Distance matrix computation from a collection of raw observation vectors stored in a rectangular array.
Function  Description 
pdist  pairwise distances between observation vectors. 
cdist  distances between between two collections of observation vectors. 
squareform  converts a square distance matrix to a condensed one and vice versa. 
Predicates for checking the validity of distance matrices, both condensed and redundant. Also contained in this module are functions for computing the number of observations in a distance matrix.
Function  Description 
is_valid_dm  checks for a valid distance matrix. 
is_valid_y  checks for a valid condensed distance matrix. 
num_obs_dm  # of observations in a distance matrix. 
num_obs_y  # of observations in a condensed distance matrix. 
Distance functions between two vectors u and v. Computing distances over a large collection of vectors is inefficient for these functions. Use pdist for this purpose.
Function  Description 
braycurtis  the BrayCurtis distance. 
canberra  the Canberra distance. 
chebyshev  the Chebyshev distance. 
cityblock  the Manhattan distance. 
correlation  the Correlation distance. 
cosine  the Cosine distance. 
dice  the Dice dissimilarity (boolean). 
euclidean  the Euclidean distance. 
hamming  the Hamming distance (boolean). 
jaccard  the Jaccard distance (boolean). 
kulsinski  the Kulsinski distance (boolean). 
mahalanobis  the Mahalanobis distance. 
matching  the matching dissimilarity (boolean). 
minkowski  the Minkowski distance. 
rogerstanimoto  the RogersTanimoto dissimilarity (boolean). 
russellrao  the RussellRao dissimilarity (boolean). 
seuclidean  the normalized Euclidean distance. 
sokalmichener  the SokalMichener dissimilarity (boolean). 
sokalsneath  the SokalSneath dissimilarity (boolean). 
sqeuclidean  the squared Euclidean distance. 
yule  the Yule dissimilarity (boolean). 
[Sta07]  “Statistics toolbox.” API Reference Documentation. The MathWorks. http://www.mathworks.com/access/helpdesk/help/toolbox/stats/. Accessed October 1, 2007. 
[Mti07]  “Hierarchical clustering.” API Reference Documentation. The Wolfram Research, Inc. http://reference.wolfram.com/mathematica/HierarchicalClustering/tutorial/HierarchicalClustering.html. Accessed October 1, 2007. 
[Gow69]  Gower, JC and Ross, GJS. “Minimum Spanning Trees and Single Linkage Cluster Analysis.” Applied Statistics. 18(1): pp. 54–64. 1969. 
[War63]  Ward Jr, JH. “Hierarchical grouping to optimize an objective function.” Journal of the American Statistical Association. 58(301): pp. 236–44. 1963. 
[Joh66]  Johnson, SC. “Hierarchical clustering schemes.” Psychometrika. 32(2): pp. 241–54. 1966. 
[Sne62]  Sneath, PH and Sokal, RR. “Numerical taxonomy.” Nature. 193: pp. 855–60. 1962. 
[Bat95]  Batagelj, V. “Comparing resemblance measures.” Journal of Classification. 12: pp. 73–90. 1995. 
[Sok58]  Sokal, RR and Michener, CD. “A statistical method for evaluating systematic relationships.” Scientific Bulletins. 38(22): pp. 1409–38. 1958. 
[Ede79]  Edelbrock, C. “Mixture model tests of hierarchical clustering algorithms: the problem of classifying everybody.” Multivariate Behavioral Research. 14: pp. 367–84. 1979. 
[Jai88]  Jain, A., and Dubes, R., “Algorithms for Clustering Data.” PrenticeHall. Englewood Cliffs, NJ. 1988. 
[Fis36]  Fisher, RA “The use of multiple measurements in taxonomic problems.” Annals of Eugenics, 7(2): 179188. 1936 
Copyright (C) Damian Eads, 20072008. New BSD License.
Computes the BrayCurtis distance between two nvectors u and v, which is defined as
Parameters: 


Returns: 

Computes the Canberra distance between two nvectors u and v, which is defined as
Parameters: 


Returns: 

