Yet another regression task for you. It seems, I did not get over it. This time with only one twist: "Pea-Sea-Yeah". Hints on how to do it can be found in it. Also, I intentionally did not provide you with a skeleton jupyter notebook template to start. You are all grown up now. I trust you. Cheers!
PA3--Fall-2021.pdf
Download PA3--Fall-2021.pdf
* Dataset files mentioned in the description above:
wiki_labeled.zip
Download wiki_labeled.zip
wiki_labeled.mat
Download wiki_labeled.mat
wiki_judge_images.zip
Download wiki_judge_images.zip
wiki_judgeX.mat
Download wiki_judgeX.mat
Age prediction from facial images In this assignment you are going to develop a program (in python) that would be able to guess age of a person given his/her photo. Roughly speaking, it is expected that you will first do the principal component analysis (PCA) to perform dimensionality reduction of the given dataset. Then, train a linear regression model on the reduced-dimension dataset to learn their age. Done! Backgrounds on PCA Problems arise when performing learning in a higher-dimensional space due to the phenomenon known as “Curse of the dimensionality” (https://en.wikipedia.org/wiki/Curse_of_dimensionality). Significant improvements can be achieved by first mapping the data into a lower-dimensional space. And you already have heard about principal component analysis, which is a fantastic method to do the same. In image learning paradigm, principal components obtained from the given images are affectionately called the “eigenfaces”. Page 1 n2×1 vector, Γ n×n image, I ������� �� ����� 5��� ���� ����������� �������� " https://en.wikipedia.org/wiki/Curse_of_dimensionality Suppose Γ is an n2×1 vector, corresponding to an n×n face image, I . Now the steps to compute the eigenfaces (i.e., the principal components): Step 1: Obtain the 2D face images, I1, I 2, ..., I m (the training faces). All faces must be of the same resolution. Step 2: Represent every image Ii as a vector Γi (as shown in the figure on the previous page) Step 3: Compute the average face vector, Ψ , dimension of which is n2×1 : Ψ= 1 m ∑i=1 m Γ i Step 4: Subtract the mean face from the original faces. This step is very essential, and is called to centerize the data. Φi=Γi−Ψ , It is also a n 2×1 dimensional vector. Step 5: If the matrix, A is represented as: A=[Φ1 T Φ2 T ⋮ Φm T ] , and it is certainly an m×n2 matrix, then compute the covariance matrix, C : C= 1 m−1∑i=1 m Φi T ΦT= 1 m−1 AT A , which is an n×n matrix. Step 6: Compute the eigenvectors ui of A T A . The dimension of each of the eigenvector will be n2 . For some reason, if you see that the dimension of AT A becomes very large, find the eigenvectors, v i of AA T instead. It can be proved that AT A and AAT have the same eigenvalues and their eigenvectors are related through this formula: ui=Av i . (The Proof can be found here: http://www.vision.jhu.edu/teaching/vision08/Handouts/case_study_pca1.pdf ) Step 7: Keep only K eigenvectors, corresponding to the K largest eigenvalues. Now you have it! You have got K eigenfaces (a.k.a., principal components). Since each of the K eigenfaces are essentially n2 dimensional vectors, out of curiosity if you do reshape the eigenfaces to n×n and display them as images, you will be astonished (or get scared!! haha) to see the eigenfaces. They may look like ghosts! Rumor has it: you will be able to recover a human from these ghosts. Just joking! But, I would like to make a note on a property of PCA that makes it one of the most beautiful (and extraordinary) algorithm. Each of the centered image, Φi in the training dataset can be represented as a linear combination of the best K (ghosts) eigenvectors (i.e., eigenfaces): Page 2 http://www.vision.jhu.edu/teaching/vision08/Handouts/case_study_pca1.pdf Step 8: So, let’s project all the original faces (after centering) from the training dataset onto this eigenfaces direction: Φ̂i=∑ j=1 K w j i u j=∑ j=1 K u j T Φiu j Here, we are projecting our original faces onto a subset of K eigenfaces, thus reducing each image from n2 dimensions down to a vector Ω of only K dimensions. Each of the normalized training face Φi is projected onto the eigenfaces by a vector, Ω i=[ w1 i w2 i ⋮ wK i ]=[ u1 T Φ i u2 T Φ i ⋮ uK T Φi ] . The images can then be reconstructed in n2 dimensions from the K dimensional Ω encodings, with some loss in accuracy, using the formula above, or if you need more elaboration, here it is: Reconstructured image=Φ̂i=(Ω1 i u1+Ω2 i u2+⋯+ΩK i uK ) More resources on this topic can be found here: https://mikedusenberry.com/on-eigenfaces Please proceed to