Complete first draft for part 1

1 files changed, 42 insertions, 5 deletions

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@@ -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