Computes distance between each pair of observation vectors in the Cartesian product of two collections of vectors. XA is a by array while XB is a by array. A by array is returned. An exception is thrown if XA and XB do not have the same number of columns.
A rectangular distance matrix Y is returned. For each and , the metric dist(u=XA[i], v=XB[j]) is computed and stored in the th entry.
The following are common calling conventions:
Y = cdist(XA, XB, 'euclidean')
Computes the distance between points using Euclidean distance (2norm) as the distance metric between the points. The points are arranged as dimensional row vectors in the matrix X.
Y = cdist(XA, XB, 'minkowski', p)
Computes the distances using the Minkowski distance (norm) where .
Y = cdist(XA, XB, 'cityblock')
Computes the city block or Manhattan distance between the points.
Y = cdist(XA, XB, 'seuclidean', V=None)
Computes the standardized Euclidean distance. The standardized Euclidean distance between two nvectors u and v is
the i’th components of the points. If not passed, it is automatically computed.
Y = cdist(XA, XB, 'sqeuclidean')
Computes the squared Euclidean distance between the vectors.
Y = cdist(XA, XB, 'cosine')
Computes the cosine distance between vectors u and v,
where is the 2norm of its argument *.
Y = cdist(XA, XB, 'correlation')
Computes the correlation distance between vectors u and v. This is
where is the Manhattan (or 1norm) of its argument, and is the common dimensionality of the vectors.
Y = cdist(XA, XB, 'hamming')
Computes the normalized Hamming distance, or the proportion of those vector elements between two nvectors u and v which disagree. To save memory, the matrix X can be of type boolean.
Y = cdist(XA, XB, 'jaccard')
Computes the Jaccard distance between the points. Given two vectors, u and v, the Jaccard distance is the proportion of those elements u[i] and v[i] that disagree where at least one of them is nonzero.
Y = cdist(XA, XB, 'chebyshev')
Computes the Chebyshev distance between the points. The Chebyshev distance between two nvectors u and v is the maximum norm1 distance between their respective elements. More precisely, the distance is given by
Computes the Canberra distance between the points. The Canberra distance between two points u and v is
Computes the BrayCurtis distance between the points. The BrayCurtis distance between two points u and v is
Computes the Mahalanobis distance between the points. The Mahalanobis distance between two points u and v is where (the VI variable) is the inverse covariance. If VI is not None, VI will be used as the inverse covariance matrix.
Computes the Yule distance between the boolean vectors. (see yule function documentation)
Computes the matching distance between the boolean vectors. (see matching function documentation)
Computes the Dice distance between the boolean vectors. (see dice function documentation)
Computes the Kulsinski distance between the boolean vectors. (see kulsinski function documentation)
Computes the RogersTanimoto distance between the boolean vectors. (see rogerstanimoto function documentation)
Computes the RussellRao distance between the boolean vectors. (see russellrao function documentation)
Computes the SokalMichener distance between the boolean vectors. (see sokalmichener function documentation)
Computes the SokalSneath distance between the vectors. (see sokalsneath function documentation)
Computes the weighted Minkowski distance between the vectors. (see sokalsneath function documentation)
Computes the distance between all pairs of vectors in X using the user supplied 2arity function f. For example, Euclidean distance between the vectors could be computed as follows:
dm = cdist(XA, XB, (lambda u, v: np.sqrt(((uv)*(uv).T).sum())))Note that you should avoid passing a reference to one of the distance functions defined in this library. For example,:
dm = cdist(XA, XB, sokalsneath)would calculate the pairwise distances between the vectors in X using the Python function sokalsneath. This would result in sokalsneath being called times, which is inefficient. Instead, the optimized C version is more efficient, and we call it using the following syntax.:
dm = cdist(XA, XB, 'sokalsneath')
Parameters: 


Returns: 

Computes the Chebyshev distance between two nvectors u and v, which is defined as
Parameters: 


Returns: 

Computes the Manhattan distance between two nvectors u and v, which is defined as
Parameters: 


Returns: 

Computes the correlation distance between two nvectors u and v, which is defined as
where is the mean of a vectors elements and n is the common dimensionality of u and v.
Parameters: 


Returns: 

Computes the Cosine distance between two nvectors u and v, which is defined as
Parameters: 


Returns: 

Computes the Dice dissimilarity between two boolean nvectors u and v, which is
where is the number of occurrences of and for .
Parameters: 


Returns: 

Computes the Euclidean distance between two nvectors u and v, which is defined as
Parameters: 


Returns: 

Computes the Hamming distance between two nvectors u and v, which is simply the proportion of disagreeing components in u and v. If u and v are boolean vectors, the Hamming distance is
where is the number of occurrences of and for .
Parameters: 


Returns: 

Returns True if the variable D passed is a valid distance matrix. Distance matrices must be 2dimensional numpy arrays containing doubles. They must have a zerodiagonal, and they must be symmetric.
Parameters: 


Returns:  Returns True if the variable D passed is a valid distance matrix. Small numerical differences in D and D.T and nonzeroness of the diagonal are ignored if they are within the tolerance specified by tol. 
Returns True if the variable y passed is a valid condensed distance matrix. Condensed distance matrices must be 1dimensional numpy arrays containing doubles. Their length must be a binomial coefficient for some positive integer n.
Parameters: 


Computes the JaccardNeedham dissimilarity between two boolean nvectors u and v, which is
where is the number of occurrences of and for .
Parameters: 


Returns: 

Computes the Kulsinski dissimilarity between two boolean nvectors u and v, which is defined as
where is the number of occurrences of and for .
Parameters: 


Returns: 

Computes the Mahalanobis distance between two nvectors u and v, which is defiend as
where VI is the inverse covariance matrix .
Parameters: 


Returns: 

Computes the Matching dissimilarity between two boolean nvectors u and v, which is defined as
where is the number of occurrences of and for .
Parameters: 


Returns: 

Computes the Minkowski distance between two vectors u and v, defined as
Parameters: 


Returns: 

Returns the number of original observations that correspond to a square, redudant distance matrix D.
Parameters: 


