這一篇繼上一篇（機器學習實踐之手寫數字識別 － 數據初識）
這一篇主要對測試集數據（train.csv）進行簡單特徵分析，並進行簡單線性迴歸識別。
識別率能夠達到家 85%左右，沒識別正確的數據也打印出來，方便對數據進行進一步分析。
代碼中分爲兩個獨立部分, 對一個文件的修改不需要調整另外的文件：
特徵提取部分代碼主要把結果輸出到train.txt文件中
驗證數據部分主要對train.txt數據進行分析，並輸出結果。
機器學習分類
根據提供數據中包含輸出數據的情況可把數據爲了：監督學習，非監督學習及半監督學習。
監督學習：數據中包含輸入數據，及其對應的輸出數據。感知機，決策樹，線性迴歸，邏輯迴歸， 支持向量機等機器學習算法
非監督學習： 數據中包含輸入數據，不提供輸出數據。聚類算法等
半監督學習： 數據中包含輸入數據，只提供部分輸出數據。增強學習等
由於提供的數據中，有原始數據(28*28*8維)， 及輸出結果，所以這是一個典型的監督學習的例子。
特徵選擇
機器學習的算法基本都是公開的， 每個算法處理邏輯都是一樣。難度主要集中在兩個方面：
1. 如何系統組合每個算法解決問題， 這裏解決問題只能是更優的問題，如讓識別率從90%提升到95%
2. 如果選擇特徵， 這是機器學習的關鍵問題，解決識別率到達90%的問題。特
輸入數據的區別分爲：
原始數據： 如當前問題的 28*28*8維的數據。
特徵工程： 人工幫助抽取特徵，如當前的對稱性，密度之類的
深度學習： 讓機器自己來學特徵。
本次實驗先人工來分特徵，先選的特徵有：
1. 長寬比： 如1的長寬比較小
2. 空間密度：把數據分爲左上， 左下，右上，右下四個方位的密度來分。 如0時四個方向相差不大。
3. 數據橫向切片數： 1時切段數都爲1. 7時也大部分爲1,其它的都可能有1有2.
4. 切片數爲1時的位置： 有靠左，有靠右，有靠上， 有靠下，有在數字中間問題。
5. 平均切片長度，及最長的數。
6. 數字中有圈的個數。
代碼如下， 把生成的特徵放在train.txt文件中：
class FeatureParser:
def __init__(self, data):
self.sections = self.getSplitResult(data)
self.updateParams()
self.parseCount(data)
self.updateZeroCount()
@staticmethod
def getSplitResult(data):
sections = {}
for i in range(28):
lst = []
cur = []
for j in range(28):
if int(data[i*28 + j]) == 0:
if len(cur) > 0:
lst.append(cur)
cur = []
continue
if len(cur) == 0:
cur = [j, j]
else:
cur[1] = j
if len(cur) > 0:
lst.append(cur)
if len(lst) > 0:
sections[i] = lst
return sections
def updateParams(self):
self.up = min(self.sections.keys())
self.down = max(self.sections.keys())
self.left = min([item[0][0] for item in self.sections.values()])
self.right = max([item[-1][1] for item in self.sections.values()])
self.x_mid = (self.right+self.left)/2
self.y_mid = (self.down+self.up)/2
self.ones = sum([1 for item in self.sections.values() if len(item) == 1])
self.twos = sum([1 for item in self.sections.values() if len(item) == 2])
self.threes = sum([1 for item in self.sections.values() if len(item) >= 3])
#對於只有一段的數字，工區分出靠近數字的左邊還是右邊 3時都會靠左，5時一左一右等。
self.one_left_up, self.one_left_down, self.one_mid, self.one_right_up, self.one_right_down = 0, 0, 0, 0, 0
for i, item in self.sections.items():
if len(item) != 1: continue
if item[0][1] <= self.x_mid:
if i < self.y_mid :
self.one_left_up += 1
else:
self.one_left_down += 1
elif item[0][0] >= self.x_mid:
if i < self.y_mid:
self.one_right_up += 1
else:
self.one_right_down += 1
else:
self.one_mid += 1
# print(" ones: ", self.one_left_up, self.one_left_down, self.one_mid, self.one_right_up, self.one_right_down, self.ones)
section_all = []
for item in self.sections.values():
for slice in item:
section_all.append(slice[1] - slice[0] + 1)
self.max_width = max(section_all)
self.avg_width = sum(section_all)/len(section_all)
def parseCount(self, data):
#把數字分成4上區域，統計每個區域的點的個數
self.left_top, self.right_top, self.left_down, self.right_down = 0, 0, 0, 0
for i in range(28):
for j in range(28):
if int(data[i*28 + j]) == 0: continue
if j < self.x_mid and i < self.y_mid : self.left_top += 1
if j > self.x_mid and i < self.y_mid: self.right_top += 1
if j < self.x_mid and i > self.y_mid: self.left_down += 1
if j > self.x_mid and i > self.y_mid: self.right_down += 1
def updateZeroCount(self):
self. zero_count = 0
