活动地址：CSDN21天学习挑战赛
引子：大佬的等式
在美国，有个牛逼的大学，叫华盛顿大学，其中有个牛逼的计算机科学教授，佩德罗·多明戈斯（Pedro Domingos），他是《终极算法》的作者，还有很多著作和头衔，不过，今天我们关注的不是这些著作和头衔，而是他写过的一个著名的方程式：
机器学习=表示+优化+评估
[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:139b2ded-bf18-4d45-aabc-8ec9ed61e2a0
[En]
[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:57ab9205-4bf5-4717-9bac-da8ebd92b78d
凸优化和非凸优化的区别
[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:baee3885-9ed9-4f4a-9e9a-ae7f8a77c094
[En]
[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:a6e93b6d-5b03-4d8f-ad14-46d5f60b593d
[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:fda2ff1d-5af5-4c2b-b654-b9ae6967563e
[En]
[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:a1c50b18-6421-41ff-9745-3068e7dde952
[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:b8379e8b-5bc9-410b-ac79-b3f9f5145b58
[En]
[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:76379009-ca93-485f-bc15-be44b4c27011
凸聚类
[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:3b620542-8def-45f7-8f58-959fed51dcb7
[En]
[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:ebddbc33-ab48-4253-aa91-824545fdc900
[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:40420f00-c050-4909-9096-1f13bec42269
[En]
[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:3a6882fb-2197-44f4-bab3-ebb7daeeac85
[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:c7e9900d-842e-40ea-b94f-79a16c0afc3f
[En]
[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:20ee3f29-da8b-4818-b0dd-5f0a3dac8fd3
无论是k-means算法还是谱聚类算法，本质都是一个非凸问题，这使得问题的解受初始值的影响很大。虽然人们已经提出了很多不同的初始化算法来提升聚类性能，但至今都没有一种最优的初始化策略出现。通过将聚类问题描述为一个凸优化问题，凸聚类算法通过凸优化算法获得聚类问题的唯一解，从而避免初始值的选取对聚类结果的影响。
上面目标函数的第一项为矩阵U与X之差的Frobenius范数，用来控制矩阵U与X的距离，第二项为矩阵U内部不同列之间距离的加权和，用来控制矩阵U内部不同列之间的距离。可以预见，能够目标函数最小的矩阵U可以使U与X接近的同时使U内列向量之间距离较小。在凸聚类算法处理后，U内部同属于一个聚类的向量距离会变小，而不属于同一个聚类的向量虽然距离也可能会变小，但是幅度不大，使得U内部的聚类模式体现得更加明显，之后只需要对矩阵U使用非常简单的聚类算法（比如k-means等），就可以获得U中列向量的聚类，它们也就对应了X中列向量的聚类。在实践中，一般使用直接比较U列向量之间距离的方法来确定聚类个数和每一个列向量所属的聚类。
凸聚类算法试图绕过初始化问题，直接针对聚类问题设计出一个凸的目标函数，从而仅仅通过非常简单的算法就能求得全局最优解。通过连续可调的参数
，凸聚类算法可以生成数目不等的聚类，从而实现对聚类个数k的间接控制。
[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:d370e562-d8b3-4bd8-bdee-151179c1de3a
[En]
[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:f825550d-1019-455e-a77a-457fbafbca4b
Original: https://blog.csdn.net/weixin_37522117/article/details/126284749
Author: 肥猪猪爸
Title: 机器学习之聚类——从教授的等式到凸聚类
原创文章受到原创版权保护。转载请注明出处：https://www.johngo689.com/563263/
转载文章受原作者版权保护。转载请注明原作者出处！