Returns:  The number of observations in the redundant distance matrix. 
Returns the number of original observations that correspond to a condensed distance matrix Y.
Parameters: 


Returns: 

Computes the pairwise distances between m original observations in ndimensional space. Returns a condensed distance matrix Y. For each and (where ), the metric dist(u=X[i], v=X[j]) is computed and stored in the :math:`ij`th entry.
See squareform for information on how to calculate the index of this entry or to convert the condensed distance matrix to a redundant square matrix.
The following are common calling conventions.
Y = pdist(X, 'euclidean')
Computes the distance between m points using Euclidean distance (2norm) as the distance metric between the points. The points are arranged as m ndimensional row vectors in the matrix X.
Y = pdist(X, 'minkowski', p)
Computes the distances using the Minkowski distance (pnorm) where .
Y = pdist(X, 'cityblock')
Computes the city block or Manhattan distance between the points.
Y = pdist(X, 'seuclidean', V=None)
Computes the standardized Euclidean distance. The standardized Euclidean distance between two nvectors u and v is
the i’th components of the points. If not passed, it is automatically computed.
Y = pdist(X, 'sqeuclidean')
Computes the squared Euclidean distance between the vectors.
Y = pdist(X, 'cosine')
Computes the cosine distance between vectors u and v,
Y = pdist(X, 'correlation')
Computes the correlation distance between vectors u and v. This is
where is the mean of the elements of vector v.
Y = pdist(X, 'hamming')
Computes the normalized Hamming distance, or the proportion of those vector elements between two nvectors u and v which disagree. To save memory, the matrix X can be of type boolean.
Y = pdist(X, 'jaccard')
Computes the Jaccard distance between the points. Given two vectors, u and v, the Jaccard distance is the proportion of those elements u[i] and v[i] that disagree where at least one of them is nonzero.
Y = pdist(X, 'chebyshev')
Computes the Chebyshev distance between the points. The Chebyshev distance between two nvectors u and v is the maximum norm1 distance between their respective elements. More precisely, the distance is given by
Computes the Canberra distance between the points. The Canberra distance between two points u and v is
Computes the BrayCurtis distance between the points. The BrayCurtis distance between two points u and v is
Computes the Mahalanobis distance between the points. The Mahalanobis distance between two points u and v is where (the VI variable) is the inverse covariance. If VI is not None, VI will be used as the inverse covariance matrix.
Computes the Yule distance between each pair of boolean vectors. (see yule function documentation)
Computes the matching distance between each pair of boolean vectors. (see matching function documentation)
Computes the Dice distance between each pair of boolean vectors. (see dice function documentation)
Computes the Kulsinski distance between each pair of boolean vectors. (see kulsinski function documentation)
Computes the RogersTanimoto distance between each pair of boolean vectors. (see rogerstanimoto function documentation)
Computes the RussellRao distance between each pair of boolean vectors. (see russellrao function documentation)
Computes the SokalMichener distance between each pair of boolean vectors. (see sokalmichener function documentation)
Computes the SokalSneath distance between each pair of boolean vectors. (see sokalsneath function documentation)
Computes the weighted Minkowski distance between each pair of vectors. (see wminkowski function documentation)
Computes the distance between all pairs of vectors in X using the user supplied 2arity function f. For example, Euclidean distance between the vectors could be computed as follows:
dm = pdist(X, (lambda u, v: np.sqrt(((uv)*(uv).T).sum())))Note that you should avoid passing a reference to one of the distance functions defined in this library. For example,:
dm = pdist(X, sokalsneath)would calculate the pairwise distances between the vectors in X using the Python function sokalsneath. This would result in sokalsneath being called times, which is inefficient. Instead, the optimized C version is more efficient, and we call it using the following syntax.:
dm = pdist(X, 'sokalsneath')
Parameters: 


Returns: 

Seealso: 

Computes the RogersTanimoto dissimilarity between two boolean nvectors u and v, which is defined as
where is the number of occurrences of and for and .
Parameters: 


Returns: 

Computes the RussellRao dissimilarity between two boolean nvectors u and v, which is defined as
where is the number of occurrences of and for .
Parameters: 


Returns: 

Returns the standardized Euclidean distance between two nvectors u and v. V is an mdimensional vector of component variances. It is usually computed among a larger collection vectors.
Parameters: 


Returns: 

Computes the SokalMichener dissimilarity between two boolean vectors u and v, which is defined as
where is the number of occurrences of and for , and .
Parameters: 


Returns: 

Computes the SokalSneath dissimilarity between two boolean vectors u and v,
where is the number of occurrences of and for and .
Parameters: 


Returns: 

Computes the squared Euclidean distance between two nvectors u and v, which is defined as
Parameters: 


Returns: 

Converts a vectorform distance vector to a squareform distance matrix, and viceversa.
Parameters: 


Returns: 

Computes the weighted Minkowski distance between two vectors u and v, defined as
Parameters: 


Returns: 

Computes the Yule dissimilarity between two boolean nvectors u and v, which is defined as
where is the number of occurrences of and for and .
Parameters: 


Returns: 
