特征工程

业务分析

经过调研，我们可以将带有以下特征的鼠标轨迹判定为机器轨迹：

• 跳变运动（鼠标由一个点直接跳到很远的另一个点）【实现】

• 横/竖直线运动（人手可能会画出横/竖直线，但是很难画出非常长的横/竖直线）【实现】

• 斜直线运动（人手可能会画出横/竖直线，但是画不出来斜直线）【实现】

• 分速度的匀速运动【实现】

• 分速度的匀变速运动【实现】

• 分速度的匀变加速运动【实现】

• 合速度的匀速运动【实现】

• 合速度的匀变速运动【实现】

• 合速度的匀变加速运动【实现】

• 轨迹点间 时间间隔非常大的运动（比如pyautogui、鼠标录制软件【普通速度】）【实现】

• 轨迹点间 时间间隔远偏离均值的运动（鼠标录制软件【适当加速】）同上

• 轨迹点间 时间间隔非常小，但是运动速度和加速度非常大的运动（鼠标录制软件【高速】）可以视为跳变

• 路径重复的运动（防止一些未知的鼠标录制软件可以躲过以上防御，这里可以加最后一层防御）【实现】

爬虫和反爬虫是一个对抗的过程，如果大家还有其他的想法，欢迎补充

特征提取

经过调研和业务分析，我们抽取了以下特征：

• 鼠标移动速度

• 鼠标移动加速度（二阶速度）

• 鼠标移动n阶速度

• 鼠标移动分速度

• 鼠标移动分加速度（二阶速度）

• 鼠标移动分n阶速度

• 鼠标移动方向角的变化

• 鼠标轨迹点之间的时间间隔

• 鼠标轨迹的向量化（可用来计算轨迹间的相似度）

通过这些特征的提取，基本可以覆盖到我们的业务需求

可视化

鼠标轨迹展示

trace_answer_unlock = [[72, 0, 1655046417887], [72, 1, 1655046417903], [70, 3, 1655046417916], [69, 5, 1655046417930], [68, 6, 1655046417951], [67, 8, 1655046417983], [67, 10, 1655046417996], [65, 15, 1655046418010], [62, 20, 1655046418023], [61, 23, 1655046418036], [59, 26, 1655046418049], [59, 27, 1655046418063], [57, 29, 1655046418076], [55, 31, 1655046418089], [54, 32, 1655046418103], [52, 34, 1655046418116], [49, 38, 1655046418129], [46, 40, 1655046418143], [42, 45, 1655046418156], [37, 50, 1655046418170], [34, 53, 1655046418183], [33, 55, 1655046418196], [30, 56, 1655046418210], [27, 57, 1655046418223], [27, 58, 1655046418236], [26, 58, 1655046418250], [24, 60, 1655046418263], [22, 63, 1655046418276], [19, 67, 1655046418290], [19, 68, 1655046418303], [18, 70, 1655046418316], [17, 71, 1655046418330], [17, 72, 1655046418345], [17, 73, 1655046418361], [17, 74, 1655046418435], [15, 75, 1655046418463], [13, 76, 1655046418476], [12, 77, 1655046418490], [11, 77, 1655046418503], [9, 78, 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mouse_track = MouseTrack(trace_answer_unlock)
mouse_track.show_track()

鼠标移动合速度

feature_dev_order1, feature_dev_order2 = mouse_track.get_feature_dev(order=2, mode="combine") 
import matplotlib.pyplot as plt
plt.plot(mouse_track.arr_trace[:len(feature_dev_order1),-1], feature_dev_order1)
plt.show()

从上图可以看出，第一个峰是答完题，向滑块验证码的快速移动，第二个峰是解锁滑块后，向提交按钮快速移动

鼠标移动合加速度

plt.plot(mouse_track.arr_trace[:len(feature_dev_order1),-1], feature_dev_order1)
plt.xlabel("time")
plt.ylabel("px/ms")
plt.show()

鼠标移动分速度(x方向)

feature_dev_order1, feature_dev_order2 = mouse_track.get_feature_dev(order=2, mode="decomposition") # contants.COMBINE
plt.plot(mouse_track.arr_trace[:len(feature_dev_order1), -1], feature_dev_order1[:, 0])
plt.xlabel("time")
plt.ylabel("x-axis px/ms")
plt.show()

鼠标移动方向角变化

feature_doa = mouse_track.get_feature_doa()
plt.plot(mouse_track.arr_trace[:len(feature_doa), -1], feature_doa)
plt.xlabel("time")
plt.ylabel("angle")
plt.show()