机器学习-算法学习随记

Posted 2022-11-23 龙鸣丿

tags:

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sklearn 官方网站：

API Reference — scikit-learn 1.0.2 documentation

卡方：

https://www.csdn.net/tags/NtzaAg1sMDU2MC1ibG9n.html

package spark2.ml

import org.apache.log4j.Level, Logger
import org.apache.spark.ml.linalg.Vectors
import org.apache.spark.ml.stat.ChiSquareTest
import org.apache.spark.sql.SparkSession

/**
  * Created by Administrator on 2020/6/28.
  */
object MLChiSquareTest 
  /**
    * 设置日志级别
    */
  Logger.getLogger("org").setLevel(Level.WARN)
  def main(args: Array[String]) 
    val spark = SparkSession
      .builder
      .appName(s"$this.getClass.getSimpleName")
      .config("spark.driver.maxResultSize", "2G")
      .master("local[2]")
      .getOrCreate()

    import spark.implicits._

    val data = Seq(
      (0.0, Vectors.dense(1.0, 1.0, 1.0)),
      (0.0, Vectors.dense(1.0, 1.0, 2.0)),
      (0.0, Vectors.dense(1.0, 1.0, 3.0)),
      (1.0, Vectors.dense(1.0, 3.0, 4.0)),
      (1.0, Vectors.dense(1.0, 3.0, 5.0)),
      (1.0, Vectors.dense(1.0, 3.0, 6.0))
    )
    val df = data.toDF("label", "features")
    val chi = ChiSquareTest.test(df, "features", "label")
    chi.show(false)

pyspark在机器学习中实战小练习

决策树以及随机森立见：pyspark在机器学习中实战小练 - 知乎

数据集：从1994年人口普查数据库中提取，字段包含http://archive.ics.uci.edu/ml/

TO DO：预测一个人新收入是否会超过5万美金

参数说明：

创建SparkSession

from pyspark.sql import SparkSession
spark=SparkSession.builder.appName('adult').getOrCreate()

读取数据

df = spark.read.csv('adult.csv', inferSchema = True, header=True) #读取csv文件
df.show(3)  #用来显示前3行

注意pyspark必须创建SparkSession才能像类似于pandas一样操作数据集

我们看看数据集

cols = df.columns #和pandas一样看列名
df.printSchema()

#找到所有的string类型的变量
#dtypes用来看数据变量类型
cat_features = [item[0] for item in df.dtypes if item[1]=='string']
# 需要删除 income列，否则标签泄露
cat_features.remove('income')
#找到所有数字变量
num_features = [item[0] for item in df.dtypes if item[1]!='string']

对于类别变量我们需要进行编码，在pyspark中提供了StringIndexer, OneHotEncoder, VectorAssembler特征编码模式

from pyspark.ml import Pipeline
from pyspark.ml.feature import StringIndexer, OneHotEncoder, VectorAssembler

stages = []
for col in cat_features:
    # 字符串转成索引
    string_index = StringIndexer(inputCol = col, outputCol = col + 'Index')
    # 转换为OneHot编码
    encoder = OneHotEncoder(inputCols=[string_index.getOutputCol()], outputCols=[col + "_one_hot"])
    # 将每个字段的转换方式 放到stages中
    stages += [string_index, encoder]

# 将income转换为索引
label_string_index = StringIndexer(inputCol = 'income', outputCol = 'label')
# 添加到stages中
stages += [label_string_index]

# 类别变量 + 数值变量
assembler_cols = [c + "_one_hot" for c in cat_features] + num_features
assembler = VectorAssembler(inputCols=assembler_cols, outputCol="features")
stages += [assembler]

# 使用pipeline完成数据处理
pipeline = Pipeline(stages=stages)
pipeline_model = pipeline.fit(df)
df = pipeline_model.transform(df)
selected_cols = ["label", "features"] + cols
df = df.select(selected_cols)

因为pyspark显示的数据比较像mysql 那样不方便观看

因此我们转成pandas

import pandas as pd
pd.DataFrame(df.take(20), columns = df.columns)

通过pandas发现，好像还有较多字符串变量，难道特征编码失败了？

因为使用VectorAssembler直接将特征转成了features这一列，因为pyspark做ML时需要特征编码好了并做成向量列

因此到这里数据的特征工程就做好了

分割数据集测试集

train, test = df.randomSplit([0.7, 0.3], seed=2021)
print(train.count())
print(test.count())

22795
9766

可以看到，训练集和测试集安装7：3的比例分割了，接下来就是构建模型进行训练

逻辑回归

from pyspark.ml.classification import LogisticRegression
# 创建模型
lr = LogisticRegression(featuresCol = 'features', labelCol = 'label',maxIter=10)
lr_model = lr.fit(train)

可以看到ML的用法和sklearn非常的像，因此使用起来也是相当的方便

#结果预测

predictions = lr_model.transform(test)

看看predictions的结构

predictions.printSchema()

抽取需要的信息

selected = predictions.select("label", "prediction", "probability", "age", "occupation")
display(selected)
selected.show(4)

技术AUC值

from pyspark.ml.evaluation import BinaryClassificationEvaluator
# 模型评估，通过原始数据 rawPrediction计算AUC
evaluator = BinaryClassificationEvaluator(rawPredictionCol="rawPrediction")
print('AUC：', evaluator.evaluate(predictions))

AUC： 0.9062153434371653

进行网格调参

from pyspark.ml.tuning import ParamGridBuilder, CrossValidator

# 创建网络参数，用于交叉验证
param_grid = (ParamGridBuilder()
             .addGrid(lr.regParam, [0.01, 0.5, 2.0])
             .addGrid(lr.elasticNetParam, [0.0, 0.5, 1.0])
             .addGrid(lr.maxIter, [1, 5, 10])
             .build())
# 五折交叉验证，设置模型，网格参数，验证方法，折数
cv = CrossValidator(estimator=lr, estimatorParamMaps=param_grid, evaluator=evaluator, numFolds=5)
# 交叉验证运行
cv_model = cv.fit(train)
# 对于测试数据，使用五折交叉验证
predictions = cv_model.transform(test)
print('AUC：', evaluator.evaluate(predictions))

