Fluent Data

低内存占用流数据建模库和服务。

该算法从输入流读取数据点，拟合模型并将更新的模型发送到输出流。

在线算法拟合一个由一组球组成的模型。每个球由其中心、半径和权重（包含在球中的点的衰减数量）描述。

安装和运行程序

安装

cargo install fluent_data

运行程序，并在标准输入中输入数据点。程序将以模型回答

fluent_data
[5,-1]
[{"center":[5.0,-1.0],"radius":null,"weight":0.0}]
[1,1]
[{"center":[1.0,1.0],"radius":4.47213595499958,"weight":1.0}]
[15,-13]
[{"center":[1.0,1.0],"radius":4.47213595499958,"weight":0.95},{"center":[18.5,-16.5],"radius":3.9597979746446663,"weight":1.0}]
[11,23]
[{"center":[1.0,1.0],"radius":4.47213595499958,"weight":0.9025},{"center":[18.5,-16.5],"radius":3.9597979746446663,"weight":0.95},{"center":[13.5,28.5],"radius":4.833218389437829,"weight":1.0}]
[31,-3]    
[{"center":[1.0,1.0],"radius":4.47213595499958,"weight":0.8573749999999999},{"center":[18.5,-16.5],"radius":3.9597979746446663,"weight":0.9025},{"center":[13.5,28.5],"radius":4.833218389437829,"weight":0.95},{"center":[34.125,0.375],"radius":3.6796738985948196,"weight":1.0}]
[10,-9]    
[{"center":[1.0,1.0],"radius":4.47213595499958,"weight":0.8145062499999999},{"center":[14.032194480946124,-12.557818659658345],"radius":8.65915237435586,"weight":1.9024999999999999},{"center":[13.5,28.5],"radius":4.833218389437829,"weight":0.9025},{"center":[34.125,0.375],"radius":3.6796738985948196,"weight":0.95}]
[6,-4]
[{"center":[1.0,1.0],"radius":4.47213595499958,"weight":0.7737809374999999},{"center":[11.264857881136951,-9.609388458225668],"radius":9.828917387831996,"weight":2.9025},{"center":[13.5,28.5],"radius":4.833218389437829,"weight":0.8573749999999999},{"center":[34.125,0.375],"radius":3.6796738985948196,"weight":0.9025}]
[-2,-5]
[{"center":[6.7297134962820016,-6.8681649994430005],"radius":15.539441192890935,"weight":4.6762809375},{"center":[13.5,28.5],"radius":4.833218389437829,"weight":0.8145062499999999},{"center":[34.125,0.375],"radius":3.6796738985948196,"weight":0.8573749999999999}]

模型表示为包含每个球的对象的 json 数组

• center 是球心，
• radius 是球的半径，
• weight 是球的权重（通过将权重除以权重的总和获得概率）。

作为服务运行

程序可以作为 websocket 服务器运行

fluent_data --service

数据点发送到 ws://0.0.0.0:9001/ws/points，模型从 ws://0.0.0.0:9001/ws/models 接收。端口号可以通过设置 PORT 环境变量进行自定义。

对于发送和接收点，可以使用 websocket 客户端 websocat。打开一个终端，用于监听模型

websocat ws://127.0.0.1:9001/ws/models

打开另一个终端并输入一些点

websocat ws://127.0.0.1:9001/ws/points
[5,-1]
[1,1]
[15,-13]
[11,23]
[31,-3]    
[10,-9]    
[6,-4]
[-2,-5]

第一个终端应显示模型

[{"center":[5.0,-1.0],"radius":null,"weight":0.0}]
[{"center":[1.0,1.0],"radius":4.47213595499958,"weight":1.0}]
[{"center":[1.0,1.0],"radius":4.47213595499958,"weight":0.95},{"center":[18.5,-16.5],"radius":3.9597979746446663,"weight":1.0}]
[{"center":[1.0,1.0],"radius":4.47213595499958,"weight":0.9025},{"center":[18.5,-16.5],"radius":3.9597979746446663,"weight":0.95},{"center":[13.5,28.5],"radius":4.833218389437829,"weight":1.0}]
[{"center":[1.0,1.0],"radius":4.47213595499958,"weight":0.8573749999999999},{"center":[18.5,-16.5],"radius":3.9597979746446663,"weight":0.9025},{"center":[13.5,28.5],"radius":4.833218389437829,"weight":0.95},{"center":[34.125,0.375],"radius":3.6796738985948196,"weight":1.0}]
[{"center":[1.0,1.0],"radius":4.47213595499958,"weight":0.8145062499999999},{"center":[14.032194480946124,-12.557818659658345],"radius":8.65915237435586,"weight":1.9024999999999999},{"center":[13.5,28.5],"radius":4.833218389437829,"weight":0.9025},{"center":[34.125,0.375],"radius":3.6796738985948196,"weight":0.95}]
[{"center":[1.0,1.0],"radius":4.47213595499958,"weight":0.7737809374999999},{"center":[11.264857881136951,-9.609388458225668],"radius":9.828917387831996,"weight":2.9025},{"center":[13.5,28.5],"radius":4.833218389437829,"weight":0.8573749999999999},{"center":[34.125,0.375],"radius":3.6796738985948196,"weight":0.9025}]
[{"center":[6.7297134962820016,-6.8681649994430005],"radius":15.539441192890935,"weight":4.6762809375},{"center":[13.5,28.5],"radius":4.833218389437829,"weight":0.8145062499999999},{"center":[34.125,0.375],"radius":3.6796738985948196,"weight":0.8573749999999999}]

使用库

请参阅 包文档。

自定义算法

请参阅 包文档中的自定义部分。

工作原理

给定一组从迄今为止接收到的数据点拟合的球，设 P 为新的进入点。设 B 为最有可能包含 P 的球 (*)。

设 B 的中心为 C，半径为 r，重量为 w。设 d 为 P 到 C 的距离：d = |PC|。

(*) “最有可能包含”的意思是，对于模型中的所有球，B 最小化 d/r 的数量。

拟合算法如下

• (I) 如果距离小于四个 B 半径，即 d < 4r，
  • 新点属于 B，B 将增量更新
    • 半径的平方设置为平均平方半径：r² <- (w.r² + d²) / (w + 1)，
    • 中心设置为平均中心：C <- (w.C + P) / (w + 1)，
    • 重量增加 1：w <- w + 1。
  • 否则创建一个新的球 B*
    • 将半径设置为距离的五分之一：r* <- d / 5，即 r*² <- d² / 25，
    • 将中心 C* 设置为使 C、P 和 C* 对齐，即 CC* = 6/5 CP，即 C* <- (-C + 5P) / 6
    • 球的重量设置为 1。
• (II) 设 B' 为 B 的最近球，即所有球中距离 CC' 最小。在上面的第一种情况下，如果它们之间的平方距离小于它们半径平方的和，即 d² < r² + r'²，则 B 和 B' 可以合并成一个球。
  • B被更新
    • 半径的平方被设置为半径平方的加权平均值，加上距离的平方 r² <- (加权.r² + 加权'.r²) / (加权 + 加权') + d²，
    • 中心被设置为中心的加权平均值 C <- (加权.C + 加权'.C) / (加权 + 加权')，
    • 权重被设置为权重的总和 w <- w + 加权'。
  • B'被丢弃。
• (III) 除了属于P的球之外的所有球的权重都以0.95的因子衰减，w <- 0.95 w。
  • 所有权重低于1/100的球都被移除，w < 1/100。