• 支持向量机回归和支持向量机Support Vector Machine(SVM) is a supervised machine learning algorithm that is usually used in solving binary classification problems. It can also be applied in multi-class ...


    Support Vector Machine(SVM) is a supervised machine learning algorithm that is usually used in solving binary classification problems. It can also be applied in multi-class classification problems and regression problems. This article represents the mathematics behind the binary-class linear Support Vector Machines. Understanding mathematics helps implement and tune the models in practice. Moreover, you can build your own support vector machine model from scratch, and compare it with the one from Scikit-Learn. For details, you can read this article along with another article of mine.

    支持向量机(SVM)是一种监督型机器学习算法,通常用于解决二进制分类问题。 它也可以应用于多类分类问题和回归问题。 本文介绍了二元类线性支持向量机背后的数学原理。 了解数学有助于在实践中实现和调整模型。 此外,您可以从头开始构建自己的支持向量机模型,并将其与Scikit-Learn的模型进行比较。 有关详细信息,您可以阅读本文以及我的另一篇文章

    Specifically, this report explains the key concepts of linear support vector machine, including the primal form and its dual form for both hard margin and soft margin case; the concept of support vectors, max-margin, and the generalization process.

    具体而言,本报告解释了线性支持向量机的关键概念,包括硬边际和软边际情况的原始形式及其对偶形式; 支持向量,最大边距和归纳过程的概念。

    Key Concepts of SVM


    Assume we have n training points, each observation i has p features (i.e. x_i has p dimensions), and is in two classes y_i=-1 or y_i = 1. Suppose we have two classes of observations that are linearly separable. That means we can draw a hyperplane through our feature space such that all instances of one class are on one side of the hyperplane, and all instances of the other class are on the opposite side. (A hyperplane in p dimensions is a p-1 dimensional subspace. In the two-dimensional example that follows, a hyperplane is just a line.) We define a hyperplane as:

    假设我们有n个训练点,每个观测值i具有p个特征(即x_i具有p个维),并且处于两类y_i = -1或y_i =1。假设我们有两类线性可分离的观测值。 这意味着我们可以在特征空间中绘制一个超平面,这样一类的所有实例都在超平面的一侧,而另一类的所有实例都在另一侧。 (p维上的超平面是p-1维子空间。在下面的二维示例中,超平面只是一条线。)我们将超平面定义为:

    where ˜w is a p-vector and ˜b is a real number. For convenience, we require that ˜w = 1, so the quantity x * ˜w + ˜b is the distance from point x to the hyperplane.

    其中〜w是p向量,〜b是实数。 为了方便起见,我们要求〜w = 1,所以数量x *〜w +〜b是从点x到超平面的距离。

    Image for post
    image from Wikipedia

    Thus we can label our classes with y = +1/-1, and the requirement that the hyperplane divides the classes becomes:

    因此,我们可以用y = + 1 / -1标记我们的类,超平面划分这些类的要求变为:

    Image for post

    How should we choose the best hyperplane?


    The approach to answering this question is to choose the plane that results in the largest margin M between the two classes, which is called the Maximal Margin Classifier.


    Image for post
    image from Wikipedia

    From the previous graph, we can see that H1 doesn’t separate the two classes; for H2 and H3, we will choose H3 because H3 has a larger margin. Mathematically, we choose ˜b and ˜w to maximize M, given the constraints:

    从上一张图中,我们可以看到H1并没有将这两个类别分开。 对于H2和H3,我们将选择H3,因为H3具有较大的边距。 在数学上,给定约束,我们选择〜b和〜w以最大化M:

    Image for post

    Defining w =˜ w / M and b =˜b / M, we can rewrite this as:

    定义w = 〜w / Mb =〜b / M ,我们可以重写为:

    Image for post


    Image for post

    The support vectors


    The support vectors are the data points that lie closest to the separating hyperplane. They are the most difficult data points to classify. Moreover, support vectors are the elements of the training set that would change the position of the dividing hyperplane if removed. The optimization algorithm to generate the weights proceeds in such a way that only the support vectors determine the weights and thus the boundary. Mathematically support vectors are defined as:

    支持向量是最靠近分离超平面的数据点。 它们是最难分类的数据点。 此外,支持向量是训练集的元素,如果被移除,它们将改变划分超平面的位置。 生成权重的优化算法以这样的方式进行:只有支持向量才能确定权重,从而确定边界。 数学上的支持向量定义为:

    Image for post

    Hard-margin SVM


    The hard-margin SVM is very strict with the support vectors crossing the hyperplane. It doesn’t allow any support vectors to be classified in the wrong class. To maximize the margin of the hyperplane, the hard-margin support vector machine is facing the optimization problem:

    硬边支持向量机非常严格,支持向量跨过超平面。 不允许将任何支持向量分类为错误的类。 为了最大化超平面的余量,硬余量支持向量机面临着优化问题:

    Image for post

    Soft-margin SVM and the hyper-parameter C


    In general, classes are not linearly separable. This may be because the class boundary is not linear, but often there is no clear boundary. To deal with this case, the support vector machine adds a set of “slack variables”, which forgive excursions of a few points into, or even across, the margin, like showing in the graph below:

    通常,类不是线性可分离的。 这可能是因为类边界不是线性的,但是通常没有明确的边界。 为了解决这种情况,支持向量机添加了一组“松弛变量”,这些宽恕原谅了到边缘甚至跨越边缘的几个点的偏移,如下图所示:

    Image for post
    image by Author

    We want to minimize the total amount of slacks while maximizing the width of the margin, which is called soft-margin support vector machine. This is more widely used, and the objective function becomes:

    我们要在使边距的宽度最大的同时,使松弛的总量最小化,这称为软边距支持向量机。 这被更广泛地使用,目标函数变为:

    Image for post

    for some constant C. This optimization problem is called the primal problem. The constant C represents the “cost” of the slack. When C is small, it is efficient to allow more points into the margin to achieve a larger margin. Larger C will produce boundaries with fewer support vectors. By increasing the number of support vectors, SVM reduces its variance, since it depends less on any individual observation. Reducing variance makes the model more generalized. Thus, decreasing C will increase the number of support vectors and reduce over-fitting.

    对于一些常数C。 此优化问题称为原始问题。 常数C代表松弛的“成本”。 当C较小时,允许有更多点进入边距以实现更大的边距是有效的。 C越大,边界越少,支持向量也越少。 通过增加支持向量的数量,SVM减少了方差,因为它较少依赖于任何单独的观察。 减少方差使模型更通用。 因此,降低C将增加支持向量的数量并减少过度拟合。

    With Lagrange multipliers:


    Image for post
    two constraints

    we can rewrite the constrained optimization problem as the primal Lagrangian function :


    Image for post

    Instead of minimizing over w, b, subject to constraints, we can maximize over the multipliers subject to the relations obtained previously for w, b. This is called the dual Lagrangian formulation:

    代替将wb最小化(受约束),我们可以使乘数最大化,该乘数受先前为wb获得的关系的约束。 这称为双重拉格朗日公式:

    Image for post

    This is now a reasonably straightforward quadratic programming problem, solved with Sequential Minimization Optimization. There are a lot of programming tools you can use to solve the optimizing problem. You can use the CVX tool in Matlab to solve this question. Or if you are familiar with python, you can use the CVXOPT package to solve it. I have another article at Medium that discusses the use of the CVXOPT package, and how to apply it to solve SVM in the dual formulation. Once we have solved this problem for \alpha, we can easily work out the coefficients:

    现在这是一个相当简单的二次规划问题,可通过顺序最小化优化解决。 您可以使用许多编程工具来解决优化问题。 您可以使用Matlab中的CVX工具来解决此问题。 或者,如果您熟悉python,则可以使用CVXOPT软件包来解决它。 我在Medium上还有另一篇文章,讨论了CVXOPT软件包的用法,以及如何将其应用于对偶公式中的SVM解决方案。 解决\ alpha的问题后,我们可以轻松计算出系数:

    Image for post

    Waling through the math behind the Support Vector Machines algorithm definitely helps understand the implementation of the model. It gives insights on choosing the right model for the right questions and choosing the right value for the hyper-parameters.

    仔细阅读支持向量机算法背后的数学知识,无疑有助于理解模型的实现。 它为选择正确的问题模型和为超参数选择正确的值提供了见解。

    Hope this helps. Thank you all for reading!

    希望这可以帮助。 谢谢大家的阅读!