AUC： 0.9054096433333642

TOD

决策树：

随机森林

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Thu Jun  7 18:08:40 2018

@author: luogan
"""

from pyspark.ml import Pipeline
from pyspark.ml.classification import DecisionTreeClassifier
from pyspark.ml.feature import StringIndexer, VectorIndexer
from pyspark.ml.evaluation import MulticlassClassificationEvaluator

from pyspark.sql import SparkSession

spark= SparkSession\\
                .builder \\
                .appName("dataFrame") \\
                .getOrCreate()


# Load the data stored in LIBSVM format as a DataFrame.
data = spark.read.format("libsvm").load("/home/luogan/lg/softinstall/spark-2.2.0-bin-hadoop2.7/data/mllib/sample_libsvm_data.txt")

# Index labels, adding metadata to the label column.
# Fit on whole dataset to include all labels in index.
labelIndexer = StringIndexer(inputCol="label", outputCol="indexedLabel").fit(data)
# Automatically identify categorical features, and index them.
# We specify maxCategories so features with > 4 distinct values are treated as continuous.
featureIndexer =\\
    VectorIndexer(inputCol="features", outputCol="indexedFeatures", maxCategories=4).fit(data)

# Split the data into training and test sets (30% held out for testing)
(trainingData, testData) = data.randomSplit([0.7, 0.3])

# Train a DecisionTree model.
dt = DecisionTreeClassifier(labelCol="indexedLabel", featuresCol="indexedFeatures")

# Chain indexers and tree in a Pipeline
pipeline = Pipeline(stages=[labelIndexer, featureIndexer, dt])

# Train model.  This also runs the indexers.
model = pipeline.fit(trainingData)

# Make predictions.
predictions = model.transform(testData)

# Select example rows to display.
predictions.select("prediction", "indexedLabel", "features").show(5)

# Select (prediction, true label) and compute test error
evaluator = MulticlassClassificationEvaluator(
    labelCol="indexedLabel", predictionCol="prediction", metricName="accuracy")
accuracy = evaluator.evaluate(predictions)
print("Test Error = %g " % (1.0 - accuracy))

treeModel = model.stages[2]
# summary only
print(treeModel)

+----------+------------+--------------------+
|prediction|indexedLabel|            features|
+----------+------------+--------------------+
|       1.0|         1.0|(692,[95,96,97,12...|
|       1.0|         1.0|(692,[100,101,102...|
|       1.0|         1.0|(692,[121,122,123...|
|       1.0|         1.0|(692,[123,124,125...|
|       1.0|         1.0|(692,[124,125,126...|
+----------+------------+--------------------+
only showing top 5 rows

Test Error = 0.0285714 
DecisionTreeClassificationModel (uid=DecisionTreeClassifier_49f5b151055db55ad5a5) of depth 1 with 3 nodes

PySpark项目实战

注：单纯拿Pyspark练练手，可无需配置Pyspark集群，直接本地配置下单机Pyspark，也可以使用线上spark集群(如: community.cloud.databricks.com)。

本项目通过PySpark实现机器学习建模全流程：包括数据的载入，数据分析，特征加工，二分类模型训练及评估。

#!/usr/bin/env python
# coding: utf-8
 
 
#  初始化SparkSession
from pyspark.sql import SparkSession
 
spark = SparkSession.builder.appName("Python Spark RF example").config("spark.some.config.option", "some-value").getOrCreate()
 
# 加载数据
df = spark.read.format('com.databricks.spark.csv').options(header='true', inferschema='true').load("./data.csv",header=True)
 
from pyspark.sql.functions import *# 数据基本信息分析
df.dtypes # Return df column names and data types
df.show()  #Display the content of df
df.head()  #Return first n rows
df.first()  #Return first row 
df.take(2)  #Return the first n rows
df.schema   # Return the schema of df
df.columns # Return the columns of df
df.count()  #Count the number of rows in df
df.distinct().count()  #Count the number of distinct rows in df
df.printSchema()  #Print the schema of df
df.explain()  #Print the (logical and physical)  plans
df.describe().show()  #Compute summary statistics 
df.groupBy('Survived').agg(avg("Age"),avg("Fare")).show()  # 聚合分析
df.select(df.Sex, df.Survived==1).show()  # 带条件查询 
df.sort("Age", ascending=False).collect() # 排序
# 特征加工
df = df.dropDuplicates()   # 删除重复值
df = df.na.fill(value=0)  # 缺失填充值
df = df.na.drop()        # 或者删除缺失值
df = df.withColumn('isMale', when(df['Sex']=='male',1).otherwise(0)) # 新增列：性别0 1
df = df.drop('_c0','Name','Sex') # 删除姓名、性别、索引列
 
# 设定特征/标签列
from pyspark.ml.feature import VectorAssembler
ignore=['Survived']
vectorAssembler = VectorAssembler(inputCols=[x for x in df.columns  
                  if x not in ignore], outputCol = 'features')
new_df = vectorAssembler.transform(df)
new_df = new_df.select(['features', 'Survived'])
 
# 划分测试集训练集
train, test = new_df.randomSplit([0.75, 0.25], seed = 12345)
 
# 模型训练
from pyspark.ml.classification import LogisticRegression
 
lr = LogisticRegression(featuresCol = 'features', 
                         labelCol='Survived')
lr_model = lr.fit(test)
 
