原文來自我的獨立blog：http://www.yuanyong.org/blog/cv/lsh-itq-sklsh-compliment
這兩天尋找idea，想來思去也沒想到好點的方法，於是把前段時間下過來的一篇《Iterative Quantization: A Procrustean Approach to Learning Binary Codes》和代碼拿出來又細讀了一番，希望可以從中獲得點啟發。
Iterative Quantization: A Procrustean Approach to Learning Binary Codes的Project請戳這里，一作是Yunchao Gong，師從Svetlana Lazebnik，第一次聽說Svetlana Lazebnik是一次在提取圖像特征時立超師兄說可以用Spatial Pyramid特征，說Svetlana Lazebnik自信得直接是”Beyond Bags of Features: ……”（超越BOW），然后下去看了一下大牛的homePage，所以對Svetlana Lazebnik有些印象。扯遠了，回歸正題。代碼下載下來后，發覺paper里做好的數據庫並沒提供，有需要請戳這里下載：代碼與數據庫。解壓文件，比較重要的有三個，cca.m、ITQ.m、RF_train.m、recall_precision.m。
實驗評價方案recall_precision.m跟我之前用過的一個評價方案不同，花了大半個下午，85%的弄明白了這個recall_precision.m評價方案。先理理一下已經完全整明白了的LSH吧。
表1
表1是對不同編碼方法的說明，從表中可以看出LSH的哈希函數是 sgn(wTx+b) 。實際上，對於采用哈希方法做檢索，分兩個階段：(1). 投影階段(Projection Stage); (2). 量化階段(Quantization Stage)。LSH投影矩陣(即哈希系列函數)是隨機產生的。Matlab中生成投影矩陣為: w=randn(size(X,2), bit), X∈Rn×d ，bit是編碼位數， g1↔w1=w(:,1) ， g2↔w2=w(:,2) ，···， gn↔wn=w(:,L) 。對於 xx ，通過 w 投影后經過閾值化(量化)后映射到哈希桶中。
1. 對於原空間數據，對於進行中心化(centre the data)后在量化階段閾值變為0，整個壓縮編碼的代碼為：
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XX = XX * randn(size(XX,2),bit); |
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Y = zeros(size(XX)); |
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Y(XX>=0)=1; %原數據中心化后，閾值設為0。大於0編碼為1，小於0編碼為0 |
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Y = compactbit(Y); %將二進制用十進制表示 |
表1中對於LSH的投影過程(Projection)是數據獨立(data-independent)，對於data-independent，[2]中指出”Generally,data-independent methods need longer codes than data-dependent methods to achieve satisfactory performance”，即要獲得比數據非獨立方法一樣滿意的表現，數據獨立方法需要更長的編碼。
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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Function: this is a geometric illustration of Draw the recall precision curve |
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%Author: Willard (Yuan Yong' English Name)%Date: 2013-07-22 |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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close all; |
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clear variables; |
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clc; |
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load cifar_10yunchao.mat; |
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X=cifar10; |
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X=X(:,1:end-1); |
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%Get the recall & precision |
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[recall{1,1}, precision{1,1}] = test(X, 16, 'LSH'); |
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[recall{1,2}, precision{1,2}] = test(X, 24, 'LSH'); |
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[recall{1,3}, precision{1,3}] = test(X, 32, 'LSH'); |
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[recall{1,4}, precision{1,4}] = test(X, 64, 'LSH'); |
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[recall{1,5}, precision{1,5}] = test(X, 128, 'LSH'); |
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% Draw the plot |
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figure; hold on;grid on; |
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plot(recall{1, 1}, precision{1, 1},'g-^','linewidth',2); |
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plot(recall{1, 2}, precision{1, 2},'b-s','linewidth',2); |
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plot(recall{1, 3}, precision{1, 3},'k-p','linewidth',2); |
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plot(recall{1, 4}, precision{1, 4},'m-d','linewidth',2); |
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plot(recall{1, 5}, precision{1, 5},'r-o','linewidth',2); |
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xlabel('Recall'); |
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ylabel('Precision'); |
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legend('LSH-16 bit','LSH-24 bit','LSH-32 bit','LSH-64 bit','LSH-128 bit','Location','NorthEast'); |
圖1
從圖1可以看出，PCA-ITQ比PCA-RR、LSH、SKLSH表現性能要佳。ITQ的代碼還在分析中，希望可以從中獲得點啟示。
2. PCA-ITQ, PCA-RR, LSH, SKLSH對比實驗
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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% Function: this is a geometric illustration of Draw the recall precision curve |
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%Author: Willard (Yuan Yong' English Name) |
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%Date: 2013-07-22 |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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close all; |
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clear variables; |
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clc; |
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load cifar_10yunchao.mat; |
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X=cifar10; |
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X=X(:,1:end-1); |
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bit=32; |
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%Get the recall & precision |
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[recall{1,1}, precision{1,1}] = test(X, bit, 'ITQ'); |
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[recall{1,2}, precision{1,2}] = test(X, bit, 'RR'); |
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[recall{1,3}, precision{1,3}] = test(X, bit, 'LSH'); |
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[recall{1,4}, precision{1,4}] = test(X, bit, 'SKLSH'); |
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% Draw the plot |
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figure; hold on;grid on; |
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plot(recall{1, 1}, precision{1, 1},'r-o','linewidth',2); |
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plot(recall{1, 2}, precision{1, 2},'b-s','linewidth',2); |
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plot(recall{1, 3}, precision{1, 3},'k-p','linewidth',2); |
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plot(recall{1, 4}, precision{1, 4},'m-d','linewidth',2); |
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plot(recall{1, 5}, precision{1, 5},'g-^','linewidth',2); |
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xlabel('Recall');ylabel('Precision');legend('PCA-ITQ','PCA-RR','LSH','SKLSH','Location','NorthEast'); |
圖2
3. PCA-ITQ檢索實例實驗主要代碼：
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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% Function: this is a PCA-ITQ demo showing the retrieval sample |
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%Author: Willard (Yuan Yong' English Name) |
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%Date: 2013-07-23 |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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clear all; |
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clc; |
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% parameters |
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bit=32; |
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averageNumberNeighbors = 50; % ground truth is 50 nearest neighbor |
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num_test = 1000; % 1000 query test point, rest are database |
