快速搜索高斯核中最大值的坐标 [英] Fast search for the coordinates of the maximum value in a gaussian kernel

问题描述

我有一个简单的代码，可以使用 scipy.stats.gaussian_kde 函数.

I have a simple code that generates a 2D gaussian kernel using scipy.stats.gaussian_kde function.

这是MWE:

def random_data(N):
    # Generate some random data.
    return np.random.uniform(0., 10., N)

# Data lists.
x_data = random_data(10000)
y_data = random_data(10000)

# Obtain the KDE for this region.
kernel = stats.gaussian_kde(np.vstack([x_data, y_data]), bw_method=0.05)

结果如下:

我需要的是一种在此KDE中获取最大值的x,y坐标的方法.

What I need is a way to obtain the x,y coordinates of the maximum value in this KDE.

对于我可以从各种来源收集到的信息，找到最大值的直接方法似乎是在细网格上评估kernel，然后仅使用np.argmax来找到它，请参见下文:

For what I could gather from various sources the direct way to locate the maximum value seem to be evaluating the kernel on a fine grid and then just use np.argmax to find it, see below:

# define grid.
xmin, xmax = min(x_data), max(x_data)
ymin, ymax = min(y_data), max(y_data)
x, y = np.mgrid[xmin:xmax:100j, ymin:ymax:100j]
positions = np.vstack([x.ravel(), y.ravel()])

# THIS IS TOO SLOW.
k_pos = kernel(positions)

# Print max value.
print k_pos[np.argmax(k_pos)]

# Print x,y coordinates of max value.
print positions.T[np.argmax(k_pos)]

问题是评估内核的速度非常慢，几乎到了对于不太大的数据集都无法使用的程度.

The issue with this is that evaluating the kernel is terribly slow, almost to the point of being unusable for not too large datasets.

是否有更好的方法来获取最大值的坐标?

Is there a better way to get the coordinates of the max value?

也被接受(也许会更好，因为它还可以进行快速绘图):是否有更快的方法可以在精细网格中评估内核?

Also accepted (perhaps even better since it would also allow fast plotting): is there a faster way to evaluate the kernel in a fine grid?

推荐答案

np.argmax(kernel)

可能就是您想要的...

might be what you're looking for...

请参阅: http://docs.scipy.org/doc/numpy/reference/generation/numpy.argmax.html

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