onevsone | 2.0976e-05 | logistic | | 7 | 6 | Accept | 0.045459 | 2.0148 | 0.032352 | 0.032413 | onevsall | 0.00083838 | svm | | 8 | 6 | Accept | 0.032352 | 8.7656 | 0.032352 | 0.032422 | onevsall | 4.4817e-08 | svm | | 9 | 6 | Accept | 0.74128 | 1.6885 | 0.032352 | 0.0324 | onevsone | 4.6093 | logistic | | 10 | 6 | Best | 0.030183 | 5.2918 | 0.030183 | 0.03016 | onevsone | 6.8351e-10 | svm | | 11 | 6 | Accept | 0.032583 | 11.351 | 0.030183 | 0.03017 | onevsone | 7.561e-08 | logistic | | 12 | 6 | Accept | 0.038213 | 2.6803 | 0.030183 | 0.030243 | onevsone | 3.8304e-05 | svm | | 13 | 6 | Accept | 0.032075 | 8.8183 | 0.030183 | 0.030252 | onevsall | 4.7331e-10 | svm | | 14 | 6 | Accept | 0.039321 | 1.7803 | 0.030183 | 0.030264 | onevsall | 4.8211e-05 | svm | | 15 | 6 | Accept | 0.035259 | 2.9937 | 0.030183 | 0.030191 | onevsone | 3.6175e-06 | svm | | 16 | 5 | Accept | 0.040521 | 5.4636 | 0.030183 | 0.030185 | onevsall | 1.224e-05 | logistic | | 17 | 5 | Accept | 0.036275 | 5.0559 | 0.030183 | 0.030185 | onevsone | 1.7186e-06 | logistic | | 18 | 6 | Accept | 0.13827 | 0.90957 | 0.030183 | 0.030183 | onevsall | 4.6063 | svm | | 19 | 6 | Accept | 0.030598 | 4.5358 | 0.030183 | 0.030251 | onevsone | 6.1338e-09 | svm | | 20 | 6 | Accept | 0.058289 | 2.5512 | 0.030183 | 0.030239 | onevsall | 0.00088491 | logistic | |==============================================================================================================================| | Iter | Active | Eval | Objective | Objective | BestSoFar | BestSoFar | Coding | Lambda | Learner | | | workers | result | | runtime | (observed) | (estim.) | | | | |==============================================================================================================================| | 21 | 6 | Accept | 0.10919 | 2.3477 | 0.030183 | 0.030234 | onevsone | 0.0027425 | logistic | | 22 | 6 | Accept | 0.031475 | 8.4684 | 0.030183 | 0.030235 | onevsall | 3.4821e-09 | svm | | 23 | 6 | Accept | 0.045274 | 3.9578 | 0.030183 | 0.030226 | onevsall | 0.00010652 | logistic | | 24 | 6 | Accept | 0.045782 | 1.9671 | 0.030183 | 0.030202 | onevsone | 0.00067026 | svm | | 25 | 6 | Accept | 0.031244 | 20.475 | 0.030183 | 0.030201 | onevsone | 4.6681e-10 | logistic | | 26 | 6 | Best | 0.029952 | 4.7633 | 0.029952 | 0.029927 | onevsone | 1.8406e-09 | svm | | 27 | 6 | Best | 0.029814 | 4.8472 | 0.029814 | 0.029915 | onevsone | 4.6362e-10 | svm | | 28 | 6 | Accept | 0.036229 | 9.8727 | 0.029814 | 0.029915 | onevsall | 7.1397e-07 | logistic | | 29 | 6 | Accept | 0.033413 | 3.7575 | 0.029814 | 0.029921 | onevsone | 6.2968e-07 | svm | | 30 | 6 | Accept | 0.033967 | 22.019 | 0.029814 | 0.029923 | onevsall | 7.3548e-08 | logistic |
__________________________________________________________
Optimization completed.
MaxObjectiveEvaluations of 30 reached.
Total function evaluations: 30
Total elapsed time: 39.9471 seconds
Total objective function evaluation time: 163.3793
Best observed feasible point:
Coding Lambda Learner
________ __________ _______
onevsone 4.6362e-10 svm
Observed objective function value = 0.029814
Estimated objective function value = 0.030009
Function evaluation time = 4.8472
Best estimated feasible point (according to models):
Coding Lambda Learner
________ __________ _______
onevsone 6.8351e-10 svm
Estimated objective function value = 0.029923
Estimated function evaluation time = 4.94
toc
Elapsed time is 41.581666 seconds.
Loss2 = loss(Cmdl,TestX,LabelTest)
Loss2 = 0.0320
This time the classification loss is lower than for the 5 feature classifier, but is still higher than the loss for the original data classifier. Again, software takes less time to create the classifier for 20 predictors than the classifier for the full data.