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load cifar_10yunchao.mat; |
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[ndata, D] = size(cifar10); |
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Xtraining= double(cifar10(1:59000,1:end-1)); |
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Xtest = double(cifar10(59001:60000,1:end-1)); |
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num_training = size(Xtraining,1); |
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% generate training ans test split and the data matrix |
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XX = [Xtraining; Xtest]; |
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% center the data, VERY IMPORTANT |
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sampleMean = mean(XX,1); |
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XX = (double(XX)-repmat(sampleMean,size(XX,1),1)); |
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% PCA |
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[pc, l] = eigs(cov(XX(1:num_training,:)),bit); |
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XX = XX * pc; |
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% ITQ |
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[Y, R] = ITQ(XX(1:num_training,:),50); |
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XX = XX*R; |
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Y = zeros(size(XX)); |
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Y(XX>=0) = 1; |
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Y = compactbit(Y>0); |
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% compute Hamming metric and compute recall precision |
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B1 = Y(1:size(Xtraining,1),:); %編碼后的訓練樣本 |
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B2 = Y(size(Xtraining,1)+1:end,:);%編碼后的測試樣本 |
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Dhamm = hammingDist(B2, B1); |
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[foo, Rank] = sort(Dhamm, 2,'ascend'); %foo為漢明距離按每行由小到大排序 |
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% show retrieval images |
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load cifar-10-batches-mat/data_batch_1.mat; |
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data1=data; |
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labels1=labels; |
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clear data labels; |
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load cifar-10-batches-mat/data_batch_2.mat; |
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data2=data; |
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labels2=labels; |
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clear data labels; |
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load cifar-10-batches-mat/data_batch_3.mat; |
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data3=data; |
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labels3=labels; |
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clear data labels; |
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load cifar-10-batches-mat/data_batch_4.mat; |
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data4=data; |
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labels4=labels; |
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clear data labels; |
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load cifar-10-batches-mat/data_batch_5.mat; |
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data5=data; |
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labels5=labels; |
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clear data labels; |
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load cifar-10-batches-mat/test_batch.mat; |
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data6=data; |
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labels6=labels; |
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clear data labels; |
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database=[data1 labels1 ;data2 labels2;data3 labels3;data4 labels4;data5 labels5;data6 labels6]; |
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cifar10labels=[labels1;labels2;labels3;labels4;labels5;labels6]; |
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%save('./data/cifar10labels.mat','cifar10labels'); |
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%index=[50001,Rank(1,1:129)]'; P001是貓 |
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%index=[50002,Rank(2,1:129)]'; P002是船 |
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%index=[59004,Rank(4,1:129)]'; Y004是貓 |
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%index=[59005,Rank(5,1:129)]'; %馬 |
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%index=[59006,Rank(6,1:129)]'; %狗 |
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%index=[59018,Rank(18,1:129)]'; % 飛機 |
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index=[59018,Rank(18,1:129)]'; % 飛機 |
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%index=[50007,Rank(7,1:129)]'; P007是automobile |
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rank=1; |
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left=0.005; |
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botton=0.895; |
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width=0.08; |
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height=0.08; |
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% show the retrieved images |
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for i=1:130 |
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j=index(i,1); |
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image1r=database(j,1:1024); |
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image1g=database(j,1025:2048); |
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image1b=database(j,2049:end-1); |
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image1rr=reshape(image1r,32,32); |
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image1gg=reshape(image1g,32,32); |
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image1bb=reshape(image1b,32,32); |
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image1(:,:,1)=image1rr'; |
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image1(:,:,2)=image1gg'; |
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image1(:,:,3)=image1bb'; |
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image1=uint8(image1); |
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if(mod(rank,13)~=0) |
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hdl1=subplot(10,13,rank,'position',[left+0.07*(mod(rank,13)-1) botton-0.09*fix(rank/13) width height]); |
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imshow(image1); |
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else |
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hdl1=subplot(10,13,rank,'position',[left+0.07*12 botton-0.09*fix(rank/14) width height]); |
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imshow(image1); |
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end |
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rank=rank+1; |
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end |
第1幅是查詢圖像，后面129是從59k的database里檢索出來的相似的圖像。
enjoy yourself~