From 6048d638ef3cb266015b153d99fb1f1bbe29b896 Mon Sep 17 00:00:00 2001 From: gzdaijie Date: Thu, 1 Aug 2019 23:35:28 +0800 Subject: [PATCH] add 9 files --- README.md | 18 +- SUMMARY.md | 6 - book.json | 46 --- gulpfile.js | 7 - ipynb/sklearn-cluster-compare.ipynb | 335 ++++++++++++++++++ .../1.md | 5 + ml/10.md | 35 ++ ml/11.md | 32 ++ ml/12.md | 52 +++ ml/13.md | 55 +++ ml/14.md | 72 ++++ ml/2.md | 42 +++ ml/3.md | 43 +++ ml/4.md | 27 ++ ml/5.md | 54 +++ ml/6.md | 49 +++ ml/7.md | 53 +++ ml/8.md | 48 +++ ml/9.md | 15 + ml/image/10.svm.png | Bin 0 -> 18450 bytes ml/image/11.F1.png | Bin 0 -> 3748 bytes ml/image/11.accuracy.png | Bin 0 -> 3814 bytes ml/image/11.confusion_matrix.png | Bin 0 -> 14629 bytes ml/image/11.precision.png | Bin 0 -> 1654 bytes ml/image/11.recall.png | Bin 0 -> 1943 bytes ml/image/13.laplace.png | Bin 0 -> 82012 bytes ml/image/13.naive.bayes.formula.png | Bin 0 -> 35404 bytes ml/image/14.decision_tree_eg.gif | Bin 0 -> 63051 bytes ml/image/14.entropy.jpg | Bin 0 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create mode 100644 ml/3.md create mode 100644 ml/4.md create mode 100644 ml/5.md create mode 100644 ml/6.md create mode 100644 ml/7.md create mode 100644 ml/8.md create mode 100644 ml/9.md create mode 100644 ml/image/10.svm.png create mode 100644 ml/image/11.F1.png create mode 100644 ml/image/11.accuracy.png create mode 100644 ml/image/11.confusion_matrix.png create mode 100644 ml/image/11.precision.png create mode 100644 ml/image/11.recall.png create mode 100644 ml/image/13.laplace.png create mode 100644 ml/image/13.naive.bayes.formula.png create mode 100644 ml/image/14.decision_tree_eg.gif create mode 100644 ml/image/14.entropy.jpg create mode 100644 ml/image/14.gain.jpg create mode 100644 ml/image/14.gain.ratio.jpg create mode 100644 ml/image/14.splitInfo.jpg create mode 100644 ml/image/4.cosine.png create mode 100644 ml/image/6.nlp.jpg create mode 100644 "ml/image/8.\346\225\260\346\215\256\346\270\205\346\264\227\344\270\216\347\211\271\345\276\201\345\244\204\347\220\206.jpg" create mode 100644 ml/image/9.cluster.algorithms.png create mode 100644 ml/image/9.cluster.question.png delete mode 100644 package.json diff --git a/README.md b/README.md index 5ac426b..0ced6a5 100644 --- a/README.md +++ b/README.md @@ -1,19 +1,5 @@ -# [机器学习面试题](https://geekcircle.github.io/machine-learning-interview-qa) +# Python&机器学习&深度学习面试笔试题 ## 序言 -持续整理、更新机器学习领域的面试笔试题,题目来源主要来源于[优达学城](http://cn.udacity.com/)、[七月在线](https://www.julyedu.com/)等。 - -## 地址 -- Github地址: [https://github.com/geekcircle/machine-learning-interview-qa](https://geekcircle.github.io/machine-learning-interview-qa) -- Gitbook地址: [https://geekcircle.github.io/machine-learning-interview-qa](https://geekcircle.github.io/machine-learning-interview-qa) - -## 友情链接 - -- [极客兔兔的博客](https://geektutu.com/series) -- [StackOverflow上票数最高的100个Python问题](https://geekcircle.github.io/stackoverflow-python-top-qa/) - -## 贡献者 -- [Dai Jie](https://github.com/gzdaijie) -- [Xu Ri](https://github.com/xurisun) -- [Tijing Wang](https://github.com/vitow) \ No newline at end of file +持续整理、更新Python、机器学习(Machine Learning)、深度学习(Deep Learning)领域的面试笔试题。 diff --git a/SUMMARY.md b/SUMMARY.md deleted file mode 100644 index 53bcad2..0000000 --- a/SUMMARY.md +++ /dev/null @@ -1,6 +0,0 @@ -# Summary - -* [序言](README.md) -* 题目 - * [1. 如何处理特征向量的缺失值](questions/1.