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Fix grammar and spelling mistakes in sequential_minimum_optimization.py (#11427)
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Tianyi Zheng
GitHub
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commit
446742387e
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@ -1,11 +1,9 @@
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"""
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Implementation of sequential minimal optimization (SMO) for support vector machines
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(SVM).
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Sequential minimal optimization (SMO) for support vector machines (SVM)
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Sequential minimal optimization (SMO) is an algorithm for solving the quadratic
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programming (QP) problem that arises during the training of support vector
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machines.
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It was invented by John Platt in 1998.
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programming (QP) problem that arises during the training of SVMs. It was invented by
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John Platt in 1998.
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Input:
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0: type: numpy.ndarray.
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@ -124,8 +122,7 @@ class SmoSVM:
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b_old = self._b
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self._b = b
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# 4: update error value,here we only calculate those non-bound samples'
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# error
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# 4: update error, here we only calculate the error for non-bound samples
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self._unbound = [i for i in self._all_samples if self._is_unbound(i)]
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for s in self.unbound:
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if s in (i1, i2):
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@ -136,7 +133,7 @@ class SmoSVM:
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+ (self._b - b_old)
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)
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# if i1 or i2 is non-bound,update there error value to zero
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# if i1 or i2 is non-bound, update their error value to zero
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if self._is_unbound(i1):
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self._error[i1] = 0
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if self._is_unbound(i2):
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@ -161,7 +158,7 @@ class SmoSVM:
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results.append(result)
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return np.array(results)
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# Check if alpha violate KKT condition
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# Check if alpha violates the KKT condition
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def _check_obey_kkt(self, index):
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alphas = self.alphas
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tol = self._tol
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@ -172,20 +169,19 @@ class SmoSVM:
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# Get value calculated from kernel function
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def _k(self, i1, i2):
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# for test samples,use Kernel function
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# for test samples, use kernel function
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if isinstance(i2, np.ndarray):
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return self.Kernel(self.samples[i1], i2)
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# for train samples,Kernel values have been saved in matrix
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# for training samples, kernel values have been saved in matrix
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else:
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return self._K_matrix[i1, i2]
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# Get sample's error
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# Get error for sample
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def _e(self, index):
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"""
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Two cases:
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1:Sample[index] is non-bound,Fetch error from list: _error
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2:sample[index] is bound,Use predicted value deduct true value: g(xi) - yi
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1: Sample[index] is non-bound, fetch error from list: _error
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2: sample[index] is bound, use predicted value minus true value: g(xi) - yi
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"""
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# get from error data
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if self._is_unbound(index):
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@ -196,7 +192,7 @@ class SmoSVM:
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yi = self.tags[index]
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return gx - yi
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# Calculate Kernel matrix of all possible i1,i2 ,saving time
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# Calculate kernel matrix of all possible i1, i2, saving time
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def _calculate_k_matrix(self):
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k_matrix = np.zeros([self.length, self.length])
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for i in self._all_samples:
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@ -206,7 +202,7 @@ class SmoSVM:
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)
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return k_matrix
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# Predict test sample's tag
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# Predict tag for test sample
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def _predict(self, sample):
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k = self._k
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predicted_value = (
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@ -222,30 +218,31 @@ class SmoSVM:
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# Choose alpha1 and alpha2
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def _choose_alphas(self):
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locis = yield from self._choose_a1()
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if not locis:
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loci = yield from self._choose_a1()
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if not loci:
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return None
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return locis
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return loci
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def _choose_a1(self):
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"""
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Choose first alpha ;steps:
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1:First loop over all sample
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2:Second loop over all non-bound samples till all non-bound samples does not
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voilate kkt condition.
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3:Repeat this two process endlessly,till all samples does not voilate kkt
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condition samples after first loop.
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Choose first alpha
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Steps:
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1: First loop over all samples
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2: Second loop over all non-bound samples until no non-bound samples violate
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the KKT condition.
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3: Repeat these two processes until no samples violate the KKT condition
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after the first loop.
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"""
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while True:
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all_not_obey = True
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# all sample
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print("scanning all sample!")
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print("Scanning all samples!")
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for i1 in [i for i in self._all_samples if self._check_obey_kkt(i)]:
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all_not_obey = False
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yield from self._choose_a2(i1)
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# non-bound sample
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print("scanning non-bound sample!")
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print("Scanning non-bound samples!")
