From 89f3737a721e3566f57a67eacb44099a37b5a3b6 Mon Sep 17 00:00:00 2001 From: nunzip Date: Wed, 7 Nov 2018 23:57:17 +0000 Subject: Complete first draft for part 1 --- report/paper.md | 47 ++++++++++++++++++++++++++++++++++++++++++----- 1 file changed, 42 insertions(+), 5 deletions(-) (limited to 'report') diff --git a/report/paper.md b/report/paper.md index e201252..78e7191 100755 --- a/report/paper.md +++ b/report/paper.md @@ -82,16 +82,53 @@ obtain are the same: ##PROVE Using the computational method for fast PCA, face reconstruction is then performed. The quality of reconstruction will depend on the amount of eigenvectors picked. -The results of varying M can be observed in the picture below. A face from class -number 21 is reconstructed as shown below withrespective M values of M=10, M=100, -M=200, M=300. The last picture is the original face. +The results of varying M can be observed in the picture below. Two faces from classes +number 21 and 2 respectively, are reconstructed as shown below with respective M values +of M=10, M=100, M=200, M=300. The last picture is the original face. -![Reconstructed Face](fig/face160rec.pdf) +![Reconstructed Face C21](fig/face160rec.pdf) +![Reconstructed Face C2](fig/face10rec.pdf) It is already observable that the improvement in reconstruction is marginal for M=200 and M=300. For such reason choosing M close to 100 is good enough for such purpose. +Observing in fact the variance ratio of the principal components, the contribution +they'll have will be very low for values above 100, hence we will require a much higher +quantity of components to improve reconstruction quality. -IT HAS TO BE DONE FOR MORE FACE IMAGES +![Variance Ratio](fig/variance.pdf) + +The analysed classification methods used for face recognition are *Nearest Neighbor* and +*alternative method* through reconstruction error. +EXPLAIN THE METHODS + +REFER TO ACCURACY GRAPH 1 FOR NN. MAYBE WE CAN ALSO ADD SAME GRAPH WITH DIFFERENT K + +A confusion matrix showing success and failure cases for Nearest Neighbor classfication +can be observed below: + +![Confusion Matrix NN, K=1](fig/pcacm.pdf) + +An example of failed classification is a test face from class 2, wrongly labeled as class 5: + +![Class 2 (left) labeled as class 5 (right)](fig/failure_2_5.pdf) + +The alternative method shows overall a better performance, with peak accuracy of 73% +for M=3. The maximum M non zero eigenvectors that can be used will in this case be at most +the amount of training samples per class minus one, since the same amount of eigenvectors +will be used for each generated class-subspace. + +![Accuracy of Alternative Method varying M](fig/alternative_accuracy.pdf) + +A confusion matrix showing success and failure cases for alternative method classfication +can be observed below: + +![Confusion Matrix alternative method, M=3](fig/altcm.pdf) + +It can be observed that even with this more accurate classification, there is one instance +of mislabel of the same face of class 2 as class 5. An additional classification failure +of class 6 labeled as class 7 can be observed below: + +![Class 6 (left) labeled as class 7 (right)](fig/failure_6_7.pdf) # Cites -- cgit v1.2.3-54-g00ecf