如何处理特征向量的缺失值.md) - diff --git a/book.json b/book.json deleted file mode 100644 index 49ceee3..0000000 --- a/book.json +++ /dev/null @@ -1,46 +0,0 @@ -{ - "title": "machine-learning-interview-qa", - "description": "stackoverflow上票数最高的100个问题", - "language": "zh-hans", - "links": { - "sidebar": { - "极客兔兔的博客": "https://geektutu.com/series", - "machine-learning-interview-qa": "https://github.com/geekcircle/machine-learning-interview-qa" - } - }, - "plugins": [ - "-highlight", - "expandable-chapters", - "splitter", - "page-footer-ex", - "prism", - "github", - "github-buttons", - "sitemap-general" - ], - "pluginsConfig": { - "sitemap-general": { - "prefix": "https://geekcircle.github.io/machine-learning-interview-qa/" - }, - "expandable-chapters": {}, - "page-footer-ex": { - "copyright": "[geekcircle](https://github.com/geekcircle)", - "markdown": true, - "update_label": "updated", - "update_format": "YYYY-MM-DD HH:mm:ss" - }, - "github": { - "url": "https://github.com/geekcircle/machine-learning-interview-qa" - }, - "github-buttons": { - "buttons": [ - { - "user": "geekcircle", - "repo": "machine-learning-interview-qa", - "type": "star", - "size": "large" - } - ] - } - } -} \ No newline at end of file diff --git a/gulpfile.js b/gulpfile.js deleted file mode 100644 index 5b63131..0000000 --- a/gulpfile.js +++ /dev/null @@ -1,7 +0,0 @@ -var deploy = require("gulp-gh-pages"); -var gulp = require("gulp"); - - -gulp.task('deploy', function () { - return gulp.src("./_book/**/*").pipe(deploy()); -}); \ No newline at end of file diff --git a/ipynb/sklearn-cluster-compare.ipynb b/ipynb/sklearn-cluster-compare.ipynb new file mode 100644 index 0000000..556c0fa --- /dev/null +++ b/ipynb/sklearn-cluster-compare.ipynb @@ -0,0 +1,335 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Cluster 聚类算法比较" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 1. 生成数据集" + ] + }, + { + "cell_type": "code", + "execution_count": 96, + "metadata": {}, + "outputs": [], + "source": [ + "import random\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline\n", + "\n", + "from sklearn.cluster import KMeans, AffinityPropagation, MeanShift, SpectralClustering, DBSCAN, Birch" + ] + }, + { + "cell_type": "code", + "execution_count": 98, + "metadata": {}, + "outputs": [], + "source": [ + "clusters_names = ['KMeans', 'AffinityPropagation', 'MeanShift', 'SpectralClustering', 'DBSCAN', 'Birch']\n", + "clusters = [KMeans, AffinityPropagation, MeanShift, SpectralClustering, DBSCAN, Birch]\n", + "\n", + "\n", + "def plot_cluster(data, label, title='Origin Cluster'):\n", + " n = np.max(label) + 1\n", + " \n", + " colors = ['r', 'b', 'y', 'g', 'c', 'm', 'k']\n", + " markers = ['o', 'x', '<', '>', '1', '2']\n", + " \n", + " plt.clf()\n", + " plt.title(title)\n", + " \n", + " for i in range(n):\n", + " cluster = np.array([data[j] for j, v in enumerate(label) if v == i])\n", + " plt.scatter(cluster[:, 0], cluster[:, 1], color=colors[i % 7], marker=markers[i % 6], label=str(i))\n", + " \n", + " plt.legend(loc = 'upper right')\n", + " \n", + "def predict_cluster(data, name, **kwargs):\n", + " method = clusters[clusters_names.index(name)]\n", + " model = method(**kwargs)\n", + " result = model.fit_predict(data)\n", + " print('result: ', result)\n", + " plot_cluster(data, result, name)" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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aEON89pDU4EpWpPOaqpYY0zLGwfTxNpL69D9vV4ySrgEuAYbSL3DI2XYsF2Pe\ntmPGGPCb6eNcbceMX8aYo7/r00iO1zwsaYJkWz0k6c3UsR27JqFLEvBFYEdE/PfMU2Uvdi3pzelr\nkHQuybY62KYY5/NN4ApJr5e0ClgNfD9PMUrqk/S69PGpaYzPtCNGSe8nqVdujIhDmZfkZjvOF2PO\ntuPqzGKXAT9IH38T+J20S+OdwIuZcmYuYszL33VEPBoRJ0bEYEQMkpRVzomI56lnO1Z79LTTb8C7\nScopjwDb09vFwHLgAeBJ4G+A49PlrwMeJ+l++B7wrjbG+IH0H/wXwD7grzOv2Uyyt7YTuChvMZLs\nGT2eLvcQcGkbY3yKpDZZmve5HG7HsjHmbDt+HXgsnf8tkoOQkHRl/I90Oz5KptspRzHm5u96zjIT\nHOlyWfR29Kn/ZmYF0TUlFzOzonNCNzMrCCd0M7OCcEI3MysIJ3Qzs4JwQjczKwgndDOzgvj/M7MM\nNhX7iLoAAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "oranges = np.array([(random.randint(200, 220), random.randint(50, 75)) for _ in range(20)])\n", + "apples = np.array([(random.randint(227, 240), random.randint(50, 75)) for _ in range(20)])\n", + "data = np.append(oranges, apples, axis=0)\n", + "label = np.array([0] * 20 + [1] * 20) \n", + "plot_cluster(data, label)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 2.1 KMeans" + ] + }, + { + "cell_type": "code", + "execution_count": 87, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "result: [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n", + " 0 0 0]\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# 点之间的距离\n", + "predict_cluster(data, 'KMeans', n_clusters=2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 2.2 Affinity Propagation" + ] + }, + { + "cell_type": "code", + "execution_count": 101, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "result: [1 0 0 0 0 1 0 1 1 0 1 0 1 0 1 0 0 1 1 0 2 2 2 2 3 2 3 3 3 2 2 2 3 2 3 2 3\n", + " 3 3 3]\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# 图之间的距离(最近邻图),n不可扩展\n", + "predict_cluster(data, 'AffinityPropagation')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 2.3. MeanShift" + ] + }, + { + "cell_type": "code", + "execution_count": 103, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "result: [2 1 1 1 1 2 1 2 2 1 2 1 2 1 2 1 1 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n", + " 0 0 0]\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# 点之间的距离,n不可扩展\n", + "predict_cluster(data, 'MeanShift')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 2.4. SpectralClustering" + ] + }, + { + "cell_type": "code", + "execution_count": 90, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "result: [0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0\n", + " 0 0 0]\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# 最近临图,n可扩展\n", + "predict_cluster(data, 'SpectralClustering', n_clusters=2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 2.5 DBSCAN" + ] + }, + { + "cell_type": "code", + "execution_count": 104, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "result: [-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1\n", + " -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1]\n" + ] + }, + { + "data": { + "image/png": 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F9yTvfwG/ABwGfBlYO2XM64FrBpfPAT4yn3NarK+ea/EbwNMHl1/X8loMxh0B3AJsA8YW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\nTkSuQmCC\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# 最近点,n不可扩展,适合非常大的n\n", + "predict_cluster(data, 'DBSCAN', min_samples=2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 2.6 Birch" + ] + }, + { + "cell_type": "code", + "execution_count": 106, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "result: [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + " 1 1 1]\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# 欧式距离,n可扩展,适合大数据集,大n\n", + "predict_cluster(data, 'Birch', n_clusters=2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 3. 参考文档\n", + "\n", + "- [sklearn 聚类官方文档](http://sklearn.apachecn.org/cn/0.19.0/modules/clustering.html)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.2" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git "a/questions/1.\345\246\202\344\275\225\345\244\204\347\220\206\347\211\271\345\276\201\345\220\221\351\207\217\347\232\204\347\274\272\345\244\261\345\200\274.md" b/ml/1.md similarity index 86% rename from "questions/1.