    翻译自: https://towardsdatascience.com/explain-support-vector-machines-in-mathematic-details-c7cc1be9f3b9


  • 一维支持向量机SVM代码(MATLAB),包括支持向量机分类和支持向量机回归SVC&SVR;。另外还包括与BP神经网络的比较结果。
  • 支持向量机 回归分析It is a common misconception that support vector machines are only useful when solving classification problems. 常见的误解是,支持向量机仅在解决分类问题时才有用。 The purpose of ...

    支持向量机 回归分析

    It is a common misconception that support vector machines are only useful when solving classification problems.


    The purpose of using SVMs for regression problems is to define a hyperplane as in the image above, and fit as many instances as is feasible within this hyperplane while at the same time limiting margin violations.


    In this way, SVMs used in this manner differ from classification tasks, where the objective is to fit the largest possible hyperplane between two separate classes (while also limiting margin violations).


    As a matter of fact, SVMs can handle regression modelling quite effectively. Let’s take hotel bookings as an example.

    实际上,SVM可以非常有效地处理回归建模。 让我们以酒店预订为例。

    预测酒店客户的平均每日房价 (Predicting Average Daily Rates Across Hotel Customers)

    Suppose that we are building a regression model to predict the average daily rate (or rate that a customer pays on average per day) for a hotel booking. A model is constructed with the following features:

    假设我们正在建立回归模型,以预测酒店预订的平均每日房价(或客户平均每天所支付的房价)。 构建具有以下特征的模型:

    • Cancellation (whether a customer cancels their booking or not)

    • Country of Origin

    • Market Segment

    • Deposit Type

    • Customer Type

    • Required Car Parking Spaces

    • Week of Arrival


    Note that the ADR values are also populated for customers that cancelled — the response variable in this case reflects the ADR that would have been paid had the customer proceeded with the booking.


    The original study by Antonio, Almeida and Nunes (2016) can be accessed from the References section below.


    建筑模型 (Model Building)

    Using the features as outlined above, the SVM model is trained and validated on the training set (H1), with the predictions compared to the actual ADR values across the test set (H2).


    The model is trained as follows:


    >>> from sklearn.svm import LinearSVR
    >>> svm_reg = LinearSVR(epsilon=1.5)
    >>> svm_reg.fit(X_train, y_train)LinearSVR(C=1.0, dual=True, epsilon=1.5, fit_intercept=True,
    intercept_scaling=1.0, loss='epsilon_insensitive', max_iter=1000,
    random_state=None, tol=0.0001, verbose=0)>>> predictions = svm_reg.predict(X_val)
    >>> predictionsarray([100.75090575, 109.08222631, 79.81544167, ..., 94.50700112,
    55.65495607, 65.5248653 ])

    Now, the same model is used on the features in the test set to generate predicted ADR values:


    bpred = svm_reg.predict(atest)

    Let’s compare the predicted ADR to actual ADR on a mean absolute error (MAE) and root mean squared error (RMSE) basis.


    >>> mean_absolute_error(btest, bpred)
    29.50931462735928>>> print('mse (sklearn): ', mean_squared_error(btest,bpred))
    >>> math.sqrt(mean_squared_error(btest, bpred))

    Note that the sensitivity of the SVM to additional training instances is set by the epsilon (ϵ) parameter, i.e. the higher the parameter, the more of an impact additional training instances has on the model results.


    In this instance, a large margin of 1.5 was used. Here is the model performance when a margin of 0.5 is used.

    在这种情况下,使用了1.5的大余量。 这是使用0.5的裕度时的模型性能。

    >>> mean_absolute_error(btest, bpred)29.622491512816826>>> print('mse (sklearn): ', mean_squared_error(btest,bpred))
    >>> math.sqrt(mean_squared_error(btest, bpred))44.7963000500928

    We can see that there has been virtually no change in the MAE or RMSE parameters through modifying the ϵ parameter.


    That said, we want to ensure that the SVM model is not overfitting. Specifically, if we find that the best fit is achieved when ϵ = 0, then this might be a sign that the model is overfitting.

    也就是说,我们要确保SVM模型不会过拟合。 具体来说,如果我们发现当ϵ = 0时达到了最佳拟合则可能表明该模型过度拟合。

    Here are the results when we set ϵ = 0.

    当我们设置ϵ = 0时,结果如下。

    • MAE: 31.86

      MAE: 31.86

    • RMSE: 47.65

      RMSE: 47.65

    Given that we are not seeing higher accuracy when ϵ = 0, there does not seem to be any evidence that overfitting is an issue in our model — at least not from this standpoint.

