Understanding argmax

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Let say I have the matrix

import numpy as np    
A = np.matrix([[1,2,3,33],[4,5,6,66],[7,8,9,99]])

I am trying to understand the function argmax, as far as I know it returns the largest value

If I tried it on Python:

np.argmax(A[1:,2])

Should I get the largest element in the second row till the end of the row (which is the third row) and along the third column? So it should be the array [6 9], and arg max should return 9? But why when I run it on Python, it returns the value 1?

And if I want to return the largest element from row 2 onwards in column 3 (which is 9), how should I modify the code?

I have checked the Python documentation but still a bit unclear. Thanks for the help and explanation.

No argmax returns the position of the largest value. max returns the largest value.

import numpy as np    
A = np.matrix([[1,2,3,33],[4,5,6,66],[7,8,9,99]])

np.argmax(A)  # 11, which is the position of 99

np.argmax(A[:,:])  # 11, which is the position of 99

np.argmax(A[:1])  # 3, which is the position of 33

np.argmax(A[:,2])  # 2, which is the position of 9

np.argmax(A[1:,2])  # 1, which is the position of 9

numpy.argmax() in Python, It contains well written, well thought and well explained computer science and numpy.argmax(array, axis = None, out = None) : Returns indices of the max  In mathematics, the arguments of the maxima (abbreviated arg max or argmax) are the points, or elements, of the domain of some function at which the function values are maximized.

It took me a while to figure this function out. Basically argmax returns you the index of the maximum value in the array. Now the array can be 1 dimensional or multiple dimensions. Following are some examples.

1 dimensional

a = [[1,2,3,4,5]]
np.argmax(a)
>>4

The array is 1 dimensional so the function simply returns the index of the maximum value(5) in the array, which is 4.

Multiple dimensions

a = [[1,2,3],[4,5,6]]
np.argmax(a)
>>5

In this example the array is 2 dimensional, with shape (2,3). Since no axis parameter is specified in the function, the numpy library flattens the array to a 1 dimensional array and then returns the index of the maximum value. In this case the array is transformed to [[1,2,3,4,5,6]] and then returns the index of 6, which is 5.

When parameter is axis = 0

a = [[1,2,3],[4,5,6]]
np.argmax(a, axis=0)
>>array([1, 1, 1])

The result here was a bit confusing to me at first. Since the axis is defined to be 0, the function will now try to find the maximum value along the rows of the matrix. The maximum value,6, is in the second row of the matrix. The index of the second row is 1. According to the documentation https://docs.scipy.org/doc/numpy-1.15.0/reference/generated/numpy.argmax.html the dimension specified in the axis parameter will be removed. Since the shape of the original matrix was (2,3) and axis specified as 0, the returned matrix will have a shape of(3,) instead, since the 2 in the original shape(2,3) is removed.The row in which the maximum value was found is now repeated for the same number of elements as the columns in the original matrix i.e. 3.

When parameter is axis = 1

a = [[1,2,3],[4,5,6]]
np.argmax(a, axis=1)
>>array([2, 2])

Same concept as above but now index of the column is returned at which the maximum value is available. In this example the maximum value 6 is in the 3rd column, index 2. The column of the original matrix with shape (2,3) will be removed, transforming to (2,) and so the return array will display two elements, each showing the index of the column in which the maximum value was found.

Arg max, For example, you may see “argmax” or “arg max” used in a research paper used to describe Develop a working understand of linear algebra. max_index = tf.argmax(x, axis = 1) The result is: [array([1, 2], dtype=int64)] This is very easy understand.

argmax is a function which gives the index of the greatest number in the given row or column and the row or column can be decided using axis attribute of argmax funcion. If we give axis=0 then it will give the index from columns and if we give axis=1 then it will give the index from rows.

In your given example A[1:, 2] it will first fetch the values from 1st row on wards and the only 2nd column value from those rows, then it will find the index of max value from into the resulted matrix.