# 模型评估
from pyspark.ml.evaluation import BinaryClassificationEvaluator
 
predictions = lr_model.transform(test)
auc = BinaryClassificationEvaluator().setLabelCol('Survived')
print('AUC of the model:' + str(auc.evaluate(predictions)))
print('features weights', lr_model.coefficientMatrix)

PySpark四：机器学习

PySpark四：机器学习_starry0001的博客-CSDN博客_pyspark 机器学习

使用pyspark进行机器学习（回归问题）_littlely_ll的博客-CSDN博客_pyspark机器学习

PySpark入门二十三：ML--随机森林_Roc Huang的博客-CSDN博客_pyspark的随机森林

机器学习决策树--分类数代码

# -*- coding: UTF-8 -*-
from matplotlib.font_manager import FontProperties
import matplotlib.pyplot as plt
from math import log
import operator


def createDataSet():
    dataSet = [[0, 0, 0, 0, 'no'],
               [0, 0, 0, 1, 'no'],
               [0, 1, 0, 1, 'yes'],
               [0, 1, 1, 0, 'yes'],
               [0, 0, 0, 0, 'no'],
               [1, 0, 0, 0, 'no'],
               [1, 0, 0, 1, 'no'],
               [1, 1, 1, 1, 'yes'],
               [1, 0, 1, 2, 'yes'],
               [1, 0, 1, 2, 'yes'],
               [2, 0, 1, 2, 'yes'],
               [2, 0, 1, 1, 'yes'],
               [2, 1, 0, 1, 'yes'],
               [2, 1, 0, 2, 'yes'],
               [2, 0, 0, 0, 'no']]
    labels = ['F1-AGE', 'F2-WORK', 'F3-HOME', 'F4-LOAN']
    return dataSet, labels


def createTree(dataset, labels, featLabels):
    classList = [example[-1] for example in dataset]
    if classList.count(classList[0]) == len(classList):
        return classList[0]
    if len(dataset[0]) == 1:
        return majorityCnt(classList)
    bestFeat = chooseBestFeatureToSplit(dataset)
    bestFeatLabel = labels[bestFeat]
    featLabels.append(bestFeatLabel)
    myTree = bestFeatLabel: 
    del labels[bestFeat]
    featValue = [example[bestFeat] for example in dataset]
    uniqueVals = set(featValue)
    for value in uniqueVals:
        sublabels = labels[:]
        myTree[bestFeatLabel][value] = createTree(splitDataSet(dataset, bestFeat, value), sublabels, featLabels)
    return myTree


def majorityCnt(classList):
    classCount = 
    for vote in classList:
        if vote not in classCount.keys(): classCount[vote] = 0
        classCount[vote] += 1
    sortedclassCount = sorted(classCount.items(), key=operator.itemgetter(1), reverse=True)
    return sortedclassCount[0][0]


def chooseBestFeatureToSplit(dataset):
    numFeatures = len(dataset[0]) - 1
    baseEntropy = calcShannonEnt(dataset)
    bestInfoGain = 0
    bestFeature = -1
    for i in range(numFeatures):
        featList = [example[i] for example in dataset]
        uniqueVals = set(featList)
        newEntropy = 0
        for val in uniqueVals:
            subDataSet = splitDataSet(dataset, i, val)
            prob = len(subDataSet) / float(len(dataset))
            newEntropy += prob * calcShannonEnt(subDataSet)
        infoGain = baseEntropy - newEntropy
        if (infoGain > bestInfoGain):
            bestInfoGain = infoGain
            bestFeature = i
    return bestFeature


def splitDataSet(dataset, axis, val):
    retDataSet = []
    for featVec in dataset:
        if featVec[axis] == val:
            reducedFeatVec = featVec[:axis]
            reducedFeatVec.extend(featVec[axis + 1:])
            retDataSet.append(reducedFeatVec)
    return retDataSet


def calcShannonEnt(dataset):
    numexamples = len(dataset)
    labelCounts = 
    for featVec in dataset:
        currentlabel = featVec[-1]
        if currentlabel not in labelCounts.keys():
            labelCounts[currentlabel] = 0
        labelCounts[currentlabel] += 1

    shannonEnt = 0
    for key in labelCounts:
        prop = float(labelCounts[key]) / numexamples
        shannonEnt -= prop * log(prop, 2)
    return shannonEnt


def getNumLeafs(myTree):
    numLeafs = 0
    firstStr = next(iter(myTree))
    secondDict = myTree[firstStr]
    for key in secondDict.keys():
        if type(secondDict[key]).__name__ == 'dict':
            numLeafs += getNumLeafs(secondDict[key])
        else:
            numLeafs += 1
    return numLeafs


def getTreeDepth(myTree):
    maxDepth = 0
    firstStr = next(iter(myTree))
    secondDict = myTree[firstStr]
    for key in secondDict.keys():
        if type(secondDict[key]).__name__ == 'dict':
            thisDepth = 1 + getTreeDepth(secondDict[key])
        else:
            thisDepth = 1
        if thisDepth > maxDepth: maxDepth = thisDepth
    return maxDepth


def plotNode(nodeTxt, centerPt, parentPt, nodeType):
    arrow_args = dict(arrowstyle="<-")
    font = FontProperties(fname=r"c:\\windows\\fonts\\simsunb.ttf", size=14)
    createPlot.ax1.annotate(nodeTxt, xy=parentPt, xycoords='axes fraction',
                            xytext=centerPt, textcoords='axes fraction',
                            va="center", ha="center", bbox=nodeType, arrowprops=arrow_args, FontProperties=font)


def plotMidText(cntrPt, parentPt, txtString):
    xMid = (parentPt[0] - cntrPt[0]) / 2.0 + cntrPt[0]
    yMid = (parentPt[1] - cntrPt[1]) / 2.0 + cntrPt[1]
    createPlot.ax1.text(xMid, yMid, txtString, va="center", ha="center", rotation=30)