    考虑到当ϵ = 0时我们看不到更高的精度,因此似乎没有任何证据表明过度拟合是我们模型中的一个问题-至少从这个角度来看不是这样。

    SVM性能与神经网络相比如何? (How Does SVM Performance Compare To A Neural Network?)

    When using the same features, how does the SVM performance accuracy compare to that of a neural network?


    Consider the following neural network configuration:


    >>> model = Sequential()
    >>> model.add(Dense(8, input_dim=8, kernel_initializer='normal', activation='elu'))
    >>> model.add(Dense(1669, activation='elu'))
    >>> model.add(Dense(1, activation='linear'))
    >>> model.summary()Model: "sequential"
    Layer (type) Output Shape Param #
    dense (Dense) (None, 8) 72
    dense_1 (Dense) (None, 1669) 15021
    dense_2 (Dense) (None, 1) 1670
    Total params: 16,763
    Trainable params: 16,763
    Non-trainable params: 0

    The model is trained across 30 epochs with a batch size of 150:


    >>> model.compile(loss='mse', optimizer='adam', metrics=['mse','mae'])
    >>> history=model.fit(X_train, y_train, epochs=30, batch_size=150, verbose=1, validation_split=0.2)
    >>> predictions = model.predict(X_test)

    The following MAE and RMSE are obtained on the test set:


    • MAE: 29.89

      MAE: 29.89

    • RMSE: 43.91

      RMSE: 43.91

    We observed that when ϵ was set to 1.5 for the SVM model, the MAE and RMSE came in at 29.5 and 44.6 respectively. In this regard, the SVM has matched the neural network in prediction accuracy on the test set.

    我们观察到 SVM模型设置为1.5 ,MAE和RMSE分别为29.5和44.6。 在这方面,SVM在测试集的预测准确性方面已与神经网络相匹配。

    结论 (Conclusion)

    It is a common misconception that SVMs are only suitable for working with classification data.


    However, we have seen in this example that the SVM model has been quite effective at predicting ADR values for the neural network.


    Many thanks for reading, and any questions or feedback appreciated.


    The GitHub repository for this example, as well as other relevant references are available below.


    Disclaimer: This article is written on an “as is” basis and without warranty. It was written with the intention of providing an overview of data science concepts, and should not be interpreted as professional advice in any way.

    免责声明:本文按“原样”撰写,不作任何担保。 它旨在提供数据科学概念的概述,并且不应以任何方式解释为专业建议。

    翻译自: https://towardsdatascience.com/support-vector-machines-and-regression-analysis-ad5d94ac857f

    支持向量机 回归分析

  • 主要介绍了libsvm支持向量机回归示例,需要的朋友可以参考下
  • 支持向量机回归

    千次阅读 2014-07-23 16:33:05
    支持向量机回归教程: http://wenku.baidu.com/view/2977157da26925c52cc5bfcc.html http://wenku.baidu.com/view/91b59bddad51f01dc281f1dd.html?re=view 最小二乘支持向量回归机: ...








  • 支持向量机回归在矿区GPS高程转换中的应用,张健,郝蒙蒙,基于统计学习理论和支持向量机原理,提出了支持向量机回归应用于矿区GPS高程转换的方法用以精化矿区似大地水准面,研究了支持向量
  • 目录 支持向量机基本思想 标准的线性支持向量回归模型 非线性支持向量机 支持向量机用于分类:硬...支持向量机回归: 希望\(f(x)\)与​\(y\)尽可能的接近。 支持向量机基本思想 英文名:support vector...