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while True:
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not_obey = True
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for i1 in [
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@ -256,17 +253,18 @@ class SmoSVM:
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not_obey = False
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yield from self._choose_a2(i1)
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if not_obey:
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print("all non-bound samples fit the KKT condition!")
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print("All non-bound samples satisfy the KKT condition!")
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break
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if all_not_obey:
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print("all samples fit the KKT condition! Optimization done!")
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print("All samples satisfy the KKT condition!")
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break
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return False
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def _choose_a2(self, i1):
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"""
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Choose the second alpha by using heuristic algorithm ;steps:
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1: Choose alpha2 which gets the maximum step size (|E1 - E2|).
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Choose the second alpha using a heuristic algorithm
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Steps:
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1: Choose alpha2 that maximizes the step size (|E1 - E2|).
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2: Start in a random point, loop over all non-bound samples till alpha1 and
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alpha2 are optimized.
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3: Start in a random point, loop over all samples till alpha1 and alpha2 are
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@ -320,7 +318,7 @@ class SmoSVM:
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k22 = k(i2, i2)
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k12 = k(i1, i2)
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# select the new alpha2 which could get the minimal objectives
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# select the new alpha2 which could achieve the minimal objectives
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if (eta := k11 + k22 - 2.0 * k12) > 0.0:
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a2_new_unc = a2 + (y2 * (e1 - e2)) / eta
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# a2_new has a boundary
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@ -335,7 +333,7 @@ class SmoSVM:
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l1 = a1 + s * (a2 - l)
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h1 = a1 + s * (a2 - h)
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# way 1
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# Method 1
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f1 = y1 * (e1 + b) - a1 * k(i1, i1) - s * a2 * k(i1, i2)
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f2 = y2 * (e2 + b) - a2 * k(i2, i2) - s * a1 * k(i1, i2)
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ol = (
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@ -353,9 +351,8 @@ class SmoSVM:
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+ s * h * h1 * k(i1, i2)
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)
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"""
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# way 2
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Use objective function check which alpha2 new could get the minimal
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objectives
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Method 2: Use objective function to check which alpha2_new could achieve the
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minimal objectives
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"""
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if ol < (oh - self._eps):
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a2_new = l
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@ -375,7 +372,7 @@ class SmoSVM:
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return a1_new, a2_new
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# Normalise data using min_max way
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# Normalize data using min-max method
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def _norm(self, data):
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if self._init:
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self._min = np.min(data, axis=0)
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@ -424,7 +421,7 @@ class Kernel:
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def _check(self):
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if self._kernel == self._rbf and self.gamma < 0:
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raise ValueError("gamma value must greater than 0")
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raise ValueError("gamma value must be non-negative")
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def _get_kernel(self, kernel_name):
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maps = {"linear": self._linear, "poly": self._polynomial, "rbf": self._rbf}
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@ -444,27 +441,27 @@ def count_time(func):
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start_time = time.time()
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func(*args, **kwargs)
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end_time = time.time()
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print(f"smo algorithm cost {end_time - start_time} seconds")
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print(f"SMO algorithm cost {end_time - start_time} seconds")
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return call_func
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@count_time
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def test_cancel_data():
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print("Hello!\nStart test svm by smo algorithm!")
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def test_cancer_data():
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print("Hello!\nStart test SVM using the SMO algorithm!")
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# 0: download dataset and load into pandas' dataframe
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if not os.path.exists(r"cancel_data.csv"):
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if not os.path.exists(r"cancer_data.csv"):
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request = urllib.request.Request( # noqa: S310
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CANCER_DATASET_URL,
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headers={"User-Agent": "Mozilla/4.0 (compatible; MSIE 5.5; Windows NT)"},
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)
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response = urllib.request.urlopen(request) # noqa: S310
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content = response.read().decode("utf-8")
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with open(r"cancel_data.csv", "w") as f:
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with open(r"cancer_data.csv", "w") as f:
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f.write(content)
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data = pd.read_csv(
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"cancel_data.csv",
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"cancer_data.csv",
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header=None,
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dtype={0: str}, # Assuming the first column contains string data
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)
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@ -480,13 +477,13 @@ def test_cancel_data():
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test_tags, test_samples = test_data[:, 0], test_data[:, 1:]
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# 3: choose kernel function, and set initial alphas to zero (optional)
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mykernel = Kernel(kernel="rbf", degree=5, coef0=1, gamma=0.5)
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my_kernel = Kernel(kernel="rbf", degree=5, coef0=1, gamma=0.5)
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al = np.zeros(train_data.shape[0])
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# 4: calculating best alphas using SMO algorithm and predict test_data samples
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mysvm = SmoSVM(
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train=train_data,
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kernel_func=mykernel,
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kernel_func=my_kernel,
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alpha_list=al,
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cost=0.4,
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b=0.0,
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@ -501,30 +498,30 @@ def test_cancel_data():
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for i in range(test_tags.shape[0]):
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if test_tags[i] == predict[i]:
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score += 1
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print(f"\nall: {test_num}\nright: {score}\nfalse: {test_num - score}")
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print(f"\nAll: {test_num}\nCorrect: {score}\nIncorrect: {test_num - score}")
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print(f"Rough Accuracy: {score / test_tags.shape[0]}")
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def test_demonstration():
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# change stdout
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print("\nStart plot,please wait!!!")