def plotTree(myTree, parentPt, nodeTxt):
    decisionNode = dict(boxstyle="sawtooth", fc="0.8")
    leafNode = dict(boxstyle="round4", fc="0.8")
    numLeafs = getNumLeafs(myTree)
    depth = getTreeDepth(myTree)
    firstStr = next(iter(myTree))
    cntrPt = (plotTree.xOff + (1.0 + float(numLeafs)) / 2.0 / plotTree.totalW, plotTree.yOff)
    plotMidText(cntrPt, parentPt, nodeTxt)
    plotNode(firstStr, cntrPt, parentPt, decisionNode)
    secondDict = myTree[firstStr]
    plotTree.yOff = plotTree.yOff - 1.0 / plotTree.totalD
    for key in secondDict.keys():
        if type(secondDict[key]).__name__ == 'dict':
            plotTree(secondDict[key], cntrPt, str(key))
        else:
            plotTree.xOff = plotTree.xOff + 1.0 / plotTree.totalW
            plotNode(secondDict[key], (plotTree.xOff, plotTree.yOff), cntrPt, leafNode)
            plotMidText((plotTree.xOff, plotTree.yOff), cntrPt, str(key))
    plotTree.yOff = plotTree.yOff + 1.0 / plotTree.totalD


def createPlot(inTree):
    fig = plt.figure(1, facecolor='white')  # 创建fig
    fig.clf()  # 清空fig
    axprops = dict(xticks=[], yticks=[])
    createPlot.ax1 = plt.subplot(111, frameon=False, **axprops)  # 去掉x、y轴
    plotTree.totalW = float(getNumLeafs(inTree))  # 获取决策树叶结点数目
    plotTree.totalD = float(getTreeDepth(inTree))  # 获取决策树层数
    plotTree.xOff = -0.5 / plotTree.totalW;
    plotTree.yOff = 1.0;  # x偏移
    plotTree(inTree, (0.5, 1.0), '')  # 绘制决策树
    plt.show()


if __name__ == '__main__':
    dataset, labels = createDataSet()
    featLabels = []
    myTree = createTree(dataset, labels, featLabels)
    createPlot(myTree)

