how to reverse normalized data after kmeans clustering in matlab

how to reverse normalized data after kmeans clustering in matlab

[Luvsan Purev]

I built a kmeans cluster where I first normalized. The model provides me with cluster centers, but they are obviously in their normalized state (center of income is -0.5).

I want to convert that -0.5 back into a non-normalized value to be able to give it a practical meaning

[Luvsan Purev]

original data =[...
    22704	94
63575	81
25026	72
31510	88
21864	90
32162	95
31585	95
20126	92
39525	97
58691	87
34870	91
28052	89
15122	94
10185	80
30220	95
9066	69
36450	93
8704	67
15140	78
38380	87
15470	85
27553	90
13349	92
11857	71
43514	96];

[Luvsan Purev]

normalized data

-0.324716668157071 0.803729170410423

2.50865116793338 -0.631501491036761

-0.163744827110803 -1.62512271819250

0.285756213950352 0.141315018973261

-0.382949375512310 0.362119736118982

0.330955886802275 0.914131528983283

0.290955562821355 0.914131528983283

-0.503435620016365 0.582924453264702

0.841393296631591 1.13493624612900

2.17006956945363 0.0309126604004010

0.518687043371308 0.472522094691842

0.0460315686712842 0.251717377546122

-0.850336176689717 0.803729170410423

-1.19259198170497 -0.741903849609621

0.196327413369092 0.914131528983283

-1.27016626686035 -1.95632979391108

0.628219992920448 0.693326811837563

-1.29526179074439 -2.17713451105680

-0.849088332960676 -0.962708566755341

0.762016570534271 0.0309126604004010

-0.826211197928261 -0.189892056745320

0.0114385675162077 0.362119736118982

-0.973248784000240 0.582924453264702

-1.07668116420740 -1.73552507676536

1.11792933191736 1.02453388755614

[Luvsan Purev]

after kmeans result

[Luvsan Purev]

how to reverse normalized data after kmeans clustering in matlab

[Luvsan Purev]

c =

-0.9534 -1.3412

0.3708 0.5216

Answer 1

[Image Analyst]

I don't believe that's true. The centroids are the actual centroids, unless you've normalized your data beforehand. Here's proof:

x = [60*rand(100, 1), 90 + 100*rand(100, 1)];
y = [30*rand(100, 1), 60+50*rand(100, 1)];
plot(x, y, '.', 'MarkerSize', 15);
grid on;
[classIndexes, classCentroids] = kmeans([x(:), y(:)], 2)

classIndexes = 200×1

1 1 1 1 1 1 1 1 1 1

classCentroids = 2×2

30.6948 14.8815 139.6902 84.3660

% Plot centroids as magenta crosshairs
hold on
plot(classCentroids(1,1), classCentroids(1,2), 'm+', 'MarkerSize', 150, 'LineWidth', 3)
plot(classCentroids(2,1), classCentroids(2,2), 'm+', 'MarkerSize', 100, 'LineWidth', 3)

[Luvsan Purev]

centroid

c =

-0.4367 0.1155

1.7468 -0.4619

[Luvsan Purev]

how to reverse normalized matrix

Answer 2

[Image Analyst]

Try this:

% Initialization steps.
clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
clear;  % Erase all existing variables. Or clearvars if you want.
workspace;  % Make sure the workspace panel is showing.
format long g;
format compact;
fontSize = 20;
markerSize = 30;
data =[...
    22704	94
    63575	81
    25026	72
    31510	88
    21864	90
    32162	95
    31585	95
    20126	92
    39525	97
    58691	87
    34870	91
    28052	89
    15122	94
    10185	80
    30220	95
    9066	69
    36450	93
    8704	67
    15140	78
    38380	87
    15470	85
    27553	90
    13349	92
    11857	71
    43514	96];
% Plot original data.
x = data(:, 1);
y = data(:, 2);
subplot(2, 2, 1);
plot(x, y, '.', 'MarkerSize', 15);
grid on;
title('Original, unscaled and unclassified data', 'FontSize',fontSize)
% First do kmeans with original data.
[classIndexes, classCentroids] = kmeans([x(:), y(:)], 2)
subplot(2, 2, 2);
plot(x(classIndexes == 1), y(classIndexes == 1), 'r.', 'MarkerSize', markerSize);
hold on;
plot(x(classIndexes == 2), y(classIndexes == 2), 'b.', 'MarkerSize', markerSize);
grid on;
% Plot centroids as magenta crosshairs
hold on
plot(classCentroids(1,1), classCentroids(1,2), 'm+', 'MarkerSize', 150, 'LineWidth', 3)
plot(classCentroids(2,1), classCentroids(2,2), 'm+', 'MarkerSize', 100, 'LineWidth', 3)
caption = sprintf('2 clusters and their centroids\nas determined from original (NOT normalized) data')
title(caption, 'FontSize',fontSize)
% Now kmeans with normalized data
[Nx, Cx, Sx] = normalize(x)
[Ny, Cy, Sy] = normalize(y)
[classIndexesN, classCentroidsN] = kmeans([Nx(:), Ny(:)], 2);
% Plot normalized data in lower left plot.
subplot(2, 2, 3);
plot(Nx(classIndexesN == 1), Ny(classIndexesN == 1), 'r.', 'MarkerSize', markerSize);
hold on;
plot(Nx(classIndexesN == 2), Ny(classIndexesN == 2), 'b.', 'MarkerSize', markerSize);
grid on;
% Plot centroids as magenta crosshairs over normalized data.
hold on
x1N = classCentroidsN(1,1);
y1N = classCentroidsN(1,2);
x2N = classCentroidsN(2,1);
y2N = classCentroidsN(2,2);
plot(x1N, y1N, 'm+', 'MarkerSize', 150, 'LineWidth', 3)
plot(x2N, y2N, 'm+', 'MarkerSize', 100, 'LineWidth', 3)
caption = sprintf('2 clusters and their centroids\nas determined from normalized data')
title(caption, 'FontSize',fontSize)
% Now unnormalize the location of the classCentroids
x1 = x1N * Sx + Cx
y1 = y1N * Sy + Cy
x2 = x2N * Sx + Cx
y2 = y2N * Sy + Cy
% Plot original data with class colors.
subplot(2, 2, 4);
plot(x(classIndexesN == 1), y(classIndexesN == 1), 'r.', 'MarkerSize', markerSize); % Plot class 1 in red
grid on;
hold on;
plot(x(classIndexesN == 2), y(classIndexesN == 2), 'b.', 'MarkerSize', markerSize); % Plot class 2 in blue
plot(x1, y1, 'm+', 'MarkerSize', 100, 'LineWidth', 3)
plot(x2, y2, 'm+', 'MarkerSize', 100, 'LineWidth', 3)
caption = sprintf('2 clusters and their centroids\nas determined from normalized data')
title(caption, 'FontSize',fontSize)

Here I show you how to normalize the data, do kmenas, and then unnormalize the centroid to the original, unnormalized location. But you need to realize that what class a point is assigned by kmeans depends on whether the data was normalized or not. Look at the data in the upper left and lower left -- which dots are in each class changes. The classes it decided to assign are different in the two cases, and thus the centroids are in different locations. In a case like this where the x axis values are so huge compared to the y values, it's probably best to normalize the data first, and then unnormalize if you want the centroids back in the original scale space.