\345\246\202\344\275\225\345\244\204\347\220\206\347\211\271\345\276\201\345\220\221\351\207\217\347\232\204\347\274\272\345\244\261\345\200\274.md" rename to ml/1.md index ed4802a..4f270af 100644 --- "a/questions/1.\345\246\202\344\275\225\345\244\204\347\220\206\347\211\271\345\276\201\345\220\221\351\207\217\347\232\204\347\274\272\345\244\261\345\200\274.md" +++ b/ml/1.md @@ -1,10 +1,15 @@ # 1. 如何处理特征向量的缺失值 + + ## 1) 缺失值较多 + 缺失值较多.直接将该特征舍弃掉,否则可能反倒会带入较大的噪声,对结果造成不良影响。 ## 2) 缺失值较少 + 缺失值较少,其余的特征缺失值都在10%以内,我们可以采取很多的方式来处理: + - 方式1: 把NaN直接作为一个特征,假设用0表示; ```python diff --git a/ml/10.md b/ml/10.md new file mode 100644 index 0000000..b46fd02 --- /dev/null +++ b/ml/10.md @@ -0,0 +1,35 @@ +# 10. 支持向量机(SVM)中的支持向量是什么意思 + + + +## 题目 + +我们在下面的二元标签的数据集上训练一个线性SVM模型 + +```python ++:(−1,1),(1,−1),(−1,−1) +−:(1,1),(2,0),(2,1) +``` + +这个模型中的支持向量是哪些? + +A. (−1,1),(1,1),(2,1) +B. (−1,1),(−1,−1),(2,1) +C. (−1,1),(1,−1),(1,1),(2,0) + +## 解析 + +![示意图](./image/10.svm.png) + +在画分割线区分红绿两类点的时候,可以问自己一个问题,你认不认为所有的点对于分割线的位置都是起决定性作用的? + +其实在特别远的区域,哪怕你增加10000个样本点,对于分割线的位置,也是没有作用的,因为分割线是由几个关键点决定的(图上三个),这几个关键点支撑起了一个分割超平面,所以这些关键点,就是支持向量。 + +## 参考文档 + +- [支持向量机(SVM)里的支持向量是什么意思 - sofasofa](http://sofasofa.io/forum_main_post.php?postid=1000255) +- [支持向量机(SVM)是什么意思?- 知乎](https://www.zhihu.com/question/21094489) + +## 答案 + +在坐标系中画一下,即可知道C是正确答案 \ No newline at end of file diff --git a/ml/11.md b/ml/11.md new file mode 100644 index 0000000..e3fa88f --- /dev/null +++ b/ml/11.md @@ -0,0 +1,32 @@ +# 11. 精确率(precision)和召回率(recall) + + + +混淆矩阵 + +- True Positive(真正, TP):将正类预测为正类数. +- True Negative(真负 , TN):将负类预测为负类数. +- False Positive(假正, FP):将负类预测为正类数 → 误报 (Type I error). +- False Negative(假负 , FN):将正类预测为负类数 → 漏报 (Type II error). + +![示意图](./image/11.confusion_matrix.png) + +精确率(precision)定义为: + +![precision](./image/11.precision.png) + +需要注意的是精确率(precision)和准确率(accuracy)是不一样的, + +![accuracy](./image/11.accuracy.png) + +在正负样本不平衡的情况下,准确率这个评价指标有很大的缺陷。比如在互联网广告里面,点击的数量是很少的,一般只有千分之几,如果用acc,即使全部预测成负类(不点击)acc 也有 99% 以上,没有意义。 + +召回率(recall,sensitivity,true positive rate)定义为: + +![recall](./image/11.recall.png) + +此外,还有`F1`值,是精确率和召回率的调和均值, + +![F1](./image/11.F1.png) + +精确率和准确率都高的情况下,`F1`值也会高。 \ No newline at end of file diff --git a/ml/12.md b/ml/12.md new file mode 100644 index 0000000..07ac002 --- /dev/null +++ b/ml/12.md @@ -0,0 +1,52 @@ +# 12. 数据挖掘中如何判断关联规则有效性 + + + +## 关联规则的三个度 + +### 1.支持度(Support) + +> Support(X→Y) = P(X,Y) / P(I) = P(X∪Y) / P(I) = num(XUY) / num(I) + +支持度表示项集{X,Y}在总项集里出现的概率。 + +其中,I表示总事务集。num()表示求事务集里特定项集出现的次数。 + +比如,num(I)表示总事务集的个数,num(X∪Y)表示含有{X,Y}的事务集的个数(个数也叫次数)。 + +### 2.置信度 (Confidence) + +> Confidence(X→Y) = P(Y|X) = P(X,Y) / P(X) = P(XUY) / P(X) + +置信度表示在先决条件X发生的情况下,由关联规则”X→Y“推出Y的概率。即在含有X的项集中,含有Y的可能性。 + +### 3.提升度(Lift) + +> Lift(X→Y) = P(Y|X) / P(Y) + +提升度表示含有X的条件下,同时含有Y的概率,与Y总体发生的概率之比。 + +满足最小支持度和最小置信度的规则,叫做“强关联规则”。 + +- Lift(X→Y)>1,“X→Y”是有效的强关联规则。 +- Lift(X→Y) <=1,“X→Y”是无效的强关联规则。 +- 特别地,Lift(X→Y) =1,X与Y相互独立。 + +## 判断规则的有效性 + +### 题目 + +已知有1000名顾客买年货,分为甲乙两组,每组各500人,其中甲组有500人买了茶叶,同时又有450人买了咖啡;乙组有450人买了咖啡,如表所示,**题目:茶叶→咖啡是一条有效的关联规则吗?** + +组次|买茶叶的人数|买咖啡的人数| +---|---|---| +甲组(500人)|500|450| +已组(500人)|0|450| + +### 答案 + +- ”茶叶→咖啡“的支持度: Support(X→Y) = 450 / 500 = 90% +- "茶叶→咖啡"的置信度为:Confidence(X→Y) = 450 / 500 = 90% +- ”茶叶→咖啡“的提升度为:Lift(X→Y) = Confidence(X→Y) / P(Y) = 90% / ((450+450)/1000) = 1 + +由于提升度Lift(X→Y) =1,表示X与Y相互独立,即是否有X,对于Y的出现无影响。也就是说,是否购买咖啡,与有没有购买茶叶无关联。即规则”茶叶→咖啡“不成立,或者说关联性很小,几乎没有,虽然它的支持度和置信度都高达90%,但它不是一条有效的关联规则。 \ No newline at end of file diff --git a/ml/13.md b/ml/13.md new file mode 100644 index 0000000..de436f6 --- /dev/null +++ b/ml/13.md @@ -0,0 +1,55 @@ +# 13. 朴素贝叶斯分类某个类别概率为0怎么办 + + + +## 题目 + +A1,A2,A3是三个特征,Y是分类结果。A1,A2,A3和Y 均只有0和1两种情况。 + +|A1|A2|A3|Y| +|:---:|:---:|:---:|:---:| +|1|1|0|1| +|0|1|1|1| +|1|0|1|0| +|0|1|0|0| +|0|0|1|0| + +### 1. 朴素贝叶斯(Naive Bayes)为什么朴素? + +朴素贝叶斯中的“朴素”二字突出了这个算法的简易性。 + +朴素贝叶斯的简易性表现该算法基于一个很朴素的假设:所有的变量都是相互独立的。用贝叶斯定理可以写成 + +![公式](./image/13.naive.bayes.formula.png) + +但是在很多情况下,所有变量两两之间独立,这几乎是不可能的。 + +> 举个例子: +> Y = 这个人是否是举重运动员。 +> X1 = 性别,X2 = 这个人能否举起100公斤的箱子。 +> 变量X1和X2显然不是独立的。 + +换句话说,朴素贝叶斯的独立性假设很傻很天真,所以预测精度往往不是很高。 + +### 2. `1,0,0` 的分类结果是什么? + +![拉普拉斯转换](./image/13.laplace.png) + +> 分母都是相同,所以只计算分子即可。 + +```python +P(Y=0) = 3/5 +P(Y=1) = 2/5 +P(Y=0|A1=1,A2=0,A3=0) = 3/5 * 1/3 * 2/3 * 1/3 = 2/45 +P(Y=1|A1=1,A2=0,A3=0) = 2/5 * 1/2 * 1/4 * 1/2 = 1/40 +``` + +> 答: **分类结果为0** + +## 结论 + +从上题可以看出,当每个类别未出现导致概率为0时,可以采用贝叶斯估计的方式来解决。当训练集较多的情况下,可以生成一个接近于0的概率代替0,接近于p的概率代替p,几乎不影响原有的先验概率分布。 + +贝叶斯估计公式中,常取λ为1,这时称之为拉普拉斯平滑(Laplace smoothing)。 + +上例仅对先验概率为0的特征采用了贝叶斯估计,一般情况下会对所有参与训练的特征都采用贝叶斯估计。 \ No newline at end of file diff --git a/ml/14.md b/ml/14.md new file mode 100644 index 0000000..165ac0d --- /dev/null +++ b/ml/14.md @@ -0,0 +1,72 @@ +# 14. 决策树 + + + +## 什么是决策树 + +决策树(decision tree)是一种基本的分类与回归方法。决策树是用样本的属性作为结点,用属性的取值作为分支的树结构。 + + +决策树的根结点是所有样本中信息量最大的属性。树的中间结点是该结点为根的子树所包含的样本子集中信息量最大的属性。决策树的叶结点是样本的类别值。决策树是一种知识表示形式,它是对所有样本数据的高度概括决策树能准确地识别所有样本的类别,也能有效地识别新样本的类别。 + + +![决策树举例](./image/14.decision_tree_eg.gif) + +## 特征选择 + +|ID|年龄|有工作|有自己的房子|信贷情况|类别(是否个给贷款)| +|:---:|:---:|:---:|:---:|:---:|:---:| +|1|青年|否|否|一般|否| +|2|青年|否|否|好|否| +|3|青年|是|否|好|是| +|4|青年|是|是|一般|是| +|5|青年|否|否|一般|否| +|6|中年|否|否|一般|否| +|7|中年|否|否|好|否| +|8|中年|是|是|好|是| +|9|中年|否|是|非常好|是| +|10|中年|否|是|非常好|是| +|11|老年|否|是|非常好|是| +|12|老年|否|是|好|是| +|13|老年|是|否|好|是| +|14|老年|是|否|非常好|是| +|15|老年|否|否|一般|否| + +信息熵(entropy)是用来衡量一个随机变量出现的期望值。如果信息的不确定性越大,熵的值也就越大,出现的各种情况也就越多。 +![信息熵](./image/14.entropy.jpg) + +信息增益(information gain)是指信息划分前后的熵的变化,也就是说由于使用这个属性分割样例而导致的期望熵降低。也就是说,信息增益就是原有信息熵与属性划分后信息熵(需要对划分后的信息熵取期望值)的差值,具体计算法如下: +![信息增益](./image/14.gain.jpg) +## ID3算法 + +决策树算法ID3的基本思想: + +首先找出最有判别力的属性,把样例分成多个子集,每个子集又选择最有判别力的属性进行划分,一直进行到所有子集仅包含同一类型的数据为止。最后得到一棵决策树。 + +J.R.Quinlan的工作主要是引进了信息论中的信息增益,他将其称为信息增益(information gain),作为属性判别能力的度量,设计了构造决策树的递归算法。 + + +ID3算法: + + 1.对当前例子集合,计算各属性的信息增益; + 2.选择信息增益最大的属性Ak; + 3.把在Ak处取值相同的例子归于同一子集,Ak取几个值就得几个子集; + 4.对既含正例又含反例的子集,递归调用建树算法; + 5.若子集仅含正例或反例,对应分枝标上P或N,返回调用处。 + +## C4.5算法 +C4.5算法是ID3算法的一种改进。 + +改进 +- 用信息增益率来选择属性,克服了用信息增益选择属性偏向选择多值属性的不足 +- 在构造树的过程中进行剪枝 +- 对连续属性进行离散化 +- 能够对不完整的数据进行处理 + +信息增益率 + +设样本集S按离散属性F的c个不同的取值划分为c个子集,则这c个子集的信息熵为: +![splitInfo](./image/14.splitInfo.jpg) +信息增益率是信息增益与信息熵的比例,如下: +![信息增益率](./image/14.gain.ratio.jpg) +## CART \ No newline at end of file diff --git a/ml/2.md b/ml/2.md new file mode 100644 index 0000000..e0b54b6 --- /dev/null +++ b/ml/2.md @@ -0,0 +1,42 @@ +# 2. 请简要说说一个完整机器学习项目的流程 + + + +## 1 抽象成数学问题 + +明确问题是进行机器学习的第一步。机器学习的训练过程通常都是一件非常耗时的事情,胡乱尝试时间成本是非常高的。 +这里的抽象成数学问题,指的我们明确我们可以获得什么样的数据,目标是一个分类还是回归或者是聚类的问题,如果都不是的话,如果划归为其中的某类问题。 + +## 2 获取数据 + +数据决定了机器学习结果的上限,而算法只是尽可能逼近这个上限。 +数据要有代表性,否则必然会过拟合。 +而且对于分类问题,数据偏斜不能过于严重,不同类别的数据数量不要有数个数量级的差距。 +而且还要对数据的量级有一个评估,多少个样本,多少个特征,可以估算出其对内存的消耗程度,判断训练过程中内存是否能够放得下。如果放不下就得考虑改进算法或者使用一些降维的技巧了。如果数据量实在太大,那就要考虑分布式了。 + +## 3 特征预处理与特征选择 + +良好的数据要能够提取出良好的特征才能真正发挥效力。 +特征预处理、数据清洗是很关键的步骤,往往能够使得算法的效果和性能得到显著提高。归一化、离散化、因子化、缺失值处理、去除共线性等,数据挖掘过程中很多时间就花在它们上面。这些工作简单可复制,收益稳定可预期,是机器学习的基础必备步骤。 +筛选出显著特征、摒弃非显著特征,需要机器学习工程师反复理解业务。这对很多结果有决定性的影响。特征选择好了,非常简单的算法也能得出良好、稳定的结果。这需要运用特征有效性分析的相关技术,如相关系数、卡方检验、平均互信息、条件熵、后验概率、逻辑回归权重等方法。 + +## 4 训练模型与调优 + +直到这一步才用到我们上面说的算法进行训练。现在很多算法都能够封装成黑盒供人使用。但是真正考验水平的是调整这些算法的(超)参数,使得结果变得更加优良。这需要我们对算法的原理有深入的理解。理解越深入,就越能发现问题的症结,提出良好的调优方案。 + +## 5 模型诊断 + +如何确定模型调优的方向与思路呢?这就需要对模型进行诊断的技术。 +过拟合、欠拟合 判断是模型诊断中至关重要的一步。常见的方法如交叉验证,绘制学习曲线等。过拟合的基本调优思路是增加数据量,降低模型复杂度。