[OpenCV] Samples 06: logistic regression

logistic regression，这个算法只能解决简单的线性二分类，在众多的机器学习分类算法中并不出众，但它能被改进为多分类，并换了另外一个名字softmax, 这可是深度学习中响当当的分类算法。

Reference: denny的学习专栏  // 臭味相投的一个博客

• Xml保存图片的方法和读取的方式。
• Mat显示内部的多个图片。
• Mat::t() 显示矩阵内容。

本文用它来进行手写数字分类。

在opencv3.0中提供了一个xml文件，里面存放了40个样本，分别是20个数字0的手写体和20个数字1的手写体。本来每个数字的手写体是一张28*28的小图片，在xml使用1*784 的向量保存在<data>中。

这个文件的位置： \opencv\sources\samples\data\data01.xml

/*//////////////////////////////////////////////////////////////////////////////////////
// IMPORTANT: READ BEFORE DOWNLOADING, COPYING, INSTALLING OR USING.

//  By downloading, copying, installing or using the software you agree to this license.
//  If you do not agree to this license, do not download, install,
//  copy or use the software.

// This is a implementation of the Logistic Regression algorithm in C++ in OpenCV.

// AUTHOR:
// Rahul Kavi rahulkavi[at]live[at]com
//

// contains a subset of data from the popular Iris Dataset (taken from
// "http://archive.ics.uci.edu/ml/datasets/Iris")

// # You are free to use, change, or redistribute the code in any way you wish for
// # non-commercial purposes, but please maintain the name of the original author.
// # This code comes with no warranty of any kind.

// #
// # You are free to use, change, or redistribute the code in any way you wish for
// # non-commercial purposes, but please maintain the name of the original author.
// # This code comes with no warranty of any kind.

// # Logistic Regression ALGORITHM

//                           License Agreement
//                For Open Source Computer Vision Library

// Copyright (C) 2000-2008, Intel Corporation, all rights reserved.
// Copyright (C) 2008-2011, Willow Garage Inc., all rights reserved.
// Third party copyrights are property of their respective owners.

// Redistribution and use in source and binary forms, with or without modification,
// are permitted provided that the following conditions are met:

//   * Redistributions of source code must retain the above copyright notice,
//     this list of conditions and the following disclaimer.

//   * Redistributions in binary form must reproduce the above copyright notice,
//     this list of conditions and the following disclaimer in the documentation
//     and/or other materials provided with the distribution.

//   * The name of the copyright holders may not be used to endorse or promote products
//     derived from this software without specific prior written permission.

// This software is provided by the copyright holders and contributors "as is" and
// any express or implied warranties, including, but not limited to, the implied
// warranties of merchantability and fitness for a particular purpose are disclaimed.
// In no event shall the Intel Corporation or contributors be liable for any direct,
// indirect, incidental, special, exemplary, or consequential damages
// (including, but not limited to, procurement of substitute goods or services;
// loss of use, data, or profits; or business interruption) however caused
// and on any theory of liability, whether in contract, strict liability,
// or tort (including negligence or otherwise) arising in any way out of
// the use of this software, even if advised of the possibility of such damage.*/

#include <iostream>

#include <opencv2/core.hpp>
#include <opencv2/ml.hpp>
#include <opencv2/highgui.hpp>

using namespace std;
using namespace cv;
using namespace cv::ml;

/*
 * Jeff --> Show mutiple-photos from Mat.
 */
static void showImage(const Mat &data, int columns, const String &name)
{
    // columns = 28
    Mat bigImage;
    for(int i = 0; i < data.rows; ++i)
    {
        //rows: number of photos.
        // vector --> reshape --> col 28, col 28 ...
        // push_back: show each pic from left to right.
        bigImage.push_back(data.row(i).reshape(0, columns));

    }
    imshow(name, bigImage.t());
}

static float calculateAccuracyPercent(const Mat &original, const Mat &predicted)
{
    return 100 * (float)countNonZero(original == predicted) / predicted.rows;
}

int main()
{
    const String filename = "../data/data01.xml";
    cout << "**********************************************************************" << endl;
    cout << filename
         << " contains digits 0 and 1 of 20 samples each, collected on an Android device" << endl;
    cout << "Each of the collected images are of size 28 x 28 re-arranged to 1 x 784 matrix"
         << endl;
    cout << "**********************************************************************" << endl;