Try RICA
Try the other feature extraction function, rica. Extract 20 features, create a classifier, and examine its loss on the test data. Use more iterations for the rica function, because rica can perform better with more iterations than sparsefilt uses.
Often prior to feature extraction, you "prewhiten" the input data as a data preprocessing step. The prewhitening step includes two transforms, decorrelation and standardization, which make the predictors have zero mean and identity covariance. rica supports only the standardization transform. You use the Standardize name-value pair argument to make the predictors have zero mean and unit variance. Alternatively, you can transform images for contrast normalization individually by applying the zscore transformation before calling sparsefilt or rica.
Mdl3 = rica(Xtrain,q,'IterationLimit',400,'Standardize',true);
Warning: Solver LBFGS was not able to converge to a solution.
NewX = transform(Mdl3,Xtrain); TestX = transform(Mdl3,Xtest); tic Cmdl = fitcecoc(NewX,LabelTrain,Learners=t, ... OptimizeHyperparameters="auto",... HyperparameterOptimizationOptions=options);
Copying objective function to workers...
Warning: Files that have already been attached are being ignored. To see which files are attached see the 'AttachedFiles' property of the parallel pool.
Done copying objective function to workers. |==============================================================================================================================| | Iter | Active | Eval | Objective | Objective | BestSoFar | BestSoFar | Coding | Lambda | Learner | | | workers | result | | runtime | (observed) | (estim.) | | | | |==============================================================================================================================| | 1 | 6 | Best | 0.048689 | 1.7274 | 0.048689 | 0.048689 | onevsone | 0.49772 | svm | | 2 | 6 | Accept | 0.062442 | 2.2582 | 0.048689 | 0.055562 | onevsone | 0.45646 | logistic | | 3 | 6 | Best | 0.032075 | 2.5078 | 0.032075 | 0.047435 | onevsone | 0.014644 | svm | | 4 | 4 | Accept | 0.035998 | 3.1521 | 0.025522 | 0.040067 | onevsall | 3.8151e-05 | svm | | 5 | 4 | Best | 0.025522 | 3.3093 | 0.025522 | 0.040067 | onevsone | 2.2518e-09 | svm | | 6 | 4 | Accept | 0.035675 | 3.1199 | 0.025522 | 0.040067 | onevsall | 1.2518e-09 | svm | | 7 | 6 | Accept | 0.077164 | 1.6918 | 0.025522 | 0.025637 | onevsone | 3.067 | svm | | 8 | 6 | Accept | 0.026445 | 3.2975 | 0.025522 | 0.031634 | onevsone | 0.0012412 | svm | | 9 | 6 | Accept | 0.025568 | 3.4501 | 0.025522 | 0.027235 | onevsone | 4.6552e-10 | svm | | 10 | 6 | Accept | 0.025614 | 3.42 | 0.025522 | 0.025585 | onevsone | 4.677e-10 | svm | | 11 | 6 | Accept | 0.025706 | 3.2351 | 0.025522 | 0.02559 | onevsone | 4.5709e-09 | svm | | 12 | 6 | Accept | 0.027783 | 2.7219 | 0.025522 | 0.02559 | onevsone | 0.0031183 | svm | | 13 | 6 | Accept | 0.025614 | 3.1778 | 0.025522 | 0.02559 | onevsone | 0.0001457 | svm | | 14 | 6 | Accept | 0.025568 | 3.0303 | 0.025522 | 0.02559 | onevsone | 1.4458e-07 | svm | | 15 | 6 | Accept | 0.027968 | 3.7776 | 0.025522 | 0.02559 | onevsone | 0.00021934 | logistic | | 16 | 6 | Accept | 0.035398 | 2.7932 | 0.025522 | 0.02559 | onevsall | 2.0683e-07 | svm | | 17 | 6 | Accept | 0.052151 | 1.5232 | 0.025522 | 0.02559 | onevsall | 0.13918 | svm | | 18 | 6 | Accept | 0.026214 | 11.715 | 0.025522 | 0.02559 | onevsone | 7.7428e-08 | logistic | | 19 | 6 | Accept | 0.16042 | 1.847 | 0.025522 | 0.025488 | onevsall | 4.6082 | logistic | | 20 | 6 | Accept | 0.033783 | 12.694 | 0.025522 | 0.025591 | onevsall | 4.6182e-10 | logistic | |==============================================================================================================================| | Iter | Active | Eval | Objective | Objective | BestSoFar | BestSoFar | Coding | Lambda | Learner | | | workers | result | | runtime | (observed) | (estim.) | | | | |==============================================================================================================================| | 21 | 6 | Best | 0.025475 | 4.0126 | 0.025475 | 0.02559 | onevsone | 3.7723e-06 | svm | | 22 | 6 | Accept | 0.038351 | 4.3279 | 0.025475 | 0.02559 | onevsall | 0.0010239 | logistic | | 23 | 6 | Accept | 0.12239 | 1.0595 | 0.025475 | 0.025591 | onevsall | 4.5914 | svm | | 24 | 6 | Accept | 0.026214 | 6.1461 | 0.025475 | 0.025591 | onevsone | 1.0019e-05 | logistic | | 25 | 6 | Accept | 0.037613 | 2.0165 | 0.025475 | 0.025591 | onevsall | 0.0031581 | svm | | 26 | 6 | Accept | 0.034936 | 2.4126 | 0.025475 | 0.02559 | onevsone | 0.0056673 | logistic | | 27 | 6 | Accept | 0.034336 | 6.0477 | 0.025475 | 0.025591 | onevsall | 2.7728e-05 | logistic | | 28 | 6 | Accept | 0.033967 | 10.413 | 0.025475 | 0.025591 | onevsall | 6.8407e-07 | logistic | | 29 | 6 | Accept | 0.02626 | 8.3859 | 0.025475 | 0.02559 | onevsone | 8.783e-07 | logistic | | 30 | 6 | Accept | 0.035582 | 2.8227 | 0.025475 | 0.02559 | onevsall | 1.3589e-08 | svm |
__________________________________________________________
Optimization completed.