欠拟合的基本调优思路是提高特征数量和质量,增加模型复杂度。 +误差分析 也是机器学习至关重要的步骤。通过观察误差样本,全面分析误差产生误差的原因:是参数的问题还是算法选择的问题,是特征的问题还是数据本身的问题…… +诊断后的模型需要进行调优,调优后的新模型需要重新进行诊断,这是一个反复迭代不断逼近的过程,需要不断地尝试, 进而达到最优状态。 + +## 6 模型融合 + +一般来说,模型融合后都能使得效果有一定提升。而且效果很好。 +工程上,主要提升算法准确度的方法是分别在模型的前端(特征清洗和预处理,不同的采样模式)与后端(模型融合)上下功夫。因为他们比较标准可复制,效果比较稳定。而直接调参的工作不会很多,毕竟大量数据训练起来太慢了,而且效果难以保证。 + +## 7 上线运行 + +这一部分内容主要跟工程实现的相关性比较大。工程上是结果导向,模型在线上运行的效果直接决定模型的成败。 不单纯包括其准确程度、误差等情况,还包括其运行的速度(时间复杂度)、资源消耗程度(空间复杂度)、稳定性是否可接受。 +这些工作流程主要是工程实践上总结出的一些经验。并不是每个项目都包含完整的一个流程。这里的部分只是一个指导性的说明,只有大家自己多实践,多积累项目经验,才会有自己更深刻的认识。 diff --git a/ml/3.md b/ml/3.md new file mode 100644 index 0000000..a13fae3 --- /dev/null +++ b/ml/3.md @@ -0,0 +1,43 @@ +# 3. 某超市研究销售记录发现买啤酒的人很大概率也会买尿布,这属于数据挖掘的哪类问题? + + + +- A 关联规则发现 +- B 聚类 +- C 分类 +- D 自然语言处理 + +## A 关联规则发现 + +关联规则就是有关联的规则,形式是这样定义的:两个不相交的非空集合X、Y,如果有X-->Y,就说X-->Y是一条关联规则。在题目的例子中,我们发现购买啤酒就一定会购买尿布,{啤酒}-->{尿布}就是一条关联规则。关联规则的强度用支持度(support)和自信度(confidence)来描述。 +支持度的定义:support(X-->Y) = |X交Y|/N=集合X与集合Y中的项在一条记录中同时出现的次数/数据记录的个数。例如:support({啤酒}-->{尿布}) = 啤酒和尿布同时出现的次数/数据记录数 +自信度的定义:confidence(X-->Y) = |X交Y|/|X| = 集合X与集合Y中的项在一条记录中同时出现的次数/集合X出现的个数 。例如:confidence({啤酒}-->{尿布}) = 啤酒和尿布同时出现的次数/啤酒出现的次数。 confidence({尿布}-->{啤酒}) = 啤酒和尿布同时出现的次数/尿布出现的次数。 +这里定义的支持度和自信度都是相对的支持度和自信度,不是绝对支持度,绝对支持度abs_support = 数据记录数N*support。 +支持度和自信度越高,说明规则越强,关联规则挖掘就是挖掘出满足一定强度的规则。 + +## B 聚类 + +Clustering(聚类): +简单地说就是把相似的东西分到一组,聚类的时候,我们并不关心某一类是什么,我们需要实现的目标只是把相似的东西聚到一起,因此,一个聚类算法通常只需要知道如何计算相似度就可以开始工作了,因此 clustering 通常并不需要使用训练数据进行学习,这在Machine Learning中被称作unsupervised learning (无监督学习)。聚类分析目的在于将相似的事物归类,同一类中的个体有较大的相似性,不同类的个体差异性很大。 + +## C 分类 + +Classification (分类): +一个 classifier会从它得到的训练集中进行“学习”,从而具备对未知数据进行分类的能力,这种提供训练数据的过程通常叫做 supervised learning (监督学习)。所谓分类,简单来说,就是根据文本的特征或属性,划分到已有的类别中。 +常用的分类算法包括:决策树分类法,朴素的贝叶斯分类算法(native Bayesian classifier)、基于支持向量机(SVM)的分类器,神经网络法,k-最近邻法(k-nearest neighbor,kNN),模糊分类法等。分类作为一种监督学习方法,要求必须事先明确知道各个类别的信息,并且断言所有待分类项都有一个类别与之对应。但是很多时候上述条件得不到满足,尤其是在处理海量数据的时候,如果通过预处理使得数据满足分类算法的要求,则代价非常大,这时候可以考虑使用聚类算法。 + +## D 自然语言处理 + +自然语言处理的主要应用范畴包括:文本朗读(Text to speech)/语音合成(Speech synthesis) +语音识别(Speech recognition) +中文自动分词(Chinese word segmentation) +词性标注(Part-of-speech tagging) +句法分析(Parsing) +自然语言生成(Natural language generation) +文本分类(Text categorization) +信息检索(Information retrieval) +信息抽取(Information extraction) +文字校对(Text-proofing) +问答系统(Question answering)等 + +> 选择A,关联规则发现 \ No newline at end of file diff --git a/ml/4.md b/ml/4.md new file mode 100644 index 0000000..7a3c738 --- /dev/null +++ b/ml/4.md @@ -0,0 +1,27 @@ +# 4. 余弦相似与欧氏距离有什么区别和联系 + + + +## 1)区别 + +假设 2人对三部电影的评分分别是 `A = [3, 3, 3]` 和 `B = [5, 5, 5]` + +那么2人的欧式距离是 根号12 = 3.46, A、B的余弦相似度是1(方向完全一致)。 + +> 余弦值的范围是[-1, 1], 越接近于1,说明2个向量的方向越相近 + +欧式距离和余弦相似度都能度量2个向量之间的相似度,但是欧式距离从2点之间的距离去考量,余弦相似从2个向量之间的夹角去考量。 +从上例可以发出,2人对三部电影的评价趋势是一致的,但是欧式距离并不能反映出这一点,余弦相似则能够很好地反应。余弦相似可以很好地规避指标刻度的差异,最常见的应用是计算 **文本的相似度** 。 + +## 2)联系 +从下图的公式可以看出,归一化后计算的欧式距离是关于余弦相似的单调函数,可以认为归一化后,余弦相似与欧式距离效果是一致的(欧式距离越小等价于余弦相似度越大)。 + +因此可以将 **求余弦相似转为求欧式距离** ,余弦相似的计算复杂度过高,转为求欧式距离后,可以借助`KDTree`(KNN算法用到)或者`BallTree`(对高维向量友好)来降低复杂度。 + +![余弦相似](./image/4.cosine.png) + + +## 3)参考链接 + +[知乎:欧氏距离和余弦相似度的区别是什么?](https://www.zhihu.com/question/19640394) + diff --git a/ml/5.md b/ml/5.md new file mode 100644 index 0000000..c9f074d --- /dev/null +++ b/ml/5.md @@ -0,0 +1,54 @@ +# 5. 下面哪个不属于数据的属性类别 + + + +- A 标称 +- B 序数 +- C 区间 +- D 相异 + +## 关于数据的属性类别的介绍 + + +数据集由数据对象组成,一个数据对象代表一个实体。数据对象又称样本、实例、数据点或对象。属性(attribute)是一个数据字段,表示数据对象的一个特征。属性向量(或特征向量)是用来描述一个给定对象的一组属性。属性有不同类型:标称属性(nominal attribute)、二元属性(binary attribute)、序数属性(ordinal attribute)、 数值属性(numerical attribute)、离散属性与连续属性。 + +### A、标称属性(nominal attribute) + +标称属性的值是一些符号或实物的名称,每个值代表某种类别、编码或状态,所以标称属性又被看做是分类型的属性(categorical)。