    支持向量机回归: 希望\(f(x)\)与​\(y\)尽可能的接近。


    英文名:support vector regression





    \[ \min \frac{1}{2}w^Tw\\ s.t -\xi<=f(x_i)-y_i<=\xi \]
    \[ \min \frac{1}{2}w^Tw+C\sum(\epsilon_i+\hat{\epsilon}_i)\\ s.t. \begin{cases}f(x_i)-y_i<=\xi+\epsilon_i\\ y_i-f(x_i)<=\xi+\hat{\epsilon}_i\\ \hat{\epsilon}_i>=0,\epsilon_i>=0 \end{cases} \]
    \[ \begin{aligned} L :=\frac{1}{2}\|\omega\|^{2} &+C \sum\left(\xi_i+\xi^{\prime}_i\right)-\sum_{i=1}^{N}\left(\eta_{i} \xi_{i}+\eta_{i}^{'} \xi_{i}6{'}\right) \\ &+\sum \alpha_{i}\left(y_{i}-\omega^{T} x_{i}-b-\varepsilon-\xi_{i}\right) \\ &+\sum \alpha_{i}^{'}\left(\omega^{T} x_{i}+b-y_{i}-\varepsilon-\xi_{i}^{\prime}\right) \end{aligned}\tag{1} \]
    \[ \frac{\partial L}{\partial \omega}=\omega-\sum\left(\alpha_{i}-\alpha_{i}\right) x_{i}=0 \Rightarrow \omega=\sum\left(\alpha_{i}-\alpha_{i}^{\prime}\right) x_{i}\tag{2} \]

    \[ \frac{\partial L}{\partial b}=\sum_{i=1}^{N}\left(\alpha_{i}-\alpha_{i}^{\prime}\right)=0 \tag{3} \]

    \[ \frac{\partial L}{\partial \xi_{i}^{\prime}}=C-\alpha_{i}^{'}-\eta_{i}^{\prime}=0 \tag{4} \]

    \[ \frac{\partial L}{\partial \xi_{i}}=C-\alpha_{i}-\eta_{i}=0 \tag{5} \]

    \[ \begin{aligned} \min L(\boldsymbol{\alpha})=& \frac{1}{2} \sum_{i=1}^{N} \sum_{j=1}^{N}\left(\alpha_{i}-\alpha_{i}^{*}\right)\left(\alpha_{j}-\alpha_{j}^{*}\right)\left\langle x_{i}, x_{j}\right\rangle \\ &+\varepsilon \sum_{i=1}^{N}\left(\alpha_{i}+\alpha_{i}^{*}\right)-\sum_{i=1}^{N} y_{i}\left(\alpha_{i}-\alpha_{i}^{*}\right) \\ \text { s.t. } & \sum_{n=1}^{N}\left(\alpha_{n}-\alpha_{n}^{*}\right)=0 \end{aligned} \]
    \[ y(x)=\sum_{i=1}^{N}\left(\alpha_{i}-\alpha_{i}^{*}\right) x_{i}^{T} x+b \]


    \[ y=f(x)+b \]
    \[ f(x)=w^T\varphi(x) \]
    \[ \min \frac{1}{2}\|\omega\|^{T}+C \sum_{i}\left(\xi_{i}+\xi_{i}^{\prime}\right)\\ \begin{cases} y\left(x_{i}\right)-\omega^{T} \varphi\left(x_{i}\right)-b \leq \xi_{i} \\ \omega^{T} \varphi\left(x_{i}\right)+b-y\left(x_{i}\right) & \leq \xi_{i} \\ \xi_{i} & \geq 0 \\ \xi_{i} & \geq 0 \end{cases} \]
    \[ \begin{aligned} L :=\frac{1}{2}\|\omega\|^{2} &+C \sum\left(\xi+\xi^{\prime}\right)-\sum\left(\eta_{i} \xi_{i}+\eta_{i} \xi_{i}^{\prime}\right) \\ &+\sum \alpha_{i}\left(y_{i}-w^{T} \varphi\left(x_{i}\right)-b-\varepsilon_{i}-\xi_{i}\right) \\ &+\sum \alpha_{\mathrm{i}}^{\prime}\left(w^{T} \varphi\left(x_{i}\right)+b-y_{i}-\varepsilon_{i}^{'}-\xi_{i}^{\prime}\right) \end{aligned} \]
    \[ \begin{cases}\frac{\partial L}{\partial w}=w-\sum\left(\alpha_{i}-\alpha_{i}\right) \varphi\left(x_{i}\right)=0\\ \frac{\partial L}{\partial b} =\sum\left(\alpha_{i}-\alpha_{i}^{\prime}\right)=0 \\ \frac{\partial L}{\partial \xi_{i}^{\prime}} =C-\alpha_{i}^{'}-\eta_{i}^{\prime}=0 \\ \frac{\partial L}{\partial \xi_{i}} =C-\alpha_{i}-\eta_{i}=0 \end{cases} \]

    \[\min _{t}-\frac{1}{2} \sum\left(\alpha_{i}-\alpha_{i}^{\prime}\right)\left(\alpha_{j}-\alpha_{j}^{\prime}\right) \varphi\left(x_{i}\right)^{T} \varphi\left(x_{j}\right)-\varepsilon \sum\left(\alpha_{i}+\alpha_{i}^{\prime}\right)+\sum y_{i}\left(\alpha_{i}-\alpha_{i}^{'}\right)\\s t . \sum\left(\alpha_{i}-\alpha_{i}^{\prime}\right)=0\]

    \[ y=\sum\left(\alpha_{i}-\alpha_{i}^{'}\right) \varphi\left(x_{i}\right)^{T} \varphi(x)+b \]


