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Commit 4467423

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Fix grammar and spelling mistakes in sequential_minimum_optimization.py (TheAlgorithms#11427)
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‎machine_learning/sequential_minimum_optimization.py‎

Lines changed: 66 additions & 69 deletions
Original file line numberDiff line numberDiff line change
@@ -1,11 +1,9 @@
11
"""
2-
Implementation of sequential minimal optimization (SMO) for support vector machines
3-
(SVM).
2+
Sequential minimal optimization (SMO) for support vector machines (SVM)
43
5-
Sequential minimal optimization (SMO) is an algorithm for solving the quadratic
6-
programming (QP) problem that arises during the training of support vector
7-
machines.
8-
It was invented by John Platt in 1998.
4+
Sequential minimal optimization (SMO) is an algorithm for solving the quadratic
5+
programming (QP) problem that arises during the training of SVMs. It was invented by
6+
John Platt in 1998.
97
108
Input:
119
0: type: numpy.ndarray.
@@ -124,8 +122,7 @@ def fit(self):
124122
b_old = self._b
125123
self._b = b
126124

127-
# 4: update error value,here we only calculate those non-bound samples'
128-
# error
125+
# 4: update error, here we only calculate the error for non-bound samples
129126
self._unbound = [i for i in self._all_samples if self._is_unbound(i)]
130127
for s in self.unbound:
131128
if s in (i1, i2):
@@ -136,7 +133,7 @@ def fit(self):
136133
+ (self._b - b_old)
137134
)
138135

139-
# if i1 or i2 is non-bound,update there error value to zero
136+
# if i1 or i2 is non-bound,update their error value to zero
140137
if self._is_unbound(i1):
141138
self._error[i1] = 0
142139
if self._is_unbound(i2):
@@ -161,7 +158,7 @@ def predict(self, test_samples, classify=True):
161158
results.append(result)
162159
return np.array(results)
163160

164-
# Check if alpha violate KKT condition
161+
# Check if alpha violates the KKT condition
165162
def _check_obey_kkt(self, index):
166163
alphas = self.alphas
167164
tol = self._tol
@@ -172,20 +169,19 @@ def _check_obey_kkt(self, index):
172169

173170
# Get value calculated from kernel function
174171
def _k(self, i1, i2):
175-
# for test samples,use Kernel function
172+
# for test samples,use kernel function
176173
if isinstance(i2, np.ndarray):
177174
return self.Kernel(self.samples[i1], i2)
178-
# for train samples,Kernel values have been saved in matrix
175+
# for training samples, kernel values have been saved in matrix
179176
else:
180177
return self._K_matrix[i1, i2]
181178

182-
# Get sample's error
179+
# Get error for sample
183180
def _e(self, index):
184181
"""
185182
Two cases:
186-
1:Sample[index] is non-bound,Fetch error from list: _error
187-
2:sample[index] is bound,Use predicted value deduct true value: g(xi) - yi
188-
183+
1: Sample[index] is non-bound, fetch error from list: _error
184+
2: sample[index] is bound, use predicted value minus true value: g(xi) - yi
189185
"""
190186
# get from error data
191187
if self._is_unbound(index):
@@ -196,7 +192,7 @@ def _e(self, index):
196192
yi = self.tags[index]
197193
return gx - yi
198194

199-
# Calculate Kernel matrix of all possible i1,i2 ,saving time
195+
# Calculate kernel matrix of all possible i1, i2, saving time
200196
def _calculate_k_matrix(self):
201197
k_matrix = np.zeros([self.length, self.length])
202198
for i in self._all_samples:
@@ -206,7 +202,7 @@ def _calculate_k_matrix(self):
206202
)
207203
return k_matrix
208204

209-
# Predict test sample's tag
205+
# Predict tag for test sample
210206
def _predict(self, sample):
211207
k = self._k
212208
predicted_value = (
@@ -222,30 +218,31 @@ def _predict(self, sample):
222218

223219
# Choose alpha1 and alpha2
224220
def _choose_alphas(self):
225-
locis = yield from self._choose_a1()
226-
if not locis:
221+
loci = yield from self._choose_a1()
222+
if not loci:
227223
return None
228-
return locis
224+
return loci
229225