the next page to find your assignment! Cheers!! Page 3 Illustration 1: An example of 4 eigenfaces Illustration 2: Any image from the training dataset can be represented as a linear combination of the best K eigenfaces. https://mikedusenberry.com/on-eigenfaces Now your assignment: Please show your works (codes+execution results) by leaving/saving the execution results in a submitted jupyter notebook. • ID: identification number of the subject (starting from 2002) • dob: the date of birth of the subject. (It is Matlab’s datenum value calculated based on total number of days since January 0, 0000.) • dob_str: the DD-MMM-YYYY format dob value. • photo_taken: when the photo was taken (only the year value) • full_path: directory path, including filename of the image • gender: Gender of the subject (0: female, 1: male, NaN if unknown) • name: name of the subject • face_location: location of the face. • face_score: detector score (the higher the better). Inf implies that no face was found in the image, and the face_location then just returns the entire image. • second_face_score: detector score of the face with the second highest score. This is useful to ignore images with more than one face. second_face_score is NaN (not a number) if no second face was detected. • age: age of the person (in years), and was calculated based on the “dob” value and the “photo_taken” values. Hint: To read/extract information from the mat file above, please use the loadmat library from scipy.io in python . [ from scipy.io import loadmat ] 2. Randomly split the dataset into 80% training and 20% test sets. 3. Compute the principal components (i.e., eigenfaces) from the training dataset by following the steps to compute principal components described in the “Backgrounds” section. Please note that: you can not call a library function to directly compute the principal components. For example: the PCA library in sklearn. However, you can use library functions to calculate the eigenvalues and eigenvectors of a square matrix. 4. Draw a scree-plot to choose a best value for K that denotes how many principal components to retain. 5. Show the top 20 ghosts (i.e., eigenfaces) in a 10x10 grid. 6. Considering the chosen K value above, project the training and test images on to the eigenfaces to reduce the dimensionality. Page 4 A# '� !� � ��������� � ������ ������� � D,� ���� ����� �� ������ �� ��� � ������ ������� �� ��� � .���/# '����� �� � � ���+���+� � ��� �� �� ���� ��� ���� +�� ����� � �! ��� D, ���� ����� �� ������ ��#�#� ��� � �! ������� ��� ���� ����� ��� ��%� � ���� ��� ��� ������ � �����!�� ��� �! ���� +�� ����� �# :�� � � ������� �� ��� ���%��+��� � �� � � �� �� ��� �� ������# �# 5 �� (����� �������� ���������������� � ��� �&� ��� ��� ��������# *�� ��%�1�� ����" �� ���� � ���� �������� B�?�A !����� ������ %��� �� ��� !���� �� ������ ��+��# ,�������� �! ���� ����� �� ��� ��&��� � ��� ��&���# )���� �������� ��� ���������������� !���� ���������� ���� ��!� ������ �! ���� �! ��� B�?�A ������0 8. Predict the test dataset (from step 2) based on the learned model in step 7, and report Root Mean Square Error (RMSE). ID,age 1,38.8 2,25 etc. 10. Repeat steps 2-8 four more times, and report average RMSE and standard deviation of the RMSE. Please make sure in step 2 you are actually randomly shuffling the dataset before splitting it every time. 11. Draw a plot (K vs RMSE) after experimenting with steps 2-8 by varying values of K. The maximum value K can take is 100x100 = 10000, so please draw the plot for the K values from the set {2, 10, 20, 40, 50, 60, 80, 100, 200}. Page 5 ��� ����� !"# � ���� � !" #$%& '()*(+ ,%-).%(, /01 !"#"$%&'()$"*+(),-."/ 2 !"#$%&#&#' ())* +%!&%, &-%'./ 0*12#'3 (12#'3 43 ())*12#'5 "+ 6./",7$&"# *))8*))1 9"7 !%# " $%&# %#"$;.6 -.$% +&,.3 !"#"$%&'()*+,-. 0-<= 7-=""> ?@A(+<)@ a+!)="=?=" =?)*!)..!(="5" +6"-="" b%#c%/="" !"#$%&#&#'="" "-.="" &#+"6-%$&"#="" %="" "7$="" $;.="" &-%'./1="" d"e.c.63="" $;.="" &#+"6-%$&"#=""><". #"$=""><. f%'.g=""><1 h/&#'="" i"76="" ./$="" 6.'6.//&"#=""><.,3><&!$ %'.="" "+="" .%!;="" "+="" $;.="" ())*="" +%!&%,="" &-%'.3="">< 26.2%6.="" %="" &0,"//"1="" +3/4="" +&,.="" e&$;="" $;.="" +",,"e&#'="" b="" k="" +"6-%$=""> Ashis Kumer Biswas Ashis Kumer Biswas Submit submission.csv along with the jupyter notebook. Programming Assignment 2 Age prediction from facial images Backgrounds on PCA Now your assignment: Please show your works (codes+execution results) by leaving/saving the execution results in a submitted jupyter notebook. For CSCI-5930 students (and extra-credit for CSCI-4930) Extra-credit for both CSCI-4930 and 5930