last_i, last_item, start_ones = 0, None, False
for i, item in self.sections.items():
if last_item is None:
last_i, last_item = i, item
continue
if len(last_item) == 1 and len(item) > 1:
start_ones = (item[0][1] +1 >= last_item[0][0] and item[-1][0]-1 <= last_item[0][1])
if start_ones and len(last_item) > 1 and len(item) == 1:
if item[0][0] - 1 <= last_item[0][1] and item[0][1]+1 >= last_item[-1][0]:
self. zero_count += 1
start_ones = False
last_i, last_item = i, item
def getFeature(self):
all_count = sum((self.left_top, self.right_top, self.left_down, self.right_down))
height = sum((self.ones, self.twos, self.threes))
return ((self.right - self.left+1)/(self.down - self.up + 1), #長寬比
self.left_top/all_count, #左上點比
self.right_top/all_count, #右上點比
self.left_down/all_count, #左下點比
self.right_down/all_count, #右下點比
self.ones/height, #一段佔比
(self.twos + self.threes)/height, #多於一段佔比
self.one_left_up/self.ones,
self.one_left_down/self.ones,
self.one_mid/self.ones,
self.one_right_up/self.ones,
self.one_right_down/self.ones,
self.max_width/self.avg_width,
self.zero_count
)
def checkFile(fileName):
line_number = 0
with open("train.txt", "w") as wFile:
with open(fileName, "r") as mFile:
for line in mFile:
line_number += 1
if line_number <= 1:continue
# if line_number > 20: break
lst = line.split(',')
# print(",".join(["%.3f" % item for item in FeatureParser(lst[1:]).getFeature()] + [str(lst[0])]) + "\n")
wFile.write(",".join(["%.3f" % item for item in FeatureParser(lst[1:]).getFeature()] + [str(lst[0])]) + "\n")
checkFile("train.csv")初步線性迴歸識別
線性迴歸分析採用sklearn來進行實現。
算法：
每個線性迴歸只對兩個數字進行分類， 這樣只相當於作是非題，查對簡單。
一共組織了45個線性迴歸器來實現兩兩識別。
最後統計45個識別器的識別結果，佔數最多的爲識別結果。
具體看下面代碼實現。
線性迴歸識別代碼：
import numpy as np
from sklearn.linear_model import LinearRegression
def load_data(filename):
tmp_data_x = []
tmp_data_y = []
with open(filename, "r") as file:
for line in file:
lst = [float(item) for item in line.split(",")]
tmp_data_x.append(lst[:-1])
tmp_data_y.append(lst[-1])
return np.array(tmp_data_x), np.array(tmp_data_y)
def load_source(filename):
with open(filename, "r") as file:
lines = file.readlines()
return lines[1:]
def show_source(data):
lst = data.split(",")
print("num: {}".format(lst[0]))
lst = lst[1:]
for i in range(28):
print(",".join(["%3s" % item for item in lst[i*28: i*28+28]]))
#加載訓練數據
data_x, data_y = load_data("train.txt")
# 加載原始數據
source_data = load_source("train.csv")
# 打印數據長度
print("len", len(data_x), len(data_y))
# 設置測試數據數量
LEN = -100
# 劃分訓練數據和測試數據 注： 當前測試中用到測試數據訓練集（train.csv）的數據， 而暫時沒有用到測試數據集的數據(test.csv)
x_train, y_train = data_x[:LEN], data_y[:LEN]
x_test, y_test = data_x[LEN:], data_y[LEN:]
# 定義45個線性分類器，並訓練數據，每個分類器只對兩個數字進行識別
RegressionDict = {}
for i in range(10):
for j in range(i+1, 10):
regr = LinearRegression()
RegressionDict["{}-{}".format(i, j)] = regr
x_train_tmp = np.array([x_train[index] for index, y in enumerate(y_train) if y in [i, j]])
y_train_tmp = np.array([0 if y == i else 1 for y in y_train if y in [i, j]])
regr.fit(x_train_tmp, y_train_tmp)
# 初始化計數器
ret_counter = []
for i in range(len(x_test)):
ret_counter.append({})
# 預測數據，並把結果放到計數器中
tmp_dict = {}
for key, regression in RegressionDict.items():
a, b = key.split('-')