附件：

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1 125:145 126:255 127:211 128:31 152:32 153:237 154:253 155:252 156:71 180:11 181:175 182:253 183:252 184:71 209:144 210:253 211:252 212:71 236:16 237:191 238:253 239:252 240:71 264:26 265:221 266:253 267:252 268:124 269:31 293:125 294:253 295:252 296:252 297:108 322:253 323:252 324:252 325:108 350:255 351:253 352:253 353:108 378:253 379:252 380:252 381:108 406:253 407:252 408:252 409:108 434:253 435:252 436:252 437:108 462:255 463:253 464:253 465:170 490:253 491:252 492:252 493:252 494:42 518:149 519:252 520:252 521:252 522:144 546:109 547:252 548:252 549:252 550:144 575:218 576:253 577:253 578:255 579:35 603:175 604:252 605:252 606:253 607:35 631:73 632:252 633:252 634:253 635:35 659:31 660:211 661:252 662:253 663:35
1 153:5 154:63 155:197 181:20 182:254 183:230 184:24 209:20 210:254 211:254 212:48 237:20 238:254 239:255 240:48 265:20 266:254 267:254 268:57 293:20 294:254 295:254 296:108 321:16 322:239 323:254 324:143 350:178 351:254 352:143 378:178 379:254 380:143 406:178 407:254 408:162 434:178 435:254 436:240 462:113 463:254 464:240 490:83 491:254 492:245 493:31 518:79 519:254 520:246 521:38 547:214 548:254 549:150 575:144 576:241 577:8 603:144 604:240 605:2 631:144 632:254 633:82 659:230 660:247 661:40 687:168 688:209 689:31
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0 125:29 126:170 127:255 128:255 129:141 151:29 152:198 153:255 154:255 155:255 156:226 157:255 158:86 178:141 179:255 180:255 181:170 182:29 184:86 185:255 186:255 187:141 204:29 205:226 206:255 207:198 208:57 213:226 214:255 215:255 216:226 217:114 231:29 232:255 233:255 234:114 241:141 242:170 243:114 244:255 245:255 246:141 259:226 260:255 261:170 269:29 270:57 273:141 274:255 275:226 286:57 287:255 288:170 302:114 303:255 304:198 314:226 315:255 331:170 332:255 333:57 342:255 343:226 360:255 361:170 370:255 371:170 388:114 389:198 398:255 399:226 416:86 417:255 426:198 427:255 444:86 445:255 454:114 455:255 456:57 472:86 473:255 482:29 483:255 484:226 500:141 501:255 511:170 512:255 513:170 528:226 529:198 539:29 540:226 541:255 542:170 555:29 556:255 557:114 568:29 569:226 570:255 571:141 582:57 583:226 584:226 598:141 599:255 600:255 601:170 602:86 607:29 608:86 609:226 610:255 611:226 612:29 627:86 628:198 629:255 630:255 631:255 632:255 633:255 634:255 635:255 636:255 637:255 638:141 639:29 657:29 658:114 659:170 660:170 661:170 662:170 663:170 664:86
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1 98:64 99:191 100:70 125:68 126:243 127:253 128:249 129:63 152:30 153:223 154:253 155:253 156:247 157:41 179:73 180:238 181:253 182:253 183:253 184:242 206:73 207:236 208:253 209:253 210:253 211:253 212:242 234:182 235:253 236:253 237:191 238:247 239:253 240:149 262:141 263:253 264:143 265:86 266:249 267:253 268:122 290:9 291:36 292:7 293:14 294:233 295:253 296:122 322:230 323:253 324:122 350:230 351:253 352:122 378:231 379:255 380:123 406:230 407:253 408:52 433:61 434:245 435:253 461:98 462:253 463:253 468:35 469:12 489:98 490:253 491:253 494:9 495:142 496:233 497:146 517:190 518:253 519:253 520:128 521:7 522:99 523:253 524:253 525:180 544:29 545:230 546:253 547:253 548:252 549:210 550:253 551:253 552:253 553:140 571:28 572:207 573:253 574:253 575:253 576:254 577:253 578:253 579:235 580:70 581:9 599:126 600:253 601:253 602:253 603:253 604:254 605:253 606:168 607:19 627:79 628:253 629:253 630:201 631:190 632:132 633:63 634:5
1 125:26 126:240 127:72 153:25 154:238 155:208 182:209 183:226 184:14 210:209 211:254 212:43 238:175 239:254 240:128 266:63 267:254 268:204 294:107 295:254 296:204 322:88 323:254 324:204 350:55 351:254 352:204 378:126 379:254 380:204 406:126 407:254 408:189 434:169 435:254 436:121 462:209 463:254 464:193 490:209 491:254 492:111 517:22 518:235 519:254 520:37 545:137 546:254 547:227 548:16 573:205 574:255 575:185 601:205 602:254 603:125 629:205 630:254 631:125 657:111 658:212 659:43
0 155:62 156:91 157:213 158:255 159:228 160:91 161:12 182:70 183:230 184:253 185:253 186:253 187:253 188:253 189:152 190:7 210:246 211:253 212:253 213:253 214:253 215:253 216:253 217:253 218:106 237:21 238:247 239:253 240:253 241:253 242:253 243:253 244:253 245:208 246:24 265:156 266:253 267:253 268:253 269:253 270:253 271:253 272:253 273:195 292:88 293:238 294:253 295:253 296:253 297:221 298:253 299:253 300:253 301:195 320:230 321:253 322:253 323:253 324:198 325:40 326:177 327:253 328:253 329:195 346:56 347:156 348:251 349:253 350:189 351:182 352:15 354:86 355:240 356:253 357:210 358:28 374:213 375:253 376:253 377:156 378:3 383:205 384:253 385:253 386:106 401:121 402:252 403:253 404:135 405:3 411:46 412:253 413:253 414:106 428:28 429:212 430:253 431:248 432:23 439:42 440:253 441:253 442:106 456:197 457:253 458:234 459:70 467:42 468:253 469:253 470:106 483:11 484:202 485:253 486:187 495:58 496:253 497:210 498:27 511:107 512:253 513:253 514:40 522:53 523:227 524:253 525:195 539:107 540:253 541:253 542:40 549:47 550:227 551:253 552:231 553:58 567:107 568:253 569:253 570:40 575:5 576:131 577:222 578:253 579:231 580:59 595:14 596:204 597:253 598:226 599:222 600:73 601:58 602:58 603:170 604:253 605:253 606:227 607:58 624:197 625:253 626:253 627:253 628:253 629:253 630:253 631:253 632:253 633:238 634:58 652:33 653:179 654:241 655:253 656:253 657:253 658:253 659:250 660:116 661:14 682:75 683:179 684:253 685:151 686:89 687:86
