从零开始在python中实现Mahalanobis距离

Question

我正在从零开始实现Mahalanobis，但是出现了一个错误。Mahalanobis距离公式是

我向下面的代码提供了错误-

from math import*
from decimal import Decimal
import numpy as np

def mahalanobis(x, y, cov=None):
    x_mean = np.mean(x)
    y_mean = np.mean(y)
    y_minus_mn = y - y_mean
    x_minus_mn_with_transpose =np.transpose(x- x_mean)
    Covariance = covar(x, y)
    inv_covmat = np.linalg.inv(Covariance)
    x_minus_mn = x - x_mean
    D_square = np.dot( x_minus_mn_with_transpose, inv_covmat, x_minus_mn)
    return D_square

def covar(x, y):
    x_mean = np.mean(x)
    y_mean = np.mean(y)
    Cov_numerator = sum(((a - x_mean)*(b - y_mean)) for a, b in zip(x, y))
    Cov_denomerator = len(x) - 1
    Covariance = (Cov_numerator / Cov_denomerator)
    return  Covariance

import pandas as pd

filepath = 'https://raw.githubusercontent.com/selva86/datasets/master/diamonds.csv'
df = pd.read_csv(filepath).iloc[:, [0,4,6]]
df.head()

X = df[['carat', 'depth', 'price']].head(500).values.tolist
Y =df[['carat', 'depth', 'price']].values.tolist

mahalanobis(X, Y)

错误-下图

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请帮帮忙。有没有人能检查和纠正我的代码？

Answer 1

X = df[['carat', 'depth', 'price']].head(500).values.tolist
Y =df[['carat', 'depth', 'price']].values.tolist

.tolist

这是功能。我觉得你需要：

.tolist()

Answer 2

您的代码中有一些错误，我将指出。

1. 使用np.cov计算协方差当您使用numpy数组时，不要重新实现所有
2. np.dot的第三个参数是输出，所以您应该编写D_square = np.dot(np.dot(x_minus_mn, inv_covmat), np.transpose(x_minus_mn))而不是D_square = np.dot( x_minus_mn_with_transpose, inv_covmat, x_minus_mn)
3. 使用X = df[['carat', 'depth', 'price']].head(500).values.tolist代替X = np.asarray(df[['carat', 'depth', 'price']].head(500).values)。如果您使用的是numpy，那么只使用numpy数组，而不是列表。

下面是您提供的代码的修改版本

import numpy as np

def mahalanobis(x, y, cov=None):
    x_mean = np.mean(x)
    Covariance = np.cov(np.transpose(y))
    inv_covmat = np.linalg.inv(Covariance)
    x_minus_mn = x - x_mean
    D_square = np.dot(np.dot(x_minus_mn, inv_covmat), np.transpose(x_minus_mn))
    return D_square

import pandas as pd

filepath = 'https://raw.githubusercontent.com/selva86/datasets/master/diamonds.csv'
df = pd.read_csv(filepath).iloc[:, [0,4,6]]
df.head()

X = np.asarray(df[['carat', 'depth', 'price']].head(500).values)
Y =np.asarray(df[['carat', 'depth', 'price']].values)

mahalanobis(X, Y)