an input module configured to receive sample data x;

a data collection module connected to the input module and configured to store a collection of data Ω⊂^p from the input module, the collection of data Ω⊂^p including a training set Ω_tr and a test set Ω_tt, wherein the collection of data Ω⊂^p is composed of m memberships or categories of elements, and the m memberships or categories are digitized as 1, 2, . . . , m, m is greater or equal to 2;

a quadratic multiform separation engine connected to the data collection module and configured to use m q-dimensional member functions f₁, . . . , f_m generated through a learning process based on the training set Ω_tr to perform classification, wherein each q-dimensional member function is defined as a quadratic function f having a form ∥Ax−b∥², for an integer q, a constant matrix A∈^q×p, and a constant vector b∈^q, where ∥·∥ denotes the Euclidean norm, thus m trained q-dimensional member functions f₁, . . . , f_m have expressions f₁(x)=∥A₁x−b₁∥², f₂(x)=∥A₂x−b₂∥², . . . , f_m(x)=∥A_mx−b_m∥², where trained matrices of constant matrices A₁, . . . , A_m and trained vectors of constant vectors b₁, . . . , b_m are solved through the learning process; wherein in the learning process, m² control parameters α_jk, j=1, . . . , m, k=1, . . . , m are set between 0 and 1, and each control parameter α_jk is used to compare with a ratio

an output module connected to the quadratic multiform separation engine and configured to derive an output result after the sample data x is processed through the quadratic multiform separation engine.