230226
def _choose_a1(self):
231227
"""
232-
Choose first alpha ;steps:
233-
1:First loop over all sample
234-
2:Second loop over all non-bound samples till all non-bound samples does not
235-
voilate kkt condition.
236-
3:Repeat this two process endlessly,till all samples does not voilate kkt
237-
condition samples after first loop.
228+
Choose first alpha
229+
Steps:
230+
1: First loop over all samples
231+
2: Second loop over all non-bound samples until no non-bound samples violate
232+
the KKT condition.
233+
3: Repeat these two processes until no samples violate the KKT condition
234+
after the first loop.
238235
"""
239236
while True:
240237
all_not_obey = True
241238
# all sample
242-
print("scanning all sample!")
239+
print("Scanning all samples!")
243240
for i1 in [i for i in self._all_samples if self._check_obey_kkt(i)]:
244241
all_not_obey = False
245242
yield from self._choose_a2(i1)
246243

247244
# non-bound sample
248-
print("scanning non-bound sample!")
245+
print("Scanning non-bound samples!")
249246
while True:
250247
not_obey = True
251248
for i1 in [
@@ -256,20 +253,21 @@ def _choose_a1(self):
256253
not_obey = False
257254
yield from self._choose_a2(i1)
258255
if not_obey:
259-
print("all non-bound samples fit the KKT condition!")
256+
print("All non-bound samples satisfy the KKT condition!")
260257
break
261258
if all_not_obey:
262-
print("all samples fit the KKT condition! Optimization done!")
259+
print("All samples satisfy the KKT condition!")
263260
break
264261
return False
265262

266263
def _choose_a2(self, i1):
267264
"""
268-
Choose the second alpha by using heuristic algorithm ;steps:
269-
1: Choose alpha2 which gets the maximum step size (|E1 - E2|).
270-
2: Start in a random point,loop over all non-bound samples till alpha1 and
265+
Choose the second alpha using a heuristic algorithm
266+
Steps:
267+
1: Choose alpha2 that maximizes the step size (|E1 - E2|).
268+
2: Start in a random point, loop over all non-bound samples till alpha1 and
271269
alpha2 are optimized.
272-
3: Start in a random point,loop over all samples till alpha1 and alpha2 are
270+
3: Start in a random point,loop over all samples till alpha1 and alpha2 are
273271
optimized.
274272
"""
275273
self._unbound = [i for i in self._all_samples if self._is_unbound(i)]
@@ -306,7 +304,7 @@ def _get_new_alpha(self, i1, i2, a1, a2, e1, e2, y1, y2):
306304
if i1 == i2:
307305
return None, None
308306

309-
# calculate L and H which bound the new alpha2
307+
# calculate L and H which bound the new alpha2
310308
s = y1 * y2
311309
if s == -1:
312310
l, h = max(0.0, a2 - a1), min(self._c, self._c + a2 - a1) # noqa: E741
@@ -320,7 +318,7 @@ def _get_new_alpha(self, i1, i2, a1, a2, e1, e2, y1, y2):
320318
k22 = k(i2, i2)
321319
k12 = k(i1, i2)
322320

323-
# select the new alpha2 which could get the minimal objectives
321+
# select the new alpha2 which could achieve the minimal objectives
324322
if (eta := k11 + k22 - 2.0 * k12) > 0.0:
325323
a2_new_unc = a2 + (y2 * (e1 - e2)) / eta
326324
# a2_new has a boundary
@@ -335,7 +333,7 @@ def _get_new_alpha(self, i1, i2, a1, a2, e1, e2, y1, y2):
335333
l1 = a1 + s * (a2 - l)
336334
h1 = a1 + s * (a2 - h)
337335