    Mat data, labels;
    {
        /*
         * Jeff --> Load xml.
         *          transform to Mat.
         * FileStorage.
         */
        cout << "loading the dataset...";
        // Step 1.
        FileStorage f;
        if(f.open(filename, FileStorage::READ))
        {
            // Step 2.
            f["datamat"] >> data;
            f["labelsmat"] >> labels;
            f.release();
        }
        else
        {
            cerr << "file can not be opened: " << filename << endl;
            return 1;
        }
        // Step 3.
        data.convertTo(data, CV_32F);
        labels.convertTo(labels, CV_32F);

        cout << "read " << data.rows << " rows of data" << endl;
    }

    Mat data_train, data_test;
    Mat labels_train, labels_test;
    for(int i = 0; i < data.rows; i++)
    {
        // Step 4.
        if(i % 2 == 0)
        {
            data_train.push_back(data.row(i));
            labels_train.push_back(labels.row(i));
        }
        else
        {
            data_test.push_back(data.row(i));
            labels_test.push_back(labels.row(i));
        }
    }
    cout << "training/testing samples count: " << data_train.rows << "/" << data_test.rows << endl;

    // display sample image
    showImage(data_train, 28, "train data");
    showImage(data_test, 28, "test data");

    /**************************************************************************/

    // simple case with batch gradient
    cout << "training...";

    // Step (1), create classifier.
    Ptr<LogisticRegression> lr1 = LogisticRegression::create();

    // Step (2),
    lr1->setLearningRate(0.001);
    lr1->setIterations(10);
    lr1->setRegularization(LogisticRegression::REG_L2);
    lr1->setTrainMethod(LogisticRegression::BATCH);
    lr1->setMiniBatchSize(1);

    // Step (3), train.
    //! [init]
    lr1->train(data_train, ROW_SAMPLE, labels_train);
    cout << "done!" << endl;

    //--------------------------------------------------------------------------

    cout << "predicting...";

    // Step (4), predict.
    Mat responses;
    lr1->predict(data_test, responses);
    cout << "done!" << endl;

    // Step (5), show prediction report
    cout << "original vs predicted:" << endl;
    // Jeff --> CV_32S is a signed 32bit integer value for each pixel.
    labels_test.convertTo(labels_test, CV_32S);

    cout << labels_test.t() << endl;
    cout << responses.t() << endl;
    cout << "accuracy: " << calculateAccuracyPercent(labels_test, responses) << "%" << endl;

    // Step (6), save the classfier
    const String saveFilename = "NewLR_Trained.xml";
    cout << "saving the classifier to " << saveFilename << endl;
    lr1->save(saveFilename);

    /****************************** End ***************************************/

    // load the classifier onto new object
    cout << "loading a new classifier from " << saveFilename << endl;
    Ptr<LogisticRegression> lr2 = StatModel::load<LogisticRegression>(saveFilename);

    // predict using loaded classifier
    cout << "predicting the dataset using the loaded classfier...";
    Mat responses2;
    lr2->predict(data_test, responses2);
    cout << "done!" << endl;

    // calculate accuracy
    cout << labels_test.t() << endl;
    cout << responses2.t() << endl;
    cout << "accuracy: " << calculateAccuracyPercent(labels_test, responses2) << "%" << endl;

    waitKey(0);
    return 0;
}

---

关于逻辑回归：http://blog.csdn.net/pakko/article/details/37878837

什么是逻辑回归？

Logistic回归与多重线性回归实际上有很多相同之处，最大的区别就在于它们的因变量不同，其他的基本都差不多。正是因为如此，这两种回归可以归于同一个家族，即广义线性模型（generalizedlinear model）。

这一家族中的模型形式基本上都差不多，不同的就是因变量不同。

• 如果是连续的，就是多重线性回归；
• 如果是二项分布，就是Logistic回归；
• 如果是Poisson分布，就是Poisson回归；
• 如果是负二项分布，就是负二项回归。

Logistic回归的因变量可以是二分类的，也可以是多分类的，但是二分类的更为常用，也更加容易解释。所以实际中最常用的就是二分类的Logistic回归。

Logistic回归的主要用途：

• 寻找危险因素：寻找某一疾病的危险因素等；
• 预测：根据模型，预测在不同的自变量情况下，发生某病或某种情况的概率有多大；
• 判别：实际上跟预测有些类似，也是根据模型，判断某人属于某病或属于某种情况的概率有多大，也就是看一下这个人有多大的可能性是属于某病。

Logistic回归主要在流行病学中应用较多，比较常用的情形是探索某疾病的危险因素，根据危险因素预测某疾病发生的概率，等等。例如，想探讨胃癌发生的危险因素，可以选择两组人群，一组是胃癌组，一组是非胃癌组，两组人群肯定有不同的体征和生活方式等。这里的因变量就是是否胃癌，即“是”或“否”，自变量就可以包括很多了，例如年龄、性别、饮食习惯、幽门螺杆菌感染等。自变量既可以是连续的，也可以是分类的。

常规步骤

Regression问题的常规步骤为：

1. 寻找h函数（即hypothesis）； ==> Sigmoid函数
2. 构造J函数（loss函数）；
3. 想办法使得J函数最小并求得回归参数（θ）

详见reference博客。