1 157:42 158:228 159:253 160:253 185:144 186:251 187:251 188:251 212:89 213:236 214:251 215:235 216:215 239:79 240:253 241:251 242:251 243:142 267:180 268:253 269:251 270:251 271:142 294:32 295:202 296:255 297:253 298:216 322:109 323:251 324:253 325:251 326:112 349:6 350:129 351:251 352:253 353:127 354:5 377:37 378:251 379:251 380:253 381:107 405:166 406:251 407:251 408:201 409:30 432:42 433:228 434:253 435:253 460:144 461:251 462:251 463:147 487:63 488:236 489:251 490:251 491:71 515:150 516:251 517:251 518:204 519:41 543:253 544:251 545:251 546:142 571:255 572:253 573:164 598:105 599:253 600:251 601:35 626:180 627:253 628:251 629:35 654:180 655:253 656:251 657:35 682:180 683:253 684:251 685:35
1 128:62 129:254 130:213 156:102 157:253 158:252 159:102 160:20 184:102 185:254 186:253 187:254 188:50 212:102 213:253 214:252 215:253 216:50 240:102 241:254 242:253 243:254 244:50 268:142 269:253 270:252 271:253 272:50 295:51 296:253 297:254 298:253 299:224 300:20 323:132 324:252 325:253 326:252 327:162 351:173 352:253 353:254 354:253 355:102 378:82 379:253 380:252 381:253 382:252 383:61 406:203 407:254 408:253 409:254 410:233 433:41 434:243 435:253 436:252 437:253 438:111 461:132 462:253 463:254 464:253 465:203 488:41 489:253 490:252 491:253 492:252 493:40 515:11 516:213 517:254 518:253 519:254 520:151 543:92 544:252 545:253 546:252 547:192 548:50 570:21 571:214 572:253 573:255 574:253 575:41 598:142 599:253 600:252 601:253 602:171 625:113 626:253 627:255 628:253 629:203 630:40 653:30 654:131 655:233 656:111
0 154:28 155:195 156:254 157:254 158:254 159:254 160:254 161:255 162:61 181:6 182:191 183:253 184:253 185:253 186:253 187:253 188:253 189:253 190:60 208:26 209:190 210:253 211:253 212:253 213:253 214:240 215:191 216:242 217:253 218:60 235:15 236:187 237:253 238:253 239:253 240:253 241:253 242:200 244:211 245:253 246:60 262:22 263:66 264:253 265:253 266:253 267:253 268:241 269:209 270:44 271:23 272:218 273:253 274:60 290:124 291:253 292:253 293:253 294:253 295:253 296:182 299:131 300:253 301:253 302:60 318:38 319:217 320:253 321:253 322:244 323:111 324:37 327:131 328:253 329:253 330:60 346:124 347:253 348:253 349:253 350:165 354:22 355:182 356:253 357:253 358:60 374:124 375:253 376:253 377:240 378:45 382:53 383:253 384:253 385:249 386:58 401:16 402:168 403:253 404:216 405:45 410:53 411:253 412:253 413:138 429:159 430:253 431:253 432:147 438:53 439:253 440:253 441:138 456:136 457:252 458:253 459:227 460:5 466:53 467:253 468:243 469:101 484:140 485:253 486:253 487:124 494:156 495:253 496:218 511:13 512:164 513:253 514:142 515:5 521:32 522:233 523:253 524:218 539:62 540:253 541:253 542:130 548:37 549:203 550:253 551:253 552:127 567:62 568:253 569:253 570:147 571:36 572:36 573:36 574:36 575:151 576:222 577:253 578:245 579:127 580:8 595:34 596:202 597:253 598:253 599:253 600:253 601:253 602:253 603:253 604:253 605:253 606:200 624:140 625:253 626:253 627:253 628:253 629:253 630:253 631:253 632:248 633:235 634:65 652:87 653:173 654:253 655:253 656:253 657:253 658:253 659:253 660:182 681:14 682:78 683:96 684:253 685:253 686:253 687:137 688:56
0 123:8 124:76 125:202 126:254 127:255 128:163 129:37 130:2 150:13 151:182 152:253 153:253 154:253 155:253 156:253 157:253 158:23 177:15 178:179 179:253 180:253 181:212 182:91 183:218 184:253 185:253 186:179 187:109 205:105 206:253 207:253 208:160 209:35 210:156 211:253 212:253 213:253 214:253 215:250 216:113 232:19 233:212 234:253 235:253 236:88 237:121 238:253 239:233 240:128 241:91 242:245 243:253 244:248 245:114 260:104 261:253 262:253 263:110 264:2 265:142 266:253 267:90 270:26 271:199 272:253 273:248 274:63 287:1 288:173 289:253 290:253 291:29 293:84 294:228 295:39 299:72 300:251 301:253 302:215 303:29 315:36 316:253 317:253 318:203 319:13 328:82 329:253 330:253 331:170 343:36 344:253 345:253 346:164 356:11 357:198 358:253 359:184 360:6 371:36 372:253 373:253 374:82 385:138 386:253 387:253 388:35 399:128 400:253 401:253 402:47 413:48 414:253 415:253 416:35 427:154 428:253 429:253 430:47 441:48 442:253 443:253 444:35 455:102 456:253 457:253 458:99 469:48 470:253 471:253 472:35 483:36 484:253 485:253 486:164 496:16 497:208 498:253 499:211 500:17 511:32 512:244 513:253 514:175 515:4 524:44 525:253 526:253 527:156 540:171 541:253 542:253 543:29 551:30 552:217 553:253 554:188 555:19 568:171 569:253 570:253 571:59 578:60 579:217 580:253 581:253 582:70 596:78 597:253 598:253 599:231 600:48 604:26 605:128 606:249 607:253 608:244 609:94 610:15 624:8 625:151 626:253 627:253 628:234 629:101 630:121 631:219 632:229 633:253 634:253 635:201 636:80 653:38 654:232 655:253 656:253 657:253 658:253 659:253 660:253 661:253 662:201 663:66