What Is Argmax in Machine Learning?, Argmax and Max Calculus. Mark Schmidt. January 6, 2016. 1 Argmax, Max, and Supremum. We define the argmax of a function f defined on a set D as argmax. This is a short post on understanding what argmax() is doing and why we need it. Some examples. Given an array the function is simply returning the maximum values along an axis. Let’s see some examples. Note: argmax() returns the position of the maximum value and not the max value.

In my first steps in python i have tested this function. And the result with this example clarified me how works argmax.

Example:

# Generating 2D array for input 
array = np.arange(20).reshape(4, 5) 
array[1][2] = 25

print("The input array: \n", array) 

# without axis
print("\nThe max element: ", np.argmax(array))
# with axis
print("\nThe indices of max element: ", np.argmax(array, axis=0)) 
print("\nThe indices of max element: ", np.argmax(array, axis=1)) 

Result Example:

The input array: 
[[ 0  1  2  3  4]
[ 5  6 25  8  9]
[10 11 12 13 14]
[15 16 17 18 19]]

The max element:  7

The indices of max element:  [3 3 1 3 3]

The indices of max element:  [4 2 4 4]

In that result we can see 3 results.

  1. The highest element in all array is in position 7.
  2. The highest element in every column is in the last row which index is 3, except on third column where the highest value is in row number two which index is 1.
  3. The highest element in every row is in the last column which index is 4, except on second row where the highest value is in third columen which index is 2.

Reference: https://www.crazygeeks.org/numpy-argmax-in-python/

I hope that it helps.

[PDF] Argmax and Max Calculus, This is how i understand it: 1. i count the sum first 2. i find the argmax. Sorry for my dummy question, but i am not realy good in this area. Thanks for your answers  argmax is a function which gives the index of the greatest number in the given row or column and the row or column can be decided using axis attribute of argmax funcion. If we give axis=0 then it will give the index from columns and if we give axis=1 then it will give the index from rows.

what argmax means?, The caret (the symbol is ∧, written as \wedge in LaTeX) means "and". The definition says that the argmax is the set of all x which are in S and satisfy f(y)≤f(x​)  numpy.argmax (array, axis = None, out = None) : Returns indices of the max element of the array in a particular axis.

How to read this Arg Max definition in plain english, ArgMax[{f, cons}, {x, y, }] gives a position at which f is maximized subject to the constraints cons. ArgMax[, x \[Element] reg] constrains x to be in the region reg. numpy.argmax¶ numpy.argmax (a, axis=None, out=None) [source] ¶ Returns the indices of the maximum values along an axis. Parameters a array_like. Input array. axis int, optional. By default, the index is into the flattened array, otherwise along the specified axis. out array, optional. If provided, the result will be inserted into this array.

ArgMax—Wolfram Language Documentation, Hence the optimal meaning for a speech utterance 0 should be Ill — argmax Pt M I 0) = arg max P(() I M)P(M_) (3.43) M M Equation (3.43) is often implemented  Note that the output of the argmax function is a set, since more than one value might achieve the maximum. The result of the argmax function might even be an innite set. For example, the argmax of cos(x) is the set containing all integer multiples of 2ˇ. We can dene the max of a function fdened on a set Das max

Comments
  • Simplest explanation with examples: crazygeeks.org/numpy-argmax-in-python
  • Yes. OP can see stackoverflow.com/questions/3584243/…
  • Sorry, OP stands for?
  • I tried np.argmax(A), but it return 10 instead of 11?
  • Short for original poster, i.e. @user71346 in this case.
  • @OP: it should be 11, since the array is zero-based and 99 is the largest and last value out of 12.
  • When axis=0, a response like [0, 2, 1] means that for the first column, the 0th element was the highest, for the second, column, the 2nd (0 indexed) element was the highest, and for the third column the 1st element is the highest. Hope that helps people like it helped me.