How does pdist2 work?

I am really confused. I have a matrix A=

    1 2
    3 4

I want to calculate dissimilarity. So I came to know that i could use euclidean to find.

   pdist2(A,A)

gives me

    0    2.828
   2.828 0

But If I calculate manually I am getting

    0    1.414
   1.414 0

Why the result is multiplied by 2?

Answer 1

[John D'Errico]

Because pdist2 computes the distances between ROWS of A. You computed the distance between the columns.

So the distance between the vector [1 2] and [3 4] is 2.8284... (or, 2*sqrt(2)).

A = [1 2;3 4];
norm(A(1,:) - A(2,:))
ans =
       2.8284

Using pdist2:

pdist2(A,A)
ans =
            0       2.8284
       2.8284            0

See that if I transpose A, then compute distances, I get what you expected.

pdist2(A',A')
ans =
            0       1.4142
       1.4142            0

Read the help for pdist2:

   pdist2 Pairwise distance between two sets of observations.
      D = pdist2(X,Y) returns a matrix D containing the Euclidean distances
      between each pair of observations in the MX-by-N data matrix X and
      MY-by-N data matrix Y. Rows of X and Y correspond to observations,

That is, it works on the ROWS of the matrices.

[Luciano La Frazia]

Hi I feel kind of silly making this question after your excellent answer, but I can't figure out how pdist2 works. I want to get the euclidean distance between two matrixes.

A = 131.1903   36.2473
   54.8736  281.1548
  102.8072  281.0851
  125.1274  269.3642
  155.6719  144.6703
   26.7995  191.9928

B = 123.7503  128.2180
  127.8487  159.0561
  136.1987  132.0602
   75.6246   13.0668
   48.9525   21.3157
  153.4662  104.5798

Applying pdist2 I get this

D = 92.2711  167.7309  154.2950  141.1529   35.9120  116.0460
  122.8542  142.2444  124.5719  110.3417   31.3222  106.2816
   95.9437  169.8322  152.7201  137.7497   23.1996  124.7402
   60.2071  268.8900  269.3933  261.0343  154.0359  185.4681
   83.5824  259.9066  265.2932  259.4816  163.1116  172.1087
   71.8717  202.2355  183.6313  167.2034   40.1511  153.9008

How pdist2 get the 154.2950 value for example?

Thanks in advance, sorry for answering the same with a larger example.

[Mohammad Al ja'idi]

the results that you should get by using the pdist2 are as follows :

  92.2711  122.8543   95.9437   60.2070   83.5823   71.8717
  167.7309  142.2444  169.8322  268.8899  259.9066  202.2356
  154.2951  124.5719  152.7200  269.3932  265.2932  183.6313
  141.1529  110.3417  137.7496  261.0343  259.4815  167.2034
   35.9119   31.3222   23.1996  154.0359  163.1116   40.1511
  116.0460  106.2815  124.7401  185.4681  172.1088  153.9009

Answer 2

[Marcela Mantilla]

Buenas tardes¡¡ Como se interpretan los resultados de una matriz obtenida de la función pdist2. Muchas gracias.

[Walter Roberson]

results(J, K) = distance between the point represented by row J of the first input and point represented by row K of the second input.