MaxObjectiveEvaluations of 30 reached.
Total function evaluations: 30
Total elapsed time: 27.1224 seconds
Total objective function evaluation time: 122.0946
Best observed feasible point:
Coding Lambda Learner
________ __________ _______
onevsone 3.7723e-06 svm
Observed objective function value = 0.025475
Estimated objective function value = 0.025475
Function evaluation time = 4.0126
Best estimated feasible point (according to models):
Coding Lambda Learner
________ _________ _______
onevsone 4.677e-10 svm
Estimated objective function value = 0.02559
Estimated function evaluation time = 3.4172
toc
Elapsed time is 28.228099 seconds.
Loss3 = loss(Cmdl,TestX,LabelTest)
Loss3 = 0.0275
The rica-based classifier has similar test loss as the 20-feature sparse filtering classifier. The classifier is relatively fast to create.
Try More Features
The feature extraction functions have few tuning parameters. One parameter that can affect results is the number of requested features. See how well classifiers work when based on 100 features, rather than the 20 features previously tried, or the 60 features in the original data. Using more features than appear in the original data is called "overcomplete" learning. Conversely, using fewer features is called "undercomplete" learning. Overcomplete learning can lead to increased classification accuracy, while undercomplete learning can save memory and time.
q = 100;
Mdl4 = sparsefilt(Xtrain,q,'IterationLimit',10);Warning: Solver LBFGS was not able to converge to a solution.
NewX = transform(Mdl4,Xtrain); TestX = transform(Mdl4,Xtest); tic Cmdl = fitcecoc(NewX,LabelTrain,Learners=t, ... OptimizeHyperparameters="auto",... HyperparameterOptimizationOptions=options);
Copying objective function to workers...
Warning: Files that have already been attached are being ignored. To see which files are attached see the 'AttachedFiles' property of the parallel pool.
Done copying objective function to workers. |==============================================================================================================================| | Iter | Active | Eval | Objective | Objective | BestSoFar | BestSoFar | Coding | Lambda | Learner | | | workers | result | | runtime | (observed) | (estim.) | | | | |==============================================================================================================================| | 1 | 6 | Best | 0.039413 | 7.4097 | 0.039413 | 0.039413 | onevsone | 9.6788e-05 | logistic | | 2 | 6 | Accept | 0.056258 | 8.2736 | 0.039413 | 0.047834 | onevsone | 0.0023908 | svm | | 3 | 6 | Accept | 0.050535 | 9.9138 | 0.039413 | 0.048735 | onevsall | 0.0001608 | logistic | | 4 | 6 | Best | 0.033967 | 13.569 | 0.033967 | 0.034082 | onevsone | 9.9249e-05 | svm | | 5 | 6 | Accept | 0.039413 | 7.9397 | 0.033967 | 0.033968 | onevsone | 9.6762e-05 | logistic | | 6 | 6 | Accept | 0.034059 | 13.408 | 0.033967 | 0.033968 | onevsone | 0.00010471 | svm | | 7 | 6 | Best | 0.033598 | 12.795 | 0.033598 | 0.033599 | onevsone | 5.9298e-05 | svm | | 8 | 6 | Best | 0.031752 | 32.351 | 0.031752 | 0.031753 | onevsall | 5.3759e-06 | svm | | 9 | 6 | Accept | 0.088841 | 4.3567 | 0.031752 | 0.031753 | onevsone | 0.0029806 | logistic | | 10 | 6 | Accept | 0.032121 | 9.7001 | 0.031752 | 0.031753 | onevsone | 1.4055e-05 | logistic | | 11 | 6 | Accept | 0.74128 | 4.2755 | 0.031752 | 0.03176 | onevsone | 1.1119 | svm | | 12 | 6 | Accept | 0.74128 | 3.1437 | 0.031752 | 0.031767 | onevsone | 1.9263 | logistic | | 13 | 6 | Accept | 0.37322 | 2.9349 | 0.031752 | 0.03177 | onevsall | 0.080099 | logistic | | 14 | 6 | Best | 0.028891 | 20.557 | 0.028891 | 0.028907 | onevsone | 5.6435e-06 | svm | | 15 | 6 | Best | 0.027875 | 16.755 | 0.027875 | 0.027886 | onevsone | 8.1017e-07 | logistic | | 16 | 6 | Best | 0.027644 | 47.389 | 0.027644 | 0.02765 | onevsall | 2.6085e-07 | logistic | | 17 | 6 | Accept | 0.18322 | 4.166 | 0.027644 | 0.027651 | onevsall | 4.6137 | svm | | 18 | 6 | Best | 0.019614 | 45.707 | 0.019614 | 0.019626 | onevsone | 2.2409e-09 | logistic | | 19 | 6 | Accept | 0.18363 | 4.9399 | 0.019614 | 0.019626 | onevsall | 0.085841 | svm | | 20 | 6 | Accept | 0.055058 | 9.7251 | 0.019614 | 0.019626 | onevsall | 0.0011989 | svm | |==============================================================================================================================| | Iter | Active | Eval | Objective | Objective | BestSoFar | BestSoFar | Coding | Lambda | Learner | | | workers | result | | runtime | (observed) | (estim.) | | | | |==============================================================================================================================| | 21 | 6 | Accept | 0.035306 | 14.675 | 0.019614 | 0.019625 | onevsall | 1.403e-05 | logistic | | 22 | 6 | Best | 0.019522 | 28.211 | 0.019522 | 0.019531 | onevsone | 7.1633e-10 | svm | | 23 | 6 | Accept | 0.038582 | 17.001 | 0.019522 | 0.01953 | onevsall | 8.8768e-05 | svm | | 24 | 6 | Accept | 0.022245 | 32.142 | 0.019522 | 0.019529 | onevsone | 3.8747e-08 | logistic | | 25 | 6 | Accept | 0.023399 | 31.652 | 0.019522 | 0.01953 | onevsone | 1.4128e-07 | svm | | 26 | 6 | Accept | 0.020168 | 31.645 | 0.019522 | 0.019535 | onevsone | 7.4304e-09 | svm | | 27 | 6 | Accept | 0.022937 | 112.17 | 0.019522 | 0.019535 | onevsall | 1.8485e-09 | svm | | 28 | 6 | Accept | 0.019614 | 27.955 | 0.019522 | 0.01955 | onevsone | 2.0284e-09 | svm | | 29 | 6 | Accept | 0.020122 | 44.919 | 0.019522 | 0.019549 | onevsone | 4.6246e-10 | logistic | | 30 | 6 | Accept | 0.020722 | 38.788 | 0.019522 | 0.019547 | onevsone | 8.9251e-09 | logistic |
__________________________________________________________
Optimization completed.
MaxObjectiveEvaluations of 30 reached.
Total function evaluations: 30
Total elapsed time: 149.9449 seconds
Total objective function evaluation time: 658.4665
Best observed feasible point:
Coding Lambda Learner
________ __________ _______
onevsone 7.1633e-10 svm
Observed objective function value = 0.019522
Estimated objective function value = 0.019563
Function evaluation time = 28.2111
Best estimated feasible point (according to models):
Coding Lambda Learner
________ __________ _______
onevsone 2.0284e-09 svm
Estimated objective function value = 0.019547
Estimated function evaluation time = 29.3667
toc
Elapsed time is 153.432841 seconds.
Loss4 = loss(Cmdl,TestX,LabelTest)
Loss4 = 0.0239
The classifier based on overcomplete sparse filtering with 100 extracted features has low test loss.
Mdl5 = rica(Xtrain,q,'IterationLimit',400,'Standardize',true);
Warning: Solver LBFGS was not able to converge to a solution.
NewX = transform(Mdl5,Xtrain); TestX = transform(Mdl5,Xtest); tic Cmdl = fitcecoc(NewX,LabelTrain,Learners=t, ... OptimizeHyperparameters="auto",... HyperparameterOptimizationOptions=options);
Copying objective function to workers...
Warning: Files that have already been attached are being ignored. To see which files are attached see the 'AttachedFiles' property of the parallel pool.