这些值不必具有有意义的序,并且不是定量的。 + +### B、二元属性(binary attribute) + +二元属性是一种标称属性,只有两个类别或状态:0或1,其中0常表示不出现,1表示出现。如果将0和1对应于false和true,二元属性则为布尔属性。 + +### C、序数属性(ordinal attribute) + +序数属性可能的取值之间具有有意义的序或秩评定,但相继值之间的差是未知的。例如,学生的成绩属性可以分为优、良、中、差四个等级;某快餐店的饮料杯具有大、中、小三个可能值。然而,具体“大”比“中”大多少是未知的。 + +序数属性可用于记录不能客观度量的主观质量评估。因此,序数属性常用于等级评定调查。如某销售部门客户服务质量的评估,0表示很不满意,1不太满意,2表示中性,3表示满意,4表示非常满意。 + +通过数据预处理中的数据规约,序数属性可以通过将数据的值域划分成有限个有序类别,将数值属性离散化而得到。应注意的是,标称、二元和序数属性都是定性的,只描述样本的特征,而不给出实际大小或数量。下面介绍提供样本定量度量的数值属性。 + +### D、数值属性(numerical attribute) + +数值属性是可度量的量,用整数或实数值表示,有区间标度和比率标度两种类型。 + +#### a) 区间标度(interval-scaled)属性 + +区间标度属性用相等的单位尺度度量。区间属性的值有序。所以,除了秩评定之外,这种属性允许比较和定量评估值之间的差。例如,身高属性是区间标度的。假设我们有一个班学生的身高统计值,将每一个人视为一个样本,将这些学生身高值排序,可以量化不同值之间的差。A同学身高170cm比B同学165cm高出5cm。 + +对于没有真正零点的摄氏温度和华氏温度,其零值不表示没有温度。例如,摄氏温度的度量单位是水在标准大气压下沸点温度与冰点温度之差的1/100。尽管可以计算温度之差,但因没有真正的零值,因此不能说10℃比5℃温暖2倍,不能用比率描述这些值。但比率标度属性存在真正的零点。 + +#### b) 比率标度(ratio-scaled)属性 + +比率标度属性的度量是比率的,可以用比率来描述两个值,即一个值是另一个值的倍数,也可以计算值之间的差。例如,不同于摄氏和华氏温度,开氏温度具有绝对零点。在零点,构成物质的粒子具有零动能。比率标度属性的例子还包括字数和工龄等计数属性,以及度量重量、高度、速度的属性。 + + +## E、离散属性与连续属性 + + +前面介绍的四种属性类型之间不是互斥的。我们还可以用许多其他方法来组织属性类型,使类型间不互斥。机器学习领域的分类算法常把属性分为离散的或连续的属性。不同类型有不同的处理方法。 + +离散属性具有有限或无限可数个值。如学生成绩属性,优、良、中、差;二元属性取1和0以及年龄属性取0到110。如一个属性可能取值的值集合是无限的,但可以建立一个与自然数的一一对应,则其也是离散属性。如果一个属性不是离散的,则它是连续的。注意:在文献中,术语 “数值属性” 和“连续属性”常可以互换使用,因此,“连续属性”也常被称为“数值属性”。 + +参考书目《无监督学习方法及其应用》 + diff --git a/ml/6.md b/ml/6.md new file mode 100644 index 0000000..d8fa362 --- /dev/null +++ b/ml/6.md @@ -0,0 +1,49 @@ +# 6. 监督学习和无监督学习 + + + +## 关键区别 + +**是否有监督(supervised),就看输入数据是否有标签(label)。输入数据有标签,则为(有)监督学习,没标签则为无监督学习。** +### 知乎的通俗回答 + +作者:王丰 +[链接](https://www.zhihu.com/question/23194489/answer/25028661) + +首先看什么是学习(learning)?一个成语就可概括:举一反三。此处以高考为例,高考的题目在上考场前我们未必做过,但在高中三年我们做过很多很多题目,懂解题方法,因此考场上面对陌生问题也可以算出答案。机器学习的思路也类似:我们能不能利用一些训练数据(已经做过的题),使机器能够利用它们(解题方法)分析未知数据(高考的题目)? + +最简单也最普遍的一类机器学习算法就是分类(classification)。对于分类,输入的训练数据有特征(feature),有标签(label)。所谓的学习,其本质就是找到特征和标签间的关系(mapping)。这样当有特征而无标签的未知数据输入时,我们就可以通过已有的关系得到未知数据标签。 + +在上述的分类过程中,如果所有训练数据都有标签,则为有监督学习(supervised learning)。如果数据没有标签,显然就是无监督学习(unsupervised learning)了,也即聚类(clustering)。目前分类算法的效果还是不错的,但相对来讲,聚类算法就有些惨不忍睹了。确实,无监督学习本身的特点使其难以得到如分类一样近乎完美的结果。这也正如我们在高中做题,答案(标签)是非常重要的,假设两个完全相同的人进入高中,一个正常学习,另一人做的所有题目都没有答案,那么想必第一个人高考会发挥更好,第二个人会发疯。 + +这时各位可能要问,既然分类如此之好,聚类如此之不靠谱,那为何我们还可以容忍聚类的存在?因为在实际应用中,标签的获取常常需要极大的人工工作量,有时甚至非常困难。例如在自然语言处理(NLP)中,Penn Chinese Treebank在2年里只完成了4000句话的标签…… + +![NLP举例](./image/6.nlp.jpg) + +这时有人可能会想,难道有监督学习和无监督学习就是非黑即白的关系吗?有没有灰呢?Good idea。灰是存在的。二者的中间带就是半监督学习(semi-supervised learning)。对于半监督学习,其训练数据的一部分是有标签的,另一部分没有标签,而没标签数据的数量常常极大于有标签数据数量(这也是符合现实情况的)。隐藏在半监督学习下的基本规律在于:数据的分布必然不是完全随机的,通过一些有标签数据的局部特征,以及更多没标签数据的整体分布,就可以得到可以接受甚至是非常好的分类结果。(此处大量忽略细节) + +因此,learning家族的整体构造是这样的: + +- 有监督学习(分类,回归) +- ↕ +- 半监督学习(分类,回归),transductive learning(分类,回归) +- ↕ +- 半监督聚类(有标签数据的标签不是确定的,类似于:肯定不是xxx,很可能是yyy) +- ↕ +- 无监督学习(聚类) + +## 概念 +### 监督学习 +通过已有的训练样本(即已知数据以及其对应的输出)来训练,从而得到一个最优模型,再利用这个模型将所有新的数据样本映射为相应的输出结果,对输出结果进行简单的判断从而实现分类的目的,那么这个最优模型也就具有了对未知数据进行分类的能力。 + +监督学习最常见的就是:分类(classification)&回归(regression) + +### 无监督学习 +输入数据没有被标记,也没有确定的结果。样本数据类别未知,需要根据样本间的相似性对样本集进行分类(聚类,clustering)试图使类内差距最小化,类间差距最大化。通俗点将就是实际应用中,不少情况下无法预先知道样本的标签,也就是说没有训练样本对应的类别,因而只能从原先没有样本标签的样本集开始学习分类器设计。 + +无监督学习最常见的就是:聚类(Clustering) + +无监督学习举例: +- 新闻分类 + + diff --git a/ml/7.md b/ml/7.md new file mode 100644 index 0000000..28fa75a --- /dev/null +++ b/ml/7.md @@ -0,0 +1,53 @@ +# 7. 熵是为消除不确定性所需要获得的信息量,投掷均匀正六面体骰子的熵是 + + + +2.6比特 + + +## 信息熵 + + +如何计算信息量的多少?在日常生活中,极少发生的事件一旦发生是容易引起人们关注的,而司空见惯的事不会引起注意,也就是说,极少见的事件所带来的信息量多。如果用统计学的术语来描述,就是出现概率小的事件信息量多。因此,事件出现得概率越小,信息量愈大。即信息量的多少是与事件发生频繁(即概率大小)成反比。 + +  1.