HIBOG: Improving the clustering accuracy by amelioratingdataset with gravitation
总结
[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:ba979c16-de16-4a40-9fe7-e7fa00333886
[En]
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优点
- 鲁棒性好,对大部分不同分布的数据集都有效;
- 运行更快
- 对超参数不敏感。
方法
思路
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[En]
[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:e4661076-ed42-4391-8306-81ab108c611b
做法
[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:033a34ad-6f76-40c1-bc28-b2908cbc8e71
[En]
[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:63cfa985-246f-4b14-b57d-3fba05fe34b7
[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:16767f33-6e1a-4955-9695-238211ed8aab
[En]
[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:b58a952f-c6f5-4360-acbe-3bff09a4b3d3
物体移动
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[En]
[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:0dfe005d-8131-4be8-a9e3-b3fb97cf942e
这个公式是物理学中位移的公式,而在这篇文章中,将v 0 v_0 v 0 设为0,m m m设为1,则得到了位移为:
S ⃗ = 1 2 F ⃗ t 2 \vec S = \frac{1}{2}\vec F t^2 S =2 1 F t 2
这里的F F F就是题目中提到的重力,而t t t则为超参。
对一个点i i i来讲,它的新坐标就可以通过原坐标o ⃗ i \vec o_i o i 加上位移S ⃗ i \vec S_i S i 来计算。其中,第三行T = t 2 2 T=\frac{t^2}{2}T =2 t 2 。第四行的转换是计算”重力部分”的内容。
; 计算重力
对一个点i i i,取它的k k k个最近邻,假设这个最近邻集合为K K K,根据最近邻与i i i的距离从小到大排序。此时,i j ij i j代表着离i第j j j近的节点,其中i 1 i1 i 1为最近的节点。所以,公式中的j j j是小于等于k k k的。
上面公式的F i j F_{ij}F i j ,可以理解为是第j j j近邻对点i i i施加的力(分力),首先,G G G的表达如下:
其中,o ⃗ \vec o o代表着该点的特征向量,而∣ ∣ ∣ ∣ 2 ||\ ||2 ∣∣∣∣2 则代表二范数,这个式子就是求出数据集中各点到其第一近邻的距离的均值,对于固定数据集而言,是一个定值。
而∣ ∣ o i 1 ⃗ − o i ⃗ ∣ ∣ 2 ||\vec{o{i1}} – \vec{o_i}||2 ∣∣o i 1 −o i ∣∣2 对于点i i i而言也是定值,所以无需讨论。
之后的一项o i 1 ⃗ − o i ⃗ \vec{o{i1}} – \vec{o_i}o i 1 −o i 的结果是向量形式,这一项表示点i i i移动的方向(向第j j j近邻移动)
接下来是分母部分,可以看出这是求i i i点与其第j j j近邻的距离,当j j j越大时(距离较远),意味着F F F就更小,这可以看作是一个加权的方式。
那么合力F i F_i F i 就可以得出是:
可以看出,距离越近的点F i j ⃗ \vec{F_{ij}}F i j 越大,即物体有向距离更近点移动的趋向。
优化
[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:8648040f-8d81-4082-a874-7d9c011e3835
[En]
[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:716f63cc-b575-4fba-ac97-3c9ba691f5f4
其中d d d为移动次数。
; 注意点
每次移动后,常数G G G还有每个点的近邻会改变,所以移动过后需要重新计算。
对于超参d d d和T T T,虽然设置得越大,数据会越适合于聚类,但是如果太大的话会导致失去原本数据的信息。文中建议是d ≤ 10 、 T ≤ 0.5 d\leq10、T\leq0.5 d ≤1 0 、T ≤0 .5。
BS3_1 12th
Original: https://blog.csdn.net/eternal_city/article/details/121323592
Author: 吾道长存
Title: HIBOG: Improving the clustering accuracy by amelioratingdataset with gravitation论文笔记
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