Done copying objective function to workers. |==============================================================================================================================| | Iter | Active | Eval | Objective | Objective | BestSoFar | BestSoFar | Coding | Lambda | Learner | | | workers | result | | runtime | (observed) | (estim.) | | | | |==============================================================================================================================| | 1 | 6 | Best | 0.030875 | 5.8653 | 0.030875 | 0.030875 | onevsone | 0.34902 | svm | | 2 | 6 | Best | 0.019845 | 6.5249 | 0.019845 | 0.025358 | onevsone | 0.0026162 | logistic | | 3 | 6 | Accept | 0.03489 | 4.6883 | 0.019845 | 0.020385 | onevsone | 0.099101 | logistic | | 4 | 6 | Accept | 0.020629 | 15 | 0.019845 | 0.019912 | onevsall | 0.00027131 | logistic | | 5 | 6 | Best | 0.015691 | 16.21 | 0.015691 | 0.015748 | onevsone | 7.8723e-09 | svm | | 6 | 6 | Best | 0.015645 | 11.998 | 0.015645 | 0.015699 | onevsone | 3.5196e-05 | logistic | | 7 | 6 | Best | 0.015368 | 18.798 | 0.015368 | 0.015369 | onevsone | 2.6623e-06 | logistic | | 8 | 6 | Accept | 0.019476 | 6.5533 | 0.015368 | 0.015369 | onevsone | 0.002019 | logistic | | 9 | 6 | Accept | 0.022106 | 19.792 | 0.015368 | 0.015369 | onevsall | 0.0019358 | svm | | 10 | 6 | Accept | 0.11496 | 4.0322 | 0.015368 | 0.01537 | onevsone | 3.4314 | logistic | | 11 | 6 | Accept | 0.021322 | 6.2828 | 0.015368 | 0.015369 | onevsone | 0.0043416 | logistic | | 12 | 6 | Accept | 0.084502 | 4.1352 | 0.015368 | 0.015369 | onevsone | 4.5974 | svm | | 13 | 6 | Accept | 0.015599 | 11.929 | 0.015368 | 0.01537 | onevsone | 5.601e-05 | logistic | | 14 | 6 | Accept | 0.018876 | 14.777 | 0.015368 | 0.01537 | onevsone | 0.0073401 | svm | | 15 | 6 | Best | 0.015138 | 16.286 | 0.015138 | 0.015138 | onevsone | 4.647e-10 | svm | | 16 | 6 | Accept | 0.022799 | 10.342 | 0.015138 | 0.015138 | onevsone | 0.052733 | svm | | 17 | 6 | Accept | 0.015322 | 18.918 | 0.015138 | 0.015139 | onevsone | 1.3043e-07 | svm | | 18 | 6 | Accept | 0.04712 | 4.7692 | 0.015138 | 0.015139 | onevsall | 0.10508 | logistic | | 19 | 6 | Accept | 0.10246 | 4.0277 | 0.015138 | 0.015139 | onevsall | 4.5714 | svm | | 20 | 6 | Accept | 0.15276 | 4.0699 | 0.015138 | 0.01514 | onevsall | 4.5936 | logistic | |==============================================================================================================================| | Iter | Active | Eval | Objective | Objective | BestSoFar | BestSoFar | Coding | Lambda | Learner | | | workers | result | | runtime | (observed) | (estim.) | | | | |==============================================================================================================================| | 21 | 6 | Best | 0.014953 | 26.102 | 0.014953 | 0.014953 | onevsone | 8.0118e-05 | svm | | 22 | 6 | Accept | 0.028291 | 7.1206 | 0.014953 | 0.014953 | onevsall | 0.005946 | logistic | | 23 | 6 | Accept | 0.015876 | 19.702 | 0.014953 | 0.014953 | onevsone | 4.6726e-10 | logistic | | 24 | 6 | Accept | 0.015091 | 23.087 | 0.014953 | 0.014953 | onevsone | 2.6545e-06 | svm | | 25 | 6 | Accept | 0.016845 | 44.235 | 0.014953 | 0.014953 | onevsall | 4.6319e-10 | svm | | 26 | 6 | Accept | 0.017076 | 54.261 | 0.014953 | 0.014953 | onevsall | 4.3174e-07 | logistic | | 27 | 6 | Accept | 0.016799 | 45.904 | 0.014953 | 0.014953 | onevsall | 4.2209e-06 | svm | | 28 | 6 | Best | 0.014768 | 27.573 | 0.014768 | 0.014768 | onevsone | 1.7625e-08 | logistic | | 29 | 6 | Accept | 0.018599 | 33.435 | 0.014768 | 0.014768 | onevsall | 0.00016625 | svm | | 30 | 6 | Accept | 0.017584 | 27.061 | 0.014768 | 0.014768 | onevsall | 1.646e-05 | logistic |
__________________________________________________________
Optimization completed.
MaxObjectiveEvaluations of 30 reached.
Total function evaluations: 30
Total elapsed time: 113.968 seconds
Total objective function evaluation time: 513.4789
Best observed feasible point:
Coding Lambda Learner
________ __________ ________
onevsone 1.7625e-08 logistic
Observed objective function value = 0.014768
Estimated objective function value = 0.014768
Function evaluation time = 27.5729
Best estimated feasible point (according to models):
Coding Lambda Learner
________ __________ ________
onevsone 1.7625e-08 logistic
Estimated objective function value = 0.014768
Estimated function evaluation time = 27.1423
toc
Elapsed time is 116.497520 seconds.
