Fits the SVC with a set of observations. Args: observations (list[ndarray]): list of observations classes (ndarray): classification of each observation (in {1, -1})
(self, observations: list[ndarray], classes: ndarray)
| 99 | return np.exp(-(self.gamma * norm_squared(vector1 - vector2))) |
| 100 | |
| 101 | def fit(self, observations: list[ndarray], classes: ndarray) -> None: |
| 102 | """ |
| 103 | Fits the SVC with a set of observations. |
| 104 | |
| 105 | Args: |
| 106 | observations (list[ndarray]): list of observations |
| 107 | classes (ndarray): classification of each observation (in {1, -1}) |
| 108 | """ |
| 109 | |
| 110 | self.observations = observations |
| 111 | self.classes = classes |
| 112 | |
| 113 | # using Wolfe's Dual to calculate w. |
| 114 | # Primal problem: minimize 1/2*norm_squared(w) |
| 115 | # constraint: yn(w . xn + b) >= 1 |
| 116 | # |
| 117 | # With l a vector |
| 118 | # Dual problem: maximize sum_n(ln) - |
| 119 | # 1/2 * sum_n(sum_m(ln*lm*yn*ym*xn . xm)) |
| 120 | # constraint: self.C >= ln >= 0 |
| 121 | # and sum_n(ln*yn) = 0 |
| 122 | # Then we get w using w = sum_n(ln*yn*xn) |
| 123 | # At the end we can get b ~= mean(yn - w . xn) |
| 124 | # |
| 125 | # Since we use kernels, we only need l_star to calculate b |
| 126 | # and to classify observations |
| 127 | |
| 128 | (n,) = np.shape(classes) |
| 129 | |
| 130 | def to_minimize(candidate: ndarray) -> float: |
| 131 | """ |
| 132 | Opposite of the function to maximize |
| 133 | |
| 134 | Args: |
| 135 | candidate (ndarray): candidate array to test |
| 136 | |
| 137 | Return: |
| 138 | float: Wolfe's Dual result to minimize |
| 139 | """ |
| 140 | s = 0 |
| 141 | (n,) = np.shape(candidate) |
| 142 | for i in range(n): |
| 143 | for j in range(n): |
| 144 | s += ( |
| 145 | candidate[i] |
| 146 | * candidate[j] |
| 147 | * classes[i] |
| 148 | * classes[j] |
| 149 | * self.kernel(observations[i], observations[j]) |
| 150 | ) |
| 151 | return 1 / 2 * s - sum(candidate) |
| 152 | |
| 153 | ly_contraint = LinearConstraint(classes, 0, 0) |
| 154 | l_bounds = Bounds(0, self.regularization) |
| 155 | |
| 156 | l_star = minimize( |
| 157 | to_minimize, np.ones(n), bounds=l_bounds, constraints=[ly_contraint] |
| 158 | ).x |
no outgoing calls
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