0 127:68 128:254 129:255 130:254 131:107 153:11 154:176 155:230 156:253 157:253 158:253 159:212 180:28 181:197 182:253 183:253 184:253 185:253 186:253 187:229 188:107 189:14 208:194 209:253 210:253 211:253 212:253 213:253 214:253 215:253 216:253 217:53 235:69 236:241 237:253 238:253 239:253 240:253 241:241 242:186 243:253 244:253 245:195 262:10 263:161 264:253 265:253 266:253 267:246 268:40 269:57 270:231 271:253 272:253 273:195 290:140 291:253 292:253 293:253 294:253 295:154 297:25 298:253 299:253 300:253 301:195 318:213 319:253 320:253 321:253 322:135 323:8 325:3 326:128 327:253 328:253 329:195 345:77 346:238 347:253 348:253 349:253 350:7 354:116 355:253 356:253 357:195 372:11 373:165 374:253 375:253 376:231 377:70 378:1 382:78 383:237 384:253 385:195 400:33 401:253 402:253 403:253 404:182 411:200 412:253 413:195 428:98 429:253 430:253 431:253 432:24 439:42 440:253 441:195 456:197 457:253 458:253 459:253 460:24 467:163 468:253 469:195 484:197 485:253 486:253 487:189 488:13 494:53 495:227 496:253 497:121 512:197 513:253 514:253 515:114 521:21 522:227 523:253 524:231 525:27 540:197 541:253 542:253 543:114 547:5 548:131 549:143 550:253 551:231 552:59 568:197 569:253 570:253 571:236 572:73 573:58 574:217 575:223 576:253 577:253 578:253 579:174 596:197 597:253 598:253 599:253 600:253 601:253 602:253 603:253 604:253 605:253 606:253 607:48 624:149 625:253 626:253 627:253 628:253 629:253 630:253 631:253 632:253 633:182 634:15 635:3 652:12 653:168 654:253 655:253 656:253 657:253 658:253 659:248 660:89 661:23
1 157:85 158:255 159:103 160:1 185:205 186:253 187:253 188:30 213:205 214:253 215:253 216:30 240:44 241:233 242:253 243:244 244:27 268:135 269:253 270:253 271:100 296:153 297:253 298:240 299:76 323:12 324:208 325:253 326:166 351:69 352:253 353:253 354:142 378:14 379:110 380:253 381:235 382:33 406:63 407:223 408:235 409:130 434:186 435:253 436:235 437:37 461:17 462:145 463:253 464:231 465:35 489:69 490:220 491:231 492:123 516:18 517:205 518:253 519:176 520:27 543:17 544:125 545:253 546:185 547:39 571:71 572:214 573:231 574:41 599:167 600:253 601:225 602:33 626:72 627:205 628:207 629:14 653:30 654:249 655:233 656:49 681:32 682:253 683:89
1 126:94 127:132 154:250 155:250 156:4 182:250 183:254 184:95 210:250 211:254 212:95 238:250 239:254 240:95 266:250 267:254 268:95 294:250 295:254 296:95 322:250 323:254 324:95 350:250 351:254 352:95 378:250 379:254 380:95 405:77 406:254 407:250 408:19 433:96 434:254 435:249 461:53 462:253 463:252 464:43 490:250 491:251 492:32 517:85 518:254 519:249 545:96 546:254 547:249 573:83 574:254 575:250 576:14 602:250 603:254 604:95 630:250 631:255 632:95 658:132 659:254 660:95
1 124:32 125:253 126:31 152:32 153:251 154:149 180:32 181:251 182:188 208:32 209:251 210:188 236:32 237:251 238:228 239:59 264:32 265:253 266:253 267:95 292:28 293:236 294:251 295:114 321:127 322:251 323:251 349:127 350:251 351:251 377:48 378:232 379:251 406:223 407:253 408:159 434:221 435:251 436:158 462:142 463:251 464:158 490:64 491:251 492:242 493:55 518:64 519:251 520:253 521:161 546:64 547:253 548:255 549:221 574:16 575:181 576:253 577:220 603:79 604:253 605:236 606:63 632:213 633:251 634:126 660:96 661:251 662:126
1 129:39 130:254 131:255 132:254 133:140 157:136 158:253 159:253 160:228 161:67 184:6 185:227 186:253 187:253 188:58 211:29 212:188 213:253 214:253 215:253 216:17 239:95 240:253 241:253 242:253 243:157 244:8 266:3 267:107 268:253 269:253 270:245 271:77 294:29 295:253 296:253 297:240 298:100 322:141 323:253 324:253 325:215 349:129 350:248 351:253 352:253 353:215 377:151 378:253 379:253 380:253 381:144 405:151 406:253 407:253 408:253 409:27 431:3 432:102 433:242 434:253 435:253 436:110 437:3 459:97 460:253 461:253 462:253 463:214 464:55 487:207 488:253 489:253 490:253 491:158 515:67 516:253 517:253 518:253 519:158 543:207 544:253 545:253 546:240 547:88 571:207 572:253 573:253 574:224 598:32 599:217 600:253 601:253 602:224 626:141 627:253 628:253 629:253 630:133 654:36 655:219 656:253 657:140 658:10
0 123:59 124:55 149:71 150:192 151:254 152:250 153:147 154:17 176:123 177:247 178:253 179:254 180:253 181:253 182:196 183:79 184:176 185:175 186:175 187:124 188:48 203:87 204:247 205:247 206:176 207:95 208:102 209:117 210:243 211:237 212:192 213:232 214:253 215:253 216:245 217:152 218:6 230:23 231:229 232:253 233:138 238:219 239:58 241:95 242:118 243:80 244:230 245:254 246:196 247:30 258:120 259:254 260:205 261:8 266:114 272:38 273:255 274:254 275:155 276:5 286:156 287:253 288:92 301:61 302:235 303:253 304:102 314:224 315:253 316:78 330:117 331:253 332:196 333:18 342:254 343:253 344:78 358:9 359:211 360:253 361:73 370:254 371:253 372:78 387:175 388:253 389:155 398:194 399:254 400:101 415:79 416:254 417:155 426:112 427:253 428:211 429:9 443:73 444:251 445:200 454:41 455:241 456:253 457:87 471:25 472:240 473:253 483:147 484:253 485:227 486:47 499:94 500:253 501:200 511:5 512:193 513:253 514:230 515:76 527:175 528:253 529:155 540:31 541:219 542:254 543:255 544:126 545:18 553:14 554:149 555:254 556:244 557:45 569:21 570:158 571:254 572:253 573:226 574:162 575:118 576:96 577:20 578:20 579:73 580:118 581:224 582:253 583:247 584:85 598:30 599:155 600:253 601:253 602:253 603:253 604:254 605:253 606:253 607:253 608:253 609:254 610:247 611:84 627:5 628:27 629:117 630:206 631:244 632:229 633:213 634:213 635:213 636:176 637:117 638:32 659:45 660:23
1 128:58 129:139 156:247 157:247 158:25 183:121 184:253 185:156 186:3 211:133 212:253 213:145 238:11 239:227 240:253 241:145 266:7 267:189 268:253 269:145 294:35 295:252 296:253 297:145 322:146 323:252 324:253 325:131 350:146 351:252 352:253 353:13 378:146 379:252 380:253 381:13 406:147 407:253 408:255 409:13 434:146 435:252 436:253 437:13 462:146 463:252 464:253 465:13 490:146 491:252 492:253 493:13 517:22 518:230 519:252 520:221 521:9 545:22 546:230 547:252 548:133 574:146 575:252 576:133 602:146 603:252 604:120 630:146 631:252 658:146 659:252