Loss5 = loss(Cmdl,TestX,LabelTest)
Loss5 = 0.0158
The classifier based on RICA with 100 extracted features has similar test loss to the classifier based on sparse filtering and 100 features, and takes less than half the time to create as the classifier trained on the original data.
Optimize Hyperparameters by Using bayesopt
Feature extraction functions have these tuning parameters:
Iteration limit
Function, either
ricaorsparsefiltParameter
LambdaNumber of learned features
qCoding, either
onevsoneoronevsall
The fitcecoc regularization parameter also affects the accuracy of the learned classifier. Include that parameter in the list of hyperparameters as well.
To search among the available parameters effectively, try bayesopt. Use the objective function in the supporting file filterica.m, which includes parameters passed from the workspace.
To remove sources of variation, fix an initial transform weight matrix.
W = randn(1e4,1e3);
Create hyperparameters for the objective function.
iterlim = optimizableVariable('iterlim',[5,500],'Type','integer'); lambda = optimizableVariable('lambda',[0,10]); solver = optimizableVariable('solver',{'r','s'},'Type','categorical'); qvar = optimizableVariable('q',[5,100],'Type','integer'); lambdareg = optimizableVariable('lambdareg',[1e-6,1],'Transform','log'); coding = optimizableVariable('coding',{'o','a'},'Type','categorical'); vars = [iterlim,lambda,solver,qvar,lambdareg,coding];
Run the optimization without the warnings that occur when the internal optimizations do not run to completion. Run for 60 iterations instead of the default 30 to give the optimization a better chance of locating a good value.
warning('off','stats:classreg:learning:fsutils:Solver:LBFGSUnableToConverge'); tic results = bayesopt(@(x) filterica(x,Xtrain,Xtest,LabelTrain,LabelTest,W),vars, ... 'UseParallel',true,'MaxObjectiveEvaluations',60);
Copying objective function to workers... Done copying objective function to workers. |===========================================================================================================================================================================| | Iter | Active | Eval | Objective | Objective | BestSoFar | BestSoFar | iterlim | lambda | solver | q | lambdareg | coding | | | workers | result | | runtime | (observed) | (estim.) | | | | | | | |===========================================================================================================================================================================| | 1 | 6 | Best | 0.52943 | 4.912 | 0.52943 | 0.52943 | 70 | 9.3497 | s | 22 | 0.030312 | o | | 2 | 6 | Best | 0.048927 | 7.0904 | 0.048927 | 0.086902 | 202 | 0.60409 | r | 9 | 0.010864 | o | | 3 | 6 | Best | 0.027201 | 12.647 | 0.027201 | 0.027592 | 190 | 0.80733 | r | 25 | 0.039332 | o | | 4 | 6 | Accept | 0.035378 | 8.6101 | 0.027201 | 0.027731 | 54 | 3.0477 | r | 61 | 0.77824 | o | | 5 | 6 | Accept | 0.25536 | 30.032 | 0.027201 | 0.027466 | 178 | 6.761 | s | 84 | 0.00066641 | o | | 6 | 6 | Accept | 0.35333 | 32.47 | 0.027201 | 0.027443 | 175 | 2.8287 | s | 92 | 0.0012333 | a | | 7 | 6 | Accept | 0.12827 | 27.117 | 0.027201 | 0.027393 | 325 | 7.3952 | s | 35 | 8.2172e-06 | a | | 8 | 6 | Accept | 0.34755 | 33.96 | 0.027201 | 0.027396 | 266 | 4.0928 | s | 60 | 0.00041521 | a | | 9 | 6 | Accept | 0.078705 | 2.0607 | 0.027201 | 0.027294 | 53 | 1.7616 | r | 7 | 0.73652 | o | | 10 | 6 | Best | 0.026029 | 6.6583 | 0.026029 | 0.026189 | 70 | 5.0943 | r | 36 | 0.30991 | o | | 11 | 6 | Accept | 0.040287 | 0.99791 | 0.026029 | 0.026218 | 9 | 4.8121 | s | 13 | 1.0643e-06 | o | | 12 | 6 | Accept | 0.055786 | 1.2549 | 0.026029 | 0.026247 | 38 | 8.6327 | s | 8 | 1.2675e-05 | o | | 13 | 6 | Best | 0.018814 | 8.233 | 0.018814 | 0.018829 | 25 | 0.0278 | r | 84 | 0.00010178 | o | | 14 | 6 | Accept | 0.53812 | 0.49606 | 0.018814 | 0.018875 | 11 | 0.18468 | r | 5 | 1.3987e-06 | o | | 15 | 6 | Best | 0.016874 | 47.355 | 0.016874 | 0.016839 | 212 | 8.9402 | r | 87 | 0.0039156 | o | | 16 | 6 | Accept | 0.52264 | 17.397 | 0.016874 | 0.016855 | 394 | 2.7795 | s | 19 | 0.007691 | o | | 17 | 6 | Accept | 0.020328 | 3.7038 | 0.016874 | 0.016822 | 8 | 3.5707 | r | 99 | 0.10314 | o | | 18 | 6 | Best | 0.015555 | 7.6923 | 0.015555 | 0.0084954 | 9 | 0.74158 | r | 97 | 0.00043623 | o | | 19 | 6 | Accept | 0.035237 | 17.017 | 0.015555 | 0.0086345 | 331 | 0.63154 | r | 20 | 1.0203e-06 | a | | 20 | 6 | Accept | 0.055538 | 0.73762 | 0.015555 | 0.011825 | 11 | 4.4459 | r | 7 | 0.00020189 | o | |===========================================================================================================================================================================| | Iter | Active | Eval | Objective | Objective | BestSoFar | BestSoFar | iterlim | lambda | solver | q | lambdareg | coding | | | workers | result | | runtime | (observed) | (estim.) | | | | | | | |===========================================================================================================================================================================| | 21 | 6 | Accept | 0.037108 | 1.0492 | 0.015555 | 0.010948 | 20 | 9.5934 | r | 8 | 0.00027665 | o | | 22 | 6 | Accept | 0.041709 | 1.9456 | 0.015555 | 0.015403 | 28 | 9.3857 | s | 17 | 2.994e-06 | o | | 23 | 6 | Accept | 0.018454 | 13.93 | 0.015555 | 0.010483 | 22 | 0.69741 | r | 97 | 1.2894e-05 | a | | 24 | 6 | Accept | 0.028586 | 11.282 | 0.015555 | 0.01139 | 35 | 3.2021 | s | 99 | 1.0644e-06 | o | | 25 | 6 | Accept | 0.039866 | 2.4192 | 0.015555 | 0.010809 | 28 | 9.8094 | s | 23 | 1.0098e-06 | a | | 26 | 6 | Accept | 0.88918 | 49.28 | 0.015555 | 0.013345 | 429 | 0.060872 | r | 52 | 0.0011157 | a | | 27 | 6 | Accept | 0.10786 | 0.53144 | 0.015555 | 0.013969 | 5 | 6.4836 | r | 6 | 1.3566e-06 | a | | 28 | 6 | Accept | 0.017484 | 56.302 | 0.015555 | 0.013962 | 474 | 1.8928 | r | 48 | 0.00063848 | o | | 29 | 6 | Accept | 0.38735 | 35.182 | 0.015555 | 0.013918 | 497 | 6.564 | s | 34 | 0.80739 | a | | 30 | 6 | Accept | 0.044439 | 13.26 | 0.015555 | 0.014003 | 497 | 5.7095 | r | 10 | 1.6015e-05 | a | | 31 | 6 | Accept | 0.033871 | 1.1249 | 0.015555 | 0.013967 | 18 | 7.7947 | r | 13 | 8.166e-06 | a | | 32 | 6 | Accept | 0.74128 | 1.6253 | 0.015555 | 0.013465 | 38 | 2.435 | s | 15 | 0.98978 | o | | 33 | 6 | Accept | 0.32977 | 19.047 | 0.015555 | 0.013292 | 497 | 7.4015 | s | 18 | 1.2428e-06 | o | | 34 | 6 | Accept | 0.13391 | 0.52899 | 0.015555 | 0.013399 | 8 | 8.6813 | s | 14 | 0.97959 | a | | 35 | 6 | Accept | 0.19883 | 0.65282 | 0.015555 | 0.013247 | 13 | 2.418 | s | 9 | 0.093133 | a | | 36 | 6 | Accept | 0.047703 | 0.61038 | 0.015555 | 0.013195 | 7 | 4.4549 | s | 7 | 1.3742e-05 | a | | 37 | 6 | Accept | 0.2922 | 20.739 | 0.015555 | 0.013686 | 498 | 0.7477 | s | 18 | 1.2496e-06 | a | | 38 | 6 | Accept | 0.03113 | 11.814 | 0.015555 | 0.013804 | 287 | 9.474 | r | 17 | 7.4789e-06 | a | | 39 | 6 | Accept | 0.05179 | 82.825 | 0.015555 | 0.014658 | 327 | 8.4596 | r | 100 | 0.99361 | a | | 40 | 6 | Accept | 0.08023 | 0.89041 | 0.015555 | 0.014749 | 28 | 5.3041 | r | 8 | 0.71177 | a | |===========================================================================================================================================================================| | Iter | Active | Eval | Objective | Objective | BestSoFar | BestSoFar | iterlim | lambda | solver | q | lambdareg | coding | | | workers | result | | runtime | (observed) | (estim.) | | | | | | | |===========================================================================================================================================================================| | 41 | 6 | Accept | 0.026725 | 10.287 | 0.015555 | 0.01503 | 13 | 1.3207 | s | 100 | 4.0387e-06 | a | | 42 | 6 | Accept | 0.054087 | 0.87185 | 0.015555 | 0.014909 | 13 | 2.0473 | s | 9 | 7.9662e-05 | o | | 43 | 6 | Accept | 0.061574 | 0.80035 | 0.015555 | 0.015371 | 18 | 2.9059 | r | 5 | 3.0653e-05 | a | | 44 | 6 | Accept | 0.053178 | 1.1839 | 0.015555 | 0.015997 | 20 | 3.5261 | s | 9 | 2.7956e-06 | a | | 45 | 6 | Accept | 0.03253 | 1.5798 | 0.015555 | 0.01643 | 29 | 4.7229 | r | 10 | 0.0023745 | o | | 46 | 6 | Accept | 0.019437 | 4.5849 | 0.015555 | 0.015791 | 12 | 1.2408 | r | 91 | 0.012225 | o | | 47 | 6 | Accept | 0.059445 | 14.142 | 0.015555 | 0.015878 | 439 | 2.1105 | r | 13 | 0.95524 | o | | 48 | 6 | Accept | 0.047275 | 11.728 | 0.015555 | 0.016694 | 488 | 2.6315 | r | 10 | 1.073e-06 | a | | 49 | 6 | Accept | 0.040995 | 4.1608 | 0.015555 | 0.015764 | 292 | 4.4442 | r | 5 | 0.00019596 | o | | 50 | 6 | Accept | 0.084049 | 0.84595 | 0.015555 | 0.016101 | 17 | 4.5231 | r | 12 | 0.94067 | a | | 51 | 6 | Accept | 0.01608 | 9.7893 | 0.015555 | 0.013937 | 27 | 8.5051 | r | 98 | 0.0014041 | o | | 52 | 6 | Accept | 0.046612 | 0.75998 | 0.015555 | 0.013516 | 6 | 3.6319 | r | 15 | 0.050078 | o | | 53 | 6 | Accept | 0.026378 | 3.9473 | 0.015555 | 0.013503 | 5 | 5.451 | s | 86 | 2.2645e-05 | o | | 54 | 6 | Accept | 0.01652 | 5.525 | 0.015555 | 0.013616 | 6 | 3.4626 | r | 99 | 0.0042698 | o | | 55 | 6 | Accept | 0.023626 | 4.3491 | 0.015555 | 0.013606 | 6 | 0.87113 | s | 90 | 4.9252e-06 | o | | 56 | 6 | Accept | 0.035756 | 1.5968 | 0.015555 | 0.013244 | 11 | 2.0662 | r | 26 | 3.9009e-05 | o | | 57 | 6 | Accept | 0.031252 | 9.0684 | 0.015555 | 0.013039 | 331 | 2.3022 | r | 11 | 3.3415e-05 | o | | 58 | 6 | Accept | 0.072441 | 12.75 | 0.015555 | 0.013042 | 492 | 2.5934 | r | 11 | 0.72574 | a | | 59 | 6 | Accept | 0.02269 | 126.16 | 0.015555 | 0.013115 | 491 | 8.0628 | r | 99 | 0.16601 | o | | 60 | 6 | Accept | 0.039891 | 11.467 | 0.015555 | 0.01292 | 497 | 4.2759 | r | 9 | 0.0019962 | o |
__________________________________________________________
Optimization completed.
MaxObjectiveEvaluations of 60 reached.
Total function evaluations: 60
Total elapsed time: 210.4583 seconds
Total objective function evaluation time: 831.0775
Best observed feasible point:
iterlim lambda solver q lambdareg coding
_______ _______ ______ __ __________ ______
9 0.74158 r 97 0.00043623 o
Observed objective function value = 0.015555
Estimated objective function value = 0.019291
Function evaluation time = 7.6923
Best estimated feasible point (according to models):
iterlim lambda solver q lambdareg coding
_______ ______ ______ __ _________ ______
27 8.5051 r 98 0.0014041 o
Estimated objective function value = 0.01292
Estimated function evaluation time = 8.4066
toc
Elapsed time is 211.892362 seconds.
warning('on','stats:classreg:learning:fsutils:Solver:LBFGSUnableToConverge');
The resulting classifier has similar loss (the "Observed objective function value") compared to the classifier using rica for 100 features trained for 400 iterations. To use this classifier, retrieve the best classification model found by bayesopt.
t = templateLinear('Lambda',results.XAtMinObjective.lambda,'Solver','lbfgs'); if results.XAtMinObjective.coding == "o" Cmdl = fitcecoc(NewX,LabelTrain,Learners=t,Coding='onevsone'); else Cmdl = fitcecoc(NewX,LabelTrain,Learners=t,Coding='onevsall'); end
See Also
rica | sparsefilt | ReconstructionICA | SparseFiltering
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