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print("\nStarting plot, please wait!")
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sys.stdout = open(os.devnull, "w")
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ax1 = plt.subplot2grid((2, 2), (0, 0))
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ax2 = plt.subplot2grid((2, 2), (0, 1))
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ax3 = plt.subplot2grid((2, 2), (1, 0))
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ax4 = plt.subplot2grid((2, 2), (1, 1))
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ax1.set_title("linear svm,cost:0.1")
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ax1.set_title("Linear SVM, cost = 0.1")
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test_linear_kernel(ax1, cost=0.1)
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ax2.set_title("linear svm,cost:500")
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ax2.set_title("Linear SVM, cost = 500")
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test_linear_kernel(ax2, cost=500)
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ax3.set_title("rbf kernel svm,cost:0.1")
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ax3.set_title("RBF kernel SVM, cost = 0.1")
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test_rbf_kernel(ax3, cost=0.1)
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ax4.set_title("rbf kernel svm,cost:500")
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ax4.set_title("RBF kernel SVM, cost = 500")
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test_rbf_kernel(ax4, cost=500)
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sys.stdout = sys.__stdout__
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print("Plot done!!!")
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print("Plot done!")
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def test_linear_kernel(ax, cost):
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@ -535,10 +532,10 @@ def test_linear_kernel(ax, cost):
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scaler = StandardScaler()
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train_x_scaled = scaler.fit_transform(train_x, train_y)
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train_data = np.hstack((train_y.reshape(500, 1), train_x_scaled))
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mykernel = Kernel(kernel="linear", degree=5, coef0=1, gamma=0.5)
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my_kernel = Kernel(kernel="linear", degree=5, coef0=1, gamma=0.5)
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mysvm = SmoSVM(
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train=train_data,
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kernel_func=mykernel,
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kernel_func=my_kernel,
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cost=cost,
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tolerance=0.001,
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auto_norm=False,
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@ -555,10 +552,10 @@ def test_rbf_kernel(ax, cost):
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scaler = StandardScaler()
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train_x_scaled = scaler.fit_transform(train_x, train_y)
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train_data = np.hstack((train_y.reshape(500, 1), train_x_scaled))
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mykernel = Kernel(kernel="rbf", degree=5, coef0=1, gamma=0.5)
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my_kernel = Kernel(kernel="rbf", degree=5, coef0=1, gamma=0.5)
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mysvm = SmoSVM(
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train=train_data,
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kernel_func=mykernel,
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kernel_func=my_kernel,
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cost=cost,
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tolerance=0.001,
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auto_norm=False,
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@ -571,11 +568,11 @@ def plot_partition_boundary(
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model, train_data, ax, resolution=100, colors=("b", "k", "r")
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):
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"""
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We can not get the optimum w of our kernel svm model which is different from linear
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svm. For this reason, we generate randomly distributed points with high desity and
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prediced values of these points are calculated by using our trained model. Then we
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could use this prediced values to draw contour map.
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And this contour map can represent svm's partition boundary.
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We cannot get the optimal w of our kernel SVM model, which is different from a
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linear SVM. For this reason, we generate randomly distributed points with high
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density, and predicted values of these points are calculated using our trained
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model. Then we could use this predicted values to draw contour map, and this contour
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map represents the SVM's partition boundary.
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"""
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train_data_x = train_data[:, 1]
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train_data_y = train_data[:, 2]
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@ -620,6 +617,6 @@ def plot_partition_boundary(
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if __name__ == "__main__":
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test_cancel_data()
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test_cancer_data()
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test_demonstration()
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plt.show()
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