1 129:28 130:247 131:255 132:165 156:47 157:221 158:252 159:252 160:164 184:177 185:252 186:252 187:252 188:164 212:177 213:252 214:252 215:223 216:78 240:177 241:252 242:252 243:197 267:114 268:236 269:252 270:235 271:42 294:5 295:148 296:252 297:252 298:230 321:14 322:135 323:252 324:252 325:252 326:230 349:78 350:252 351:252 352:252 353:252 354:162 377:78 378:252 379:252 380:252 381:252 382:9 405:78 406:252 407:252 408:252 409:252 410:9 432:32 433:200 434:252 435:252 436:252 437:105 438:3 459:10 460:218 461:252 462:252 463:252 464:105 465:8 487:225 488:252 489:252 490:252 491:240 492:69 514:44 515:237 516:252 517:252 518:228 519:85 541:59 542:218 543:252 544:252 545:225 546:93 568:65 569:208 570:252 571:252 572:252 573:175 596:133 597:252 598:252 599:252 600:225 601:68 624:133 625:252 626:252 627:244 628:54 652:133 653:252 654:252 655:48
0 156:13 157:6 181:10 182:77 183:145 184:253 185:190 186:67 207:11 208:77 209:193 210:252 211:252 212:253 213:252 214:238 215:157 216:71 217:26 233:10 234:78 235:193 236:252 237:252 238:252 239:252 240:253 241:252 242:252 243:252 244:252 245:228 246:128 247:49 248:5 259:6 260:78 261:194 262:252 263:252 264:252 265:252 266:252 267:252 268:253 269:217 270:192 271:232 272:252 273:252 274:252 275:252 276:135 277:3 286:4 287:147 288:252 289:252 290:252 291:252 292:252 293:252 294:252 295:252 296:175 297:26 299:40 300:145 301:235 302:252 303:252 304:252 305:104 314:208 315:252 316:252 317:252 318:252 319:252 320:252 321:133 322:48 323:48 329:71 330:236 331:252 332:252 333:230 342:253 343:185 344:170 345:252 346:252 347:252 348:173 349:22 358:102 359:252 360:252 361:252 370:24 371:141 372:243 373:252 374:252 375:186 376:5 386:8 387:220 388:252 389:252 398:70 399:247 400:252 401:252 402:165 403:37 414:81 415:251 416:252 417:194 426:255 427:253 428:253 429:251 430:69 441:39 442:231 443:253 444:253 445:127 454:253 455:252 456:249 457:127 468:6 469:147 470:252 471:252 472:190 473:5 482:253 483:252 484:216 495:7 496:145 497:252 498:252 499:252 500:69 510:253 511:252 512:223 513:16 522:25 523:185 524:252 525:252 526:252 527:107 528:8 538:167 539:252 540:252 541:181 542:18 549:105 550:191 551:252 552:252 553:235 554:151 555:10 566:37 567:221 568:252 569:252 570:210 571:193 572:96 573:73 574:130 575:188 576:194 577:227 578:252 579:252 580:235 581:128 595:97 596:220 597:252 598:252 599:252 600:252 601:252 602:252 603:252 604:253 605:252 606:252 607:236 608:70 624:40 625:174 626:252 627:252 628:252 629:252 630:252 631:252 632:253 633:197 634:138 635:29 653:5 654:23 655:116 656:143 657:143 658:143 659:143 660:24 661:10
0 127:28 128:164 129:254 130:233 131:148 132:11 154:3 155:164 156:254 157:234 158:225 159:254 160:204 182:91 183:254 184:235 185:48 186:32 187:166 188:251 189:92 208:33 209:111 210:214 211:205 212:49 215:24 216:216 217:210 235:34 236:217 237:254 238:254 239:211 244:87 245:237 246:43 262:34 263:216 264:254 265:254 266:252 267:243 268:61 272:38 273:248 274:182 290:171 291:254 292:184 293:205 294:175 295:36 301:171 302:227 317:28 318:234 319:190 320:13 321:193 322:157 329:124 330:238 331:26 345:140 346:254 347:131 349:129 350:157 357:124 358:254 359:95 373:201 374:238 375:56 377:70 378:103 385:124 386:254 387:148 400:62 401:255 402:210 413:150 414:254 415:122 428:86 429:254 430:201 431:15 440:28 441:237 442:246 443:44 456:128 457:254 458:143 468:34 469:243 470:227 484:62 485:254 486:210 496:58 497:249 498:179 512:30 513:240 514:210 524:207 525:254 526:64 541:216 542:231 543:34 551:129 552:248 553:170 554:9 569:131 570:254 571:170 577:17 578:129 579:248 580:225 581:24 597:50 598:245 599:245 600:184 601:106 602:106 603:106 604:133 605:231 606:254 607:244 608:53 626:67 627:249 628:254 629:254 630:254 631:254 632:254 633:251 634:193 635:40 655:38 656:157 657:248 658:166 659:166 660:139 661:57
0 129:105 130:255 131:219 132:67 133:67 134:52 156:20 157:181 158:253 159:253 160:253 161:253 162:226 163:69 182:4 183:129 184:206 185:253 186:253 187:253 188:253 189:253 190:253 191:130 209:9 210:141 211:253 212:253 213:253 214:253 215:253 216:253 217:253 218:253 219:166 220:20 237:134 238:253 239:253 240:253 241:253 242:253 243:253 244:253 245:253 246:253 247:253 248:65 262:2 263:83 264:207 265:246 266:253 267:253 268:253 269:253 270:253 271:249 272:234 273:247 274:253 275:253 276:65 290:83 291:253 292:253 293:253 294:253 295:253 296:189 297:253 298:253 299:205 301:179 302:253 303:253 304:65 317:85 318:234 319:253 320:253 321:253 322:253 323:157 324:26 325:164 326:151 327:83 329:179 330:253 331:253 332:65 344:65 345:237 346:253 347:253 348:253 349:67 350:36 351:14 353:15 354:12 357:179 358:253 359:253 360:65 371:4 372:141 373:253 374:253 375:221 376:158 377:23 385:179 386:253 387:253 388:65 399:129 400:253 401:253 402:241 403:62 412:72 413:226 414:253 415:175 416:24 426:119 427:247 428:253 429:253 430:206 439:8 440:134 441:253 442:253 443:130 454:132 455:253 456:253 457:194 458:27 467:125 468:253 469:253 470:253 471:130 481:45 482:213 483:253 484:253 485:112 493:70 494:170 495:247 496:253 497:253 498:89 499:43 509:67 510:253 以上是关于机器学习-算法学习随记的主要内容，如果未能解决你的问题，请参考以下文章 
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