  • 半监督支持向量机回归模型研究,冀杰,程玉虎,利用支持向量机和K近邻学习器的优点,提出一种半监督支持向量机回归模型。支持向量机通过选择高置信度的未标记样本加以标记,并��
  • <p>Lyapunov 指数是描述动力学系统混沌性质的重要...参数进行优化, 推导了支持向量机回归应用于计算Lyapunov 指数的公式. 通过对混沌序列进行仿真实验, 仿真结果 表明, 在小样本数据情况下, 此方法可行有效.</p>
  • 现有最小二乘支持向量机回归的训练和模型输出的计算需要较长的时间,不适合在线实时训练.对此,提出一种在线稀疏最小二乘支持向量机回归,其训练算法采用样本字典,减少了训练样本的计算量.训练样本采用序贯加入的方式,...
  • 支持向量机回归算法的研究与应用
  • 书籍简介支持向量机 (Support Vector Machine, SVM) 是建立在统计学理论最新进展基础上的新一代学习系统。本书是第一本全面介绍支持向量机的著作。支持向量机是在20世纪90年代初提出的,随之引发了对这种技术的广泛...
  • 支持向量机用于回归预测的源代码。
  • 回归——支持向量机回归(SVR)

    万次阅读 2018-05-04 15:15:07
    支持向量机回归(SVR)是支持向量机在回归问题上的应用模型。支持向量机回归模型基于不同的损失函数产生了很多变种。本文仅介绍基于ϵϵ\epsilon不敏感损失函数的SVR模型。 核心思想 找到一个分离超平面...
  • 支持向量机回归的参数选择方法
  • 基于支持向量机回归的水体重金属激光诱导击穿光谱定量分析研究
  • 基于支持向量机回归的T-S模糊模型自组织算法及应用
  • 常用回归算法: 线性回归不拟合非线性; 支持向量机回归很好拟合非线性; KNN回归可以拟合非线性,周围样本平均值。
  • 为了学习支持向量机,我们可以先从逻辑回归开始,看看如何经过小小的改动能得到支持向量机。在逻辑回归中,假设函数 h_θ(x) 为:图像为:对于一个样本来说,代价函数为:当 y =1 时,第二项为 0,只需要考虑第一...
  • 针对最小二乘支持向量机处理大规模数据集耗时长且受内存限制的特点,将局部多模型方法与Map-Reduce编程模式相结合,提出一种并行最小二乘支持向量机回归模型。模型由两组MapReduce过程组成,首先按照输入样本集对...
  • 本期导读机器学习简单实践——支持向量机Oct.17201901概念02特点03应用04线性分类器05实践模块1 概念在机器学习中,支持向量机(英语:support vector machine,常简称为SVM)是在分类与回归分析中分析数据的监督式...
  • 针对制造业产品销售时序具有多维、小样本、非线性、多峰等特征,提出一种混沌果蝇支持向量机回归的产品销售预测方法。将混沌理论引入到果蝇优化算法中,从而提高果蝇种群多样性和搜索的遍历性,并在寻优过程中加入...
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  • 支持向量机回归程序

    热门讨论 2013-07-06 09:23:31
  • 对期 货价格 进行 了预测 , 并 将其 与最 常使 用 的高 斯核 支持 向量机 进行 了对 比. 经 比较 , 在处 理实 际期 货数 据 时 , M orlet小 波核 和 M arr 小波 核在绝 大多 数情 况下 , 都 能取得 比高斯 核更...
  • 论文 基于支持向量机回归机的曲面拟合技术
  • 首先支持向量机不是一种机器,而是一种机器学习算法。是一种监督学习算法,用来解决分类问题的。支持向量又是啥意思?通俗的理解就是,分类器中最靠近决策边界(Logistic回归里面提到过决策边界的概念)的那些点,也...



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