Euclidian distance showing different result for different formula

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d = (query_feature' - train_feature').^2; % Eucledian distance
d_1 = sqrt(sum((query_feature' - train_feature') .^ 2))
The method with d is giving some error in retrieval, but when using d_1 it always give 100% accurate retrival (all retrieved images are similar as query image)
What can be wrong? Any suggestions appreciated.
new_user on 29 Dec 2021
Edited: new_user on 29 Dec 2021
db = 'CBIR';
[fn, pn] = uigetfile(db);
im = fullfile(pn, fn);
outputFlder = fullfile('Test'); %returns full path of last arugument
rootFolder = fullfile(outputFlder); %variable storing path
images_query = imageDatastore(rootFolder, 'IncludeSubfolders',true, 'LabelSource','foldernames'); %%'ReadFcn', @readCBIR
%R = imread("99 (5).jpeg"); % Read image
R = imread(im); % Read image
Input_Layer_Size_q = net.Layers(1).InputSize(1:2); % (1:2 = 1st 2 elemnts of input size), input layer size stored in this variable (Input_layer_size)
Resized_Test_image_q = augmentedImageDatastore(Input_Layer_Size_q, R, 'ColorPreprocessing','gray2rgb'); %% For defining test image replace "Testing _image with test folder
%Extract feature
train_feature = activations(net, Resized_Training_image, 'Animal Feature Learner', 'OutputAs', 'Rows');
query_feature = activations(net, Resized_Test_image_q, 'Animal Feature Learner', 'OutputAs', 'Rows');
%Equation 2
a = query_feature; % transposing
b = transpose(1-a);
%Equation 3
c = zeros(Number_of_Classes,Number_of_Training_images);
d = (query_feature' - train_feature').^2; % Eucledian distance
% d = sqrt(sum((query_feature' - train_feature') .^ 2)); % other method eucledian: giving all images from same category maybe something is wrong
for e = 1 : Number_of_Training_images
f = b.*d(:,e);
c(:, e) = f;
c = sqrt(sum(c))';
% Fetch top 25 similar images
g = sort(c);
[~, n] = sort(c);
n = n(1:50);
files = cell(1, 50);
for h =1:50
files{h} = Training_image.Files{n(h)};
%Display query image
% Display retrived images

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Answers (2)

John D'Errico
John D'Errico on 29 Dec 2021
What you write in d is simply not Euclidean distance What can be wrong? Your belief that it is so? What you write in d1 IS a Euclidean distance computation, so that it works should be no surprise.
  1 Comment
new_user on 29 Dec 2021
but giving all the time 100% retrival accuracy using pretrained CNN is ok?
I mean I am using pretrained CNN to extract features and then measuing the similarity between them using d & d_1. So, the result for d_1 are 100% always.

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Meg Noah
Meg Noah on 29 Dec 2021
Some code - look at the sizes of the arrays to see why:
nsamples = 25;
ncomponents = 4;
s = RandStream('dsfmt19937','Seed',1123581321);
query_feature = rand(s,nsamples,ncomponents);
train_feature = rand(s,1,ncomponents);
% relative vector between query vectors and training vector
d = (query_feature' - train_feature').^2;
% Three ways to compute Eucledian distance between query vectors and a
% training vector
d_1 = sqrt(sum((query_feature' - train_feature') .^ 2))';
d_2 = sqrt(sum(bsxfun(@minus, query_feature, train_feature).^2,2));
d_3 = vecnorm((query_feature'-train_feature'),2)';
Meg Noah
Meg Noah on 29 Dec 2021
The code snippet above creates the distances as vectors - arrays that are nsamples in rows and with one column. What matrix deimension is your code expecting?

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