Regarding Lagrange Multiplier in SVM

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charu shree
charu shree 2023-3-23
回答： Parag 2025-4-10
Hello all, In my work I am using SVM for classification. I had trained the SVM classifier and also obtained the Lagrangian multiplier (α) which is a column vector .
My query is how we can use this Lagrangian multiplier (α) to predict the labels of the data points.
Any help in this regard will be highly appreciated.
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charu shree
charu shree 2023-3-24
Thank you sir for your response....
I am using the paper " Supervised Learning-Based Semi-Blind Detection for Generalized Space Shift Keying MIMO Systems" for my work.
I am using SVM method for classification. The SVM classifier is trained using the training data in vector having dimension , the labels in vector having dimension .
So as per equation (5) of this paper, I had obtained 16 different α of dimension .
My query in mathematical form is as follows:
How can I predict the labels of the test data say in vector having dimension 404 x 4 ?
charu shree
charu shree 2023-3-24
Any hint will help me in moving ahead in tackling this problem...

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回答（1 个）

Parag
Parag 2025-4-10
Hi @charu shree,
To predict the labels for your test data (e.g., a 404 × 4 matrix), using SVM trained in a one-vs-all setting with 16 classifiers, you can follow this approach:
  • Each SVM classifier corresponds to one class and provides a decision score using the learned parameters (α, support vectors, labels, and bias).
  • For each test vector, compute the decision score from all 16 classifiers using the kernel function (e.g., linear).
  • Stack all scores in a matrix of size 404 × 16.
  • Assign each test vector the class label of the classifier with the highest score (i.e., maximum margin decision function output).
This approach implements the standard prediction step in multi-class SVM, aligned with the formulation in the paper.
% Inputs (assumed precomputed and available):
% X_test : 404 x 4 test data matrix
% supportVectors : N x 4 training vectors
% alpha : 1x16 cell array, each cell contains alpha vector for a class
% labels : N x 16 label matrix in one-vs-all format (+1/-1 per class)
% b : 16 x 1 bias vector for each classifier
numTest = size(X_test, 1);
numClasses = 16;
F = zeros(numTest, numClasses); % Stores decision scores
for k = 1:numClasses
% Linear kernel: dot product
K = X_test * supportVectors'; % 404 x N
F(:, k) = K * (alpha{k} .* labels(:, k)) + b(k);
end
% Predict class with highest score
[~, predicted_labels] = max(F, [], 2); % Output: 404 x 1 vector of predicted classes
Hope it helps!

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