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,
and columns correspond to variables. D is an MX-by-MY matrix, with the
(I,J) entry equal to distance between observation I in X and
observation J in Y.
D = PDIST2(X,Y,DISTANCE) computes D using DISTANCE. Choices are:
'euclidean' - Euclidean distance (default)
'squaredeuclidean' - Squared Euclidean distance
'seuclidean' - Standardized Euclidean distance. Each
coordinate difference between rows in X and Y
is scaled by dividing by the corresponding
element of the standard deviation computed
from X, S=NANSTD(X). To specify another value
for S, use
D = PDIST2(X,Y,'seuclidean',S).
'fasteuclidean' - Euclidean distance computed by using an
alternative algorithm that saves time. This
faster algorithm can, in some cases, reduce
accuracy.
'fastsquaredeuclidean'
- Squared Euclidean distance computed by using an
alternative algorithm that saves time. This
faster algorithm can, in some cases, reduce
accuracy.
'fastseuclidean' - Standardized Euclidean distance computed by using
an alternative algorithm that saves time. This
faster algorithm can, in some cases, reduce
accuracy.
'cityblock' - City Block distance
'minkowski' - Minkowski distance. The default exponent is 2.
To specify a different exponent, use
D = PDIST2(X,Y,'minkowski',P), where the
exponent P is a scalar positive value.
'chebychev' - Chebychev distance (maximum coordinate
difference)
'mahalanobis' - Mahalanobis distance, using the sample
covariance of X as computed by NANCOV. To
compute the distance with a different
covariance, use
D = PDIST2(X,Y,'mahalanobis',C), where the
matrix C is symmetric and positive definite.
'cosine' - One minus the cosine of the included angle
between observations (treated as vectors)
'correlation' - One minus the sample linear correlation
between observations (treated as sequences of
values).
'spearman' - One minus the sample Spearman's rank
correlation between observations (treated as
sequences of values)
'hamming' - Hamming distance, percentage of coordinates
that differ
'jaccard' - One minus the Jaccard coefficient, the
percentage of nonzero coordinates that differ
function - A distance function specified using @, for
example @DISTFUN
A distance function must be of the form
function D2 = DISTFUN(ZI,ZJ),
taking as arguments a 1-by-N vector ZI containing a single observation
from X or Y, an M2-by-N matrix ZJ containing multiple observations from
X or Y, and returning an M2-by-1 vector of distances D2, whose Jth
element is the distance between the observations ZI and ZJ(J,:).
For built-in distance metrics, the distance between observation I in X
and observation J in Y will be NaN if observation I in X or observation
J in Y contains NaNs.
D = PDIST2(X,Y,DISTANCE,'Smallest',K) returns a K-by-MY matrix D
containing the K smallest pairwise distances to observations in X for
each observation in Y. PDIST2 sorts the distances in each column of D
in ascending order. D = PDIST2(X,Y,DISTANCE, 'Largest',K) returns the K
largest pairwise distances sorted in descending order. If K is greater
than MX, PDIST2 returns an MX-by-MY distance matrix. For each
observation in Y, PDIST2 finds the K smallest or largest distances by
computing and comparing the distance values to all the observations in
X.
[D,I] = PDIST2(X,Y,DISTANCE,'Smallest',K) returns a K-by-MY matrix I
containing indices of the observations in X corresponding to the K
smallest pairwise distances in D. [D,I] = PDIST2(X,Y,DISTANCE,
'Largest',K) returns indices corresponding to the K largest pairwise
distances.
D = PDIST2(X,Y,DISTANCE,'CacheSize',CACHESIZE) uses an intermediate
matrix stored in cache to compute D, when 'Distance' is one of
{'fasteuclidean','fastsquaredeuclidean','fastseuclidean'}.
'CacheSize' can be a positive scalar or 'maximal'. The default is 1e3.
If numeric, 'CacheSize' specifies the cache size in megabytes (MB) to
allocate for an intermediate matrix.
If 'maximal', pdist2 attempts to allocate enough memory for an entire
intermediate matrix whose size is MX-by-MY (MX is the number of rows
of the input data X, and MY is the number of rows of the input data Y).
'CacheSize' does not have to be large enough for an entire intermediate
matrix, but it must be at least large enough to hold an MX-by-1 vector.
Otherwise, the regular algorithm of computing Euclidean distance will
be used instead. If the specified cache size exceeds the available
memory, MATLAB issues an out-of-memory error.
Example:
% Compute the ordinary Euclidean distance
X = randn(100, 5);
Y = randn(25, 5);
D = pdist2(X,Y,'euclidean'); % euclidean distance
% Compute the Euclidean distance with each coordinate difference
% scaled by the standard deviation
Dstd = pdist2(X,Y,'seuclidean');
% Use a function handle to compute a distance that weights each
% coordinate contribution differently.
Wgts = [.1 .3 .3 .2 .1]; % coordinate weights
weuc = @(XI,XJ,W)(sqrt((XI - XJ).^2 * W'));
Dwgt = pdist2(X,Y, @(Xi,Xj) weuc(Xi,Xj,Wgts));
See also PDIST, KNNSEARCH, CREATENS, KDTreeSearcher,
ExhaustiveSearcher.
Documentation for pdist2
doc pdist2
Other uses of pdist2
gpuArray/pdist2 tall/pdist2