y_test_predict = regression.predict(x_test)
tmp_dict[key] = [a if item <= 0.5 else b for item in y_test_predict]
for i, item in enumerate(tmp_dict[key]):
ret_counter[i][item] = ret_counter[i].get(item, 0) + 1
# 統計預測數據， 計算測試準確率
ok_count = 0
err_count = 0
for i, item in enumerate(y_test):
ret = int(sorted(ret_counter[i].items(), key=lambda x:x[1],reverse=True)[0][0])
if ret == int(item):
ok_count += 1
else:
# 打印出錯的數據
print("\n")
show_source(source_data[i-100])
print(x_test[i])
print(sorted(ret_counter[i].items(), key=lambda x:x[1],reverse=True), int(item))
err_count += 1
print(" %d ok: %.2f%% err: %.2f%%" % (ok_count+err_count, 100.0* ok_count/(ok_count+err_count), 100.0* err_count/(ok_count+err_count)))
輸出結果
len 42000 42000
/Library/Frameworks/Python.framework/Versions/3.4/lib/python3.4/site-packages/scipy/linalg/basic.py:884: RuntimeWarning: internal gelsd driver lwork query error, required iwork dimension not returned. This is likely the result of LAPACK bug 0038, fixed in LAPACK 3.2.2 (released July 21, 2010). Falling back to 'gelss' driver.
warnings.warn(mesg, RuntimeWarning)
num: 5
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[ 1. 0.12 0.38 0.196 0.304 0.9 0.1 0. 0. 0.611
0.111 0.278 2.506 0. ]
[('3', 9), ('5', 8), ('2', 7), ('7', 6), ('1', 5), ('4', 4), ('9', 3), ('8', 2), ('6', 1)] 5
num: 8
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[ 0.7 0.27 0.203 0.223 0.304 0.35 0.65 0. 0. 1. 0.
0. 2.676 2. ]
[('0', 9), ('8', 8), ('9', 7), ('4', 6), ('6', 5), ('3', 4), ('2', 3), ('5', 2), ('7', 1)] 8
num: 1
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[ 0.5 0.208 0.448 0. 0.344 0.95 0.05 0. 0. 0.316
0.158 0.526 1.969 0. ]
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num: 5
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[ 0.85 0.274 0.14 0.268 0.318 0.8 0.2 0.375 0. 0.562
0.062 0. 2. 0. ]
[('6', 9), ('5', 8), ('3', 7), ('2', 6), ('1', 5), ('4', 4), ('0', 3), ('8', 2), ('7', 1)] 5
num: 3
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[ 1.176 0.351 0.093 0.166 0.391 0.824 0.176 0.071 0. 0.857 0.
0.071 1.818 0. ]
[('2', 9), ('3', 8), ('5', 7), ('4', 5), ('1', 4), ('6', 4), ('8', 3), ('0', 3), ('7', 2)] 3
num: 4
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num: 5
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0. 2.62 1. ]
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num: 4
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[ 0.7 0.24 0.364 0.155 0.24 0.8 0.2 0. 0. 0.625
0.188 0.188 2.233 1. ]
[('9', 9), ('4', 7), ('7', 7), ('3', 7), ('5', 5), ('8', 4), ('0', 2), ('1', 2), ('2', 2)] 4
num: 1
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[ 0.7 0.025 0.457 0.123 0.395 0.9 0.1 0. 0. 0.278 0.5
0.222 1.358 0. ]
[('3', 9), ('1', 8), ('2', 7), ('7', 6), ('5', 5), ('6', 4), ('4', 3), ('0', 2), ('9', 1)] 1
num: 3
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[ 1. 0.371 0.171 0.137 0.32 0.9 0.1 0.167 0. 0.556 0.
0.278 2.263 0. ]
[('5', 9), ('3', 8), ('2', 7), ('4', 6), ('7', 5), ('9', 4), ('1', 3), ('8', 2), ('6', 1)] 3
num: 3
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[ 0.8 0.231 0.331 0.201 0.237 0.65 0.35 0. 0. 0.615 0.
