Method for learning data classification in two separate classes separated by a region divider of order 1 or 2
First Claim
1. A method for teaching a neurone with a quadratic activation function to classify data according to two distinct classes (c11, c12) separated by a separating surface (S), this neurone being a binary neurone having N connections coming from an input and receiving as an input N numbers representing a data item intended to be classified using a learning base containing a plurality of known data, each input of the neurone being affected by a weight (wi) of the corresponding connection,characterised in that it includes the following steps:
- a) defining a cost function (Cσ
) by determining, as a function of a parameter describing the separating surface, a stability (γ
μ
) of each data item (μ
) of the learning base, the cost function being the sum of all the costs determined for all the data in the learning base with;
where A is any value, B is any positive real number, P is the number of data items in the learning base, γ
μ
is the stability of the data item μ
, and T+, T− and
σ
are two parameters of the cost function;
b) initialising the weights (wi), the radii (ri), the parameters (T+ and T−
, with T+<
T−
), a learning rate ε and
speeds of the temperature decreasing (δ
T+ and δ
T−
);
c) minimising, with respect to the weight of the connections (Wi) and the radii (ri), the cost function (Cσ
) by successive iterations during which the parameters (T+ and T−
) decrease at speeds of the temperature decreasing (δ
T+ and δ
T−
) as far as a predefined stop criterion;
d) obtaining values of the weights of the connections and the radii of the neurone.
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Abstract
A method for learning to classify data according to two distinct classes (c11, c12) separated by a separating surface (S), by means of a neurone of the binary type comprising a parameter describing the separating surface and whose inputs are weighted by a weight (wi), and including the following steps:
a) defining a cost function C:
b) initializing the weights (Wi), the radii (ri), the parameters (σ, T+, T−), the learning rate (ε) and speeds of the temperature decreasing (δT+, δT−);
c) minimizing the cost function C by successive iterations;
d) obtaining the values of the weights of the connections and radii of the neurone.
Application to the classification and recognition of shapes by a neural network.
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Citations
3 Claims
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1. A method for teaching a neurone with a quadratic activation function to classify data according to two distinct classes (c11, c12) separated by a separating surface (S), this neurone being a binary neurone having N connections coming from an input and receiving as an input N numbers representing a data item intended to be classified using a learning base containing a plurality of known data, each input of the neurone being affected by a weight (wi) of the corresponding connection,
characterised in that it includes the following steps: -
a) defining a cost function (Cσ
) by determining, as a function of a parameter describing the separating surface, a stability (γ
μ
) of each data item (μ
) of the learning base, the cost function being the sum of all the costs determined for all the data in the learning base with;
where A is any value, B is any positive real number, P is the number of data items in the learning base, γ
μ
is the stability of the data item μ
, and T+, T− and
σ
are two parameters of the cost function;
b) initialising the weights (wi), the radii (ri), the parameters (T+ and T−
, with T+<
T−
), a learning rate ε and
speeds of the temperature decreasing (δ
T+ and δ
T−
);
c) minimising, with respect to the weight of the connections (Wi) and the radii (ri), the cost function (Cσ
) by successive iterations during which the parameters (T+ and T−
) decrease at speeds of the temperature decreasing (δ
T+ and δ
T−
) as far as a predefined stop criterion;
d) obtaining values of the weights of the connections and the radii of the neurone. - View Dependent Claims (2, 3)
where μ
is the label of the pattern, xμ
i is the value of the pattern μ
for the ith input, yμ
is the class of the pattern μ
, N is the number of inputs and connections of the neurone, wi is the weight of the connection between the input i and the neurone and rj the radius parameter for the ith input.
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3. A method according to claim 1, characterised in that the stability of each data item is
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μ = y μ [ ∑ i = 1 N [ ( w i - x i μ ) 2 - r i 2 ] ] where μ
is the label of the pattern, xμ
i is the value of the pattern μ
for the ith input, yμ
is the class of the pattern μ
, N is the number of inputs and connections of the neurone, wi is the weight of the connection between the input i and the neurone and ri is the radius parameter for the ith input.
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Specification