338-
# way 1
336+
# Method 1
339337
f1 = y1 * (e1 + b) - a1 * k(i1, i1) - s * a2 * k(i1, i2)
340338
f2 = y2 * (e2 + b) - a2 * k(i2, i2) - s * a1 * k(i1, i2)
341339
ol = (
@@ -353,9 +351,8 @@ def _get_new_alpha(self, i1, i2, a1, a2, e1, e2, y1, y2):
353351
+ s * h * h1 * k(i1, i2)
354352
)
355353
"""
356-
# way 2
357-
Use objective function check which alpha2 new could get the minimal
358-
objectives
354+
Method 2: Use objective function to check which alpha2_new could achieve the
355+
minimal objectives
359356
"""
360357
if ol < (oh - self._eps):
361358
a2_new = l
@@ -375,7 +372,7 @@ def _get_new_alpha(self, i1, i2, a1, a2, e1, e2, y1, y2):
375372

376373
return a1_new, a2_new
377374

378-
# Normalise data using min_max way
375+
# Normalize data using min-max method
379376
def _norm(self, data):
380377
if self._init:
381378
self._min = np.min(data, axis=0)
@@ -424,7 +421,7 @@ def _rbf(self, v1, v2):
424421

425422
def _check(self):
426423
if self._kernel == self._rbf and self.gamma < 0:
427-
raise ValueError("gamma value must greater than 0")
424+
raise ValueError("gamma value must be non-negative")
428425

429426
def _get_kernel(self, kernel_name):
430427
maps = {"linear": self._linear, "poly": self._polynomial, "rbf": self._rbf}
@@ -444,27 +441,27 @@ def call_func(*args, **kwargs):
444441
start_time = time.time()
445442
func(*args, **kwargs)
446443
end_time = time.time()
447-
print(f"smo algorithm cost {end_time - start_time} seconds")
444+
print(f"SMO algorithm cost {end_time - start_time} seconds")
448445

449446
return call_func
450447

451448

452449
@count_time
453-
def test_cancel_data():
454-
print("Hello!\nStart test svm by smo algorithm!")
450+
def test_cancer_data():
451+
print("Hello!\nStart test SVM using the SMO algorithm!")
455452
# 0: download dataset and load into pandas' dataframe
456-
if not os.path.exists(r"cancel_data.csv"):
453+
if not os.path.exists(r"cancer_data.csv"):
457454
request = urllib.request.Request( # noqa: S310
458455
CANCER_DATASET_URL,
459456
headers={"User-Agent": "Mozilla/4.0 (compatible; MSIE 5.5; Windows NT)"},
460457
)
461458
response = urllib.request.urlopen(request) # noqa: S310
462459
content = response.read().decode("utf-8")
463-
with open(r"cancel_data.csv", "w") as f:
460+
with open(r"cancer_data.csv", "w") as f:
464461
f.write(content)
465462

466463
data = pd.read_csv(
467-
"cancel_data.csv",
464+
"cancer_data.csv",
468465
header=None,
469466
dtype={0: str}, # Assuming the first column contains string data
470467
)
@@ -479,14 +476,14 @@ def test_cancel_data():
479476
train_data, test_data = samples[:328, :], samples[328:, :]
480477
test_tags, test_samples = test_data[:, 0], test_data[:, 1:]
481478

482-
# 3: choose kernel function,and set initial alphas to zero(optional)
483-
mykernel = Kernel(kernel="rbf", degree=5, coef0=1, gamma=0.5)
479+
# 3: choose kernel function,and set initial alphas to zero(optional)
480+
my_kernel = Kernel(kernel="rbf", degree=5, coef0=1, gamma=0.5)
484481
al = np.zeros(train_data.shape[0])
485482

486483
# 4: calculating best alphas using SMO algorithm and predict test_data samples
487484
mysvm = SmoSVM(
488485
train=train_data,
489-
kernel_func=mykernel,
486+
kernel_func=my_kernel,
490487
alpha_list=al,
491488
cost=0.4,
492489
b=0.0,
@@ -501,30 +498,30 @@ def test_cancel_data():
501498
for i in range(test_tags.shape[0]):
502499
if test_tags[i] == predict[i]:
503500
score += 1
504-
print(f"\nall: {test_num}\nright: {score}\nfalse: {test_num - score}")
501+
print(f"\nAll: {test_num}\nCorrect: {score}\nIncorrect: {test_num - score}")
505502
print(f"Rough Accuracy: {score / test_tags.shape[0]}")
506503