如已知事件Xi已发生,则表示Xi所含有或所提供的信息量 + + +H(Xi) = − logP(Xi) + +  例题:若估计在一次国际象棋比赛中谢军获得冠军的可能性为0.1(记为事件A),而在另一次国际象棋比赛中她得到冠军的可能性为0.9(记为事件B)。试分别计算当你得知她获得冠军时,从这两个事件中获得的信息量各为多少? + +      H(A)=-log2 P(0.1)≈3.32(比特) + +      H(B)=-log2 P(0.9)≈0.152(比特) + +  2.统计信息量的计算公式为: +H(X)=$$sum^{n}_{i=1}P(Xi)log P(Xi)$$ + +Xi —— 表示第i个状态(总共有n种状态); + +P(Xi)——表示第i个状态出现的概率; + +H(X)——表示用以消除这个事物的不确定性所需要的信息量。 + +  例题:向空中投掷硬币,落地后有两种可能的状态,一个是正面朝上,另一个是反面朝上,每个状态出现的概率为1/2。如投掷均匀的正六面体的骰子,则可能会出现的状态有6个,每一个状态出现的概率均为1/6。试通过计算来比较状态的不肯定性与硬币状态的不肯定性的大小。 + +H(硬币)= -\sum^{n}_{i=1}P(Xi)log P(Xi) + += -(2×1/2)×logP2(1/2)≈1(比特) + +H(骰子)= -\sum^{n}_{i=1}P(Xi)log P(Xi) + += -6×(1/6)×logP2(1/6)≈2.6(比特) + +  由以上计算可以得出两个推论: + +  [推论1] 当且仅当某个P(Xi)=1,其余的都等于0时, H(X)= 0。 + +  [推论2]当且仅当某个P(Xi)=1/n,i=1, 2,……, n时,H(X)有极大值log n。 +数值属性是可度量的量,用整数或实数值表示,有区间标度和比率标度两种类型。 + + + + + diff --git a/ml/8.md b/ml/8.md new file mode 100644 index 0000000..94c7bae --- /dev/null +++ b/ml/8.md @@ -0,0 +1,48 @@ +# 8. 数据清洗与特征处理 + + + +## 数据清洗 +清洗标注数据,主要是数据采样和样本过滤 + +**数据采样** + +数据采样,例如对于分类问题:选取正例,负例。对于回归问题,需要采集数据。对于采样得到的样本,根据需要,需要设定样本权重。当模型不能使用全部的数据来训练时,需要对数据进行采样,设定一定的采样率。采样的方法包括随机采样,固定比例采样等方法。 + +**样本过滤** + +1.结合业务情况进行数据的过滤,例如去除crawler抓取,spam,作弊等数据。 + +2.异常点检测,采用异常点检测算法对样本进行分析,常用的异常点检测算法包括: + +- 偏差检测,例如聚类,最近邻等。 +- 基于统计的异常点检测算法 +例如极差,四分位数间距,均差,标准差等,这种方法适合于挖掘单变量的数值型数据。全距(Range),又称极差,是用来表示统计资料中的变异量数(measures of variation) ,其最大值与最小值之间的差距;四分位距通常是用来构建箱形图,以及对概率分布的简要图表概述。 +- 基于距离的异常点检测算法,主要通过距离方法来检测异常点,将数据集中与大多数点之间距离大于某个阈值的点视为异常点,主要使用的距离度量方法有绝对距离 ( 曼哈顿距离 ) 、欧氏距离和马氏距离等方法。 +- 基于密度的异常点检测算法,考察当前点周围密度,可以发现局部异常点,例如LOF算法 + +## 特征处理 + +### 特征处理与分析 + +在对特征进行分类后,下面介绍下对特征常用的处理方法。包括1.特征归一化,离散化,缺省值处理。2.特征降维方法。3.特征选择方法等。 + +特征归一化,离散化,缺省值处理 +主要用于单个特征的处理。 + +**归一化** + +不同的特征有不同的取值范围,在有些算法中,例如线性模型或者距离相关的模型像聚类模型、knn模型等,特征的取值范围会对最终的结果产生较大影响,例如二元特征的取值范围为[0,1],而距离特征取值可能是[0,正无穷),在实际使用中会对距离进行截断,例如[0,3000000],但是这两个特征由于取值范围不一致导致了模型可能会更偏向于取值范围较大的特征,为了平衡取值范围不一致的特征,需要对特征进行归一化处理,将特征取值归一化到[0,1]区间。常用的归一化方法包括1.函数归一化,通过映射函数将特征取值映射到[0,1]区间,例如最大最小值归一化方法,是一种线性的映射。还有通过非线性函数的映射,例如log函数等。2.分维度归一化,可以使用最大最小归一化方法,但是最大最小值选取的是所属类别的最大最小值,即使用的是局部最大最小值,不是全局的最大最小值。3.排序归一化,不管原来的特征取值是什么样的,将特征按大小排序,根据特征所对应的序给予一个新的值。 + +**离散化** + +在上面介绍过连续值的取值空间可能是无穷的,为了便于表示和在模型中处理,需要对连续值特征进行离散化处理。常用的离散化方法包括等值划分和等量划分。等值划分是将特征按照值域进行均分,每一段内的取值等同处理。例如某个特征的取值范围为[0,10],我们可以将其划分为10段,[0,1),[1,2),...,[9,10)。等量划分是根据样本总数进行均分,每段等量个样本划分为1段。例如距离特征,取值范围[0,3000000],现在需要切分成10段,如果按照等比例划分的话,会发现绝大部分样本都在第1段中。使用等量划分就会避免这种问题,最终可能的切分是[0,100),[100,300),[300,500),..,[10000,3000000],前面的区间划分比较密,后面的比较稀疏。 + +**缺省值处理** + +有些特征可能因为无法采样或者没有观测值而缺失,例如距离特征,用户可能禁止获取地理位置或者获取地理位置失败,此时需要对这些特征做特殊的处理,赋予一个缺省值。缺省值如何赋予,也有很多种方法。例如单独表示,众数,平均值等。 + +![数据清洗与特征处理](./image/8.数据清洗与特征处理.jpg) + +### 参考 +[https://tech.meituan.com/machinelearning-data-feature-process.html](https://tech.meituan.com/machinelearning-data-feature-process.html) \ No newline at end of file diff --git a/ml/9.md b/ml/9.md new file mode 100644 index 0000000..0e9b783 --- /dev/null +++ b/ml/9.md @@ -0,0 +1,15 @@ +# 9. 猜测这种划分最可能是什么聚类算法的结果 + + + +![划分结果](./image/9.cluster.question.png) + +## 以下是各个算法的比较 + +![比较](./image/9.cluster.algorithms.png) + +## 各个聚类算法比较的Python代码 + +[python代码链接](https://github.com/geektutu/interview-questions/tree/master/ipynb/sklearn-cluster-compare.ipynb) + +> 最可能是KMean算法 \ No newline at end of file diff --git a/ml/image/10.svm.png b/ml/image/10.svm.png new file mode 100644 index 0000000000000000000000000000000000000000..da51fe21c93bb4e80ab9ac29b860687736c5b8da GIT binary patch literal 18450 zcmZ^~cQ{A!f0G84TM@L7;$H#|9yQ*&-^4nP9c)zv#YJ0l|_wY9Z7n}jQ&iN3V4+#kgTU%Q-xdUE$S%3DAr>3U5 z>Ly#uzorL$T3K0%j*ec#{>IL3eEu*J<5^KzS-G*iyS%*Y=;&BqU!R_y{yw3jxVYF& 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