0.385 2.077 1. ]
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num: 4
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
[ 1.25 0.195 0.201 0.377 0.227 0.438 0.562 0.286 0. 0.571 0.
0.143 2.532 0. ]
[('5', 9), ('2', 8), ('6', 7), ('0', 6), ('4', 5), ('3', 4), ('8', 3), ('9', 2), ('1', 1)] 4
num: 8
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 29,226,170, 29, 0, 0, 0,114,255,114, 0, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 57,255,255,198,226,226,255,255,141, 0, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 57,114,198,255,255,198, 86, 0, 0, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
[ 0.8 0.307 0.27 0.088 0.336 0.35 0.65 0. 0. 0.714 0.
0.286 2.891 1. ]
[('0', 8), ('9', 8), ('4', 7), ('8', 6), ('3', 6), ('7', 3), ('5', 3), ('2', 3), ('6', 1)] 8
num: 5
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0, 0, 0, 58,191,136,136,136,172,255,202,197,241, 56, 0, 0, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0, 0, 0, 92,252,253,253,253,253,253,253,253,253,206, 0, 0, 0, 0, 0, 0, 0, 0
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0,243,247,163,120, 65, 65, 65, 62, 8, 23, 0, 0, 0, 0, 0, 0, 0, 0
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0, 0, 0, 0, 0, 0, 0, 0, 0, 90,252,253,253,253,221,167,201,233,253,162, 0, 0, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,215,253,216,112, 18, 0, 0, 45,229,239, 50, 0, 0, 0, 0, 0, 0, 0
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0, 0, 0, 0, 0, 0, 0, 32,113, 13, 0, 0, 0, 0, 0, 0, 0, 0,137,253, 70, 0, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0, 72,253, 35, 0, 0, 0, 0, 0, 0, 0, 12,202,253, 70, 0, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0, 72,253,159, 2, 0, 0, 0, 0, 0, 0,130,253,253, 70, 0, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0, 25,223,253, 33, 0, 0, 0, 0, 0, 44,208,253,253, 70, 0, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0, 0, 99,246,161, 60, 0, 31, 20,164,247,253,253,219, 20, 0, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0, 0, 0,225,253,248,201,226,217,253,253,253,244, 84, 0, 0, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0, 0, 0, 81,202,253,253,253,253,253,253,201, 80, 0, 0, 0, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 67,135,135,190,190,135, 28, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
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[ 0.7 0.243 0.284 0.213 0.26 0.6 0.4 0.083 0. 0.833 0.
0.083 1.822 0. ]
[('3', 9), ('5', 8), ('8', 5), ('4', 5), ('0', 4), ('9', 4), ('2', 4), ('1', 3), ('7', 2), ('6', 1)] 5
num: 9
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 34,159,222,138, 34, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0, 0, 17, 99,253,252,252,252,252, 95, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0, 0, 93,252,253,208,100, 69,205,247, 67, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0, 0,187,252,253, 92, 0, 0, 74,253,185, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0, 64,248,252,232, 8, 0, 0, 0,253,227, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0,185,253,253,106, 0, 0, 0, 11,255,253, 69, 62,138, 22, 0, 0, 0, 0, 0, 0, 0
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0, 0, 0, 0, 0, 0, 0,184,252,252, 0, 0, 0, 0, 94,161, 79, 0,207,252,230, 0, 0, 0, 0, 0, 0, 0
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0, 0, 0, 0, 0, 0, 0,123,253,253, 64, 0, 0, 0, 0, 0, 0, 7,212,253,231, 0, 0, 0, 0, 0, 0, 0
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0, 0, 0, 0, 0, 0, 0, 0, 68,246,253,135, 19, 0, 0, 81,197,252,252,252,230, 0, 0, 0, 0, 0, 0, 0
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 33,211,252,252,252,253,231,106,211,252,230, 0, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 85,116,116, 53, 0, 0,145,253,233, 9, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 93,252,253,113, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 25,236,253,240, 50, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,230,253,252, 69, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 73,243,117, 6, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
[ 0.8 0.308 0.208 0.176 0.308 0.45 0.55 0.111 0. 0.444 0.
0.444 2.491 1. ]
[('8', 7), ('9', 7), ('4', 6), ('0', 6), ('3', 6), ('5', 6), ('2', 4), ('6', 2), ('7', 1)] 9
100 ok: 85.00% err: 15.00%