507504

508505
def test_demonstration():
509506
# change stdout
510-
print("\nStart plot,please wait!!!")
507+
print("\nStarting plot,please wait!")
511508
sys.stdout = open(os.devnull, "w")
512509

513510
ax1 = plt.subplot2grid((2, 2), (0, 0))
514511
ax2 = plt.subplot2grid((2, 2), (0, 1))
515512
ax3 = plt.subplot2grid((2, 2), (1, 0))
516513
ax4 = plt.subplot2grid((2, 2), (1, 1))
517-
ax1.set_title("linear svm,cost:0.1")
514+
ax1.set_title("Linear SVM, cost = 0.1")
518515
test_linear_kernel(ax1, cost=0.1)
519-
ax2.set_title("linear svm,cost:500")
516+
ax2.set_title("Linear SVM, cost = 500")
520517
test_linear_kernel(ax2, cost=500)
521-
ax3.set_title("rbf kernel svm,cost:0.1")
518+
ax3.set_title("RBF kernel SVM, cost = 0.1")
522519
test_rbf_kernel(ax3, cost=0.1)
523-
ax4.set_title("rbf kernel svm,cost:500")
520+
ax4.set_title("RBF kernel SVM, cost = 500")
524521
test_rbf_kernel(ax4, cost=500)
525522

526523
sys.stdout = sys.__stdout__
527-
print("Plot done!!!")
524+
print("Plot done!")
528525

529526

530527
def test_linear_kernel(ax, cost):
@@ -535,10 +532,10 @@ def test_linear_kernel(ax, cost):
535532
scaler = StandardScaler()
536533
train_x_scaled = scaler.fit_transform(train_x, train_y)
537534
train_data = np.hstack((train_y.reshape(500, 1), train_x_scaled))
538-
mykernel = Kernel(kernel="linear", degree=5, coef0=1, gamma=0.5)
535+
my_kernel = Kernel(kernel="linear", degree=5, coef0=1, gamma=0.5)
539536
mysvm = SmoSVM(
540537
train=train_data,
541-
kernel_func=mykernel,
538+
kernel_func=my_kernel,
542539
cost=cost,
543540
tolerance=0.001,
544541
auto_norm=False,
@@ -555,10 +552,10 @@ def test_rbf_kernel(ax, cost):
555552
scaler = StandardScaler()
556553
train_x_scaled = scaler.fit_transform(train_x, train_y)
557554
train_data = np.hstack((train_y.reshape(500, 1), train_x_scaled))
558-
mykernel = Kernel(kernel="rbf", degree=5, coef0=1, gamma=0.5)
555+
my_kernel = Kernel(kernel="rbf", degree=5, coef0=1, gamma=0.5)
559556
mysvm = SmoSVM(
560557
train=train_data,
561-
kernel_func=mykernel,
558+
kernel_func=my_kernel,
562559
cost=cost,
563560
tolerance=0.001,
564561
auto_norm=False,
@@ -571,11 +568,11 @@ def plot_partition_boundary(
571568
model, train_data, ax, resolution=100, colors=("b", "k", "r")
572569
):
573570
"""
574-
We can not get the optimum w of our kernel svm model which is different from linear
575-
svm. For this reason, we generate randomly distributed points with high desity and
576-
prediced values of these points are calculated by using our trained model. Then we
577-
could use this prediced values to draw contour map.
578-
And this contour map can represent svm's partition boundary.
571+
We cannot get the optimal w of our kernel SVM model, which is different from a
572+
linear SVM. For this reason, we generate randomly distributed points with high
573+
density, and predicted values of these points are calculated using our trained
574+
model. Then we could use this predicted values to draw contour map, and this contour
575+
map represents the SVM's partition boundary.
579576
"""
580577
train_data_x = train_data[:, 1]
581578
train_data_y = train_data[:, 2]
@@ -620,6 +617,6 @@ def plot_partition_boundary(
620617

621618

622619
if __name__ == "__main__":
623-
test_cancel_data()
620+
test_cancer_data()
624621
test_demonstration()
625622
plt.show()

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