Compute distance (dissimilarity) matrix

はじめる前に
新機能一覧
Maple ワークシートの作成
Mapleワークシートを共有
Maple ウィンドウのカスタマイズ
Maple システムのカスタマイズ
コネクティビティ
Mathematics
数学
物理
プログラミング
グラフィックス
Student パッケージ
Science and Engineering
科学・エンジニアリング
アプリケーションと例題
リファレンス
システム
MapleSim
MapleSim ツールボックス
MapleSim ヘルプ
Tasks
Toolboxes
- BlockImporter
- Global Optimization
- Grid Computing
- Maple-NAG Connector
  - General information
  - Computational Routines
    - a02 (Complex Arithmetic)
    - c02 (Zeros of Polynomials)
    - c05 (Roots of One or More Transcendental Equations)
    - c06 (Fourier Transforms)
    - d01 (Quadrature)
    - d02 (Ordinary Differential Equations)
    - d03 (Partial Differential Equations)
    - d06 (Mesh Generation)
    - e01 (Interpolation)
    - e02 (Curve and Surface Fitting)
    - e04 (Minimizing or Maximizing a Function)
    - f01 (Matrix Factorizations)
    - f02 (Eigenvalues and Eigenvectors)
    - f03 (Determinants)
    - f04 (Simultaneous Linear Equations)
    - f06 (Linear Algebra Support Functions)
    - f07 (Linear Equations (LAPACK))
    - f08 (Least-squares and Eigenvalue Problems (LAPACK))
    - f11 (Large Scale Linear Systems)
    - f16 (NAG Interface to BLAS)
    - g01 (Simple Calculations on Statistical Data)
    - g02 (Correlation and Regression Analysis)
    - g03 (Multivariate Methods)
      - g03 Introduction
      - g03aac (nag_mv_prin_comp)
      - g03acc (nag_mv_canon_var)
      - g03adc (nag_mv_canon_corr)
      - g03bac (nag_mv_orthomax)
      - g03bcc (nag_mv_procustes)
      - g03cac (nag_mv_factor)
      - g03ccc (nag_mv_fac_score)
      - g03dac (nag_mv_discrim)
      - g03dbc (nag_mv_discrim_mahaldist)
      - g03dcc (nag_mv_discrim_group)
      - g03eac (nag_mv_distance_mat)
      - g03ecc (nag_mv_hierar_cluster_analysis)
      - g03efc (nag_mv_kmeans_cluster_analysis)
      - g03ehc (nag_mv_dendrogram)
      - g03ejc (nag_mv_cluster_indicator)
      - g03fac (nag_mv_prin_coord_analysis)
      - g03fcc (nag_mv_ordinal_multidimscale)
      - g03zac (nag_mv_z_scores)
    - g04 (Analysis of Variance)
    - g05 (Random Number Generators)
    - g07 (Univariate Estimation)
    - g08 (Nonparametric Statistics)
    - g10 (Smoothing in Statistics)
    - g11 (Contingency Table Analysis)
    - g12 (Survival Analysis)
    - g13 (Time Series Analysis)
    - h (Operations Research)
    - m01 (Sorting)
    - s (Approximations of Special Functions)
    - x01 (Mathematical Constants)
    - x02 (Machine Constants)
    - x04 (Input-Output Utilities)
  - Getting Started
  - Example Worksheet
エラーメッセージガイド
マニュアル
数学アプリ

NAG[g03eac] NAG[nag_mv_distance_mat] - Compute distance (dissimilarity) matrix

Calling Sequence

g03eac(update, dist, scale, x, isx, s, d, 'n'=n, 'm'=m, 'tdx'=tdx, 'fail'=fail)

nag_mv_distance_mat(. . .)

Parameters

update - String;

On entry: indicates whether or not an existing matrix is to be updated.

The matrix is updated and distances are added to .

The matrix is initialized to zero before the distances are added to .

Constraint: "Nag_MatUp" or "Nag_NoMatUp". .

dist - String;

On entry: indicates which type of distances are computed.

Absolute distances.

Euclidean distances.

Euclidean squared distances.

Constraint: "Nag_DistAbs", "Nag_DistEuclid" or "Nag_DistSquared". .

scale - String;

On entry: indicates the standardization of the variables to be used.

Standard deviation.

Range.

Standardizations given in array .

Unscaled.

Constraint: "Nag_VarScaleStd", "Nag_VarScaleRange", "Nag_VarScaleUser" or "Nag_NoVarScale". .

x - Matrix(1..n, 1..tdx, datatype=float[8], order=C_order);

On entry: must contain the value of the th variable for the th object, for ; .

isx - Vector(1..m, datatype=integer[kernelopts('wordsize')/8]);

On entry: indicates whether or not the th variable in x is to be included in the distance computations.

If the th variable is included, for ; otherwise it is not referenced.

Constraint: for at least one , , for . .

s - Vector(1..m, datatype=float[8]);

On entry: if and then must contain the scaling for variable , for .

Constraint: if and , , for . .

On exit: if and then contains the standard deviation of the variable in the th column of x.

If and then contains the range of the variable in the th column of x.

If and then and if then s is unchanged.

d - Vector(1.., datatype=float[8]);

Note: the dimension, dim, of the array d must be at least .

On entry: if then d must contain the strictly lower triangle of the distance matrix to be updated. must be stored packed by rows, i.e., , must contain .

Constraint: if , , for . .

On exit: the strictly lower triangle of the distance matrix stored packed by rows, i.e., is contained in , .

'n'=n - integer; (optional)

Default value: the first dimension of the array x.

On entry: the number of observations, .

Constraint: . .

'm'=m - integer; (optional)

Default value: the first dimension of the arrays isx, s and the second dimension of the arrays isx, sthe array x.

On entry: the total number of variables in array x.

Constraint: . .

'tdx'=tdx - integer; (optional)

On entry: the second dimension of the array x as declared in the function from which nag_mv_distance_mat (g03eac) is called.

Constraint: . .

'fail'=fail - table; (optional)

The NAG error argument, see the documentation for NagError.

Description

	Purpose
	nag_mv_distance_mat (g03eac) computes a distance (dissimilarity) matrix.

Description

Given objects, a distance or dissimilarity matrix, is a symmetric matrix with zero diagonal elements such that the th element represents how far apart or how dissimilar the th and th objects are.

Let be an by data matrix of observations of variables on objects, then the distance between object and object , , can be defined as:

$d[jk]={(∑),D,(x[ji]/s[i],,,x[ki]/s[i])}^alpha$

where and are the th and th elements of , is a standardization for the th variable and is a suitable function. Three functions are provided in nag_mv_distance_mat (g03eac):

a. Euclidean distance: and .

b. Euclidean squared distance: and .

c. Absolute distance (city block metric): and .

Three standardizations are available:

Standard deviation:

Range:

User supplied values of .

In addition to the above distances there are a large number of other dissimilarity measures, particularly for dichotomous variables (see Krzanowski (1990) and Everitt (1974)). For the dichotomous case these measures are simple to compute and can, if suitable scaling is used, be combined with the distances computed by nag_mv_distance_mat (g03eac) using the updating option.

Dissimilarity measures for variables can be based on the correlation coefficient for continuous variables and contingency table statistics for dichotomous data, see the g02 Chapter Introduction and the g11 Chapter Introduction respectively.

nag_mv_distance_mat (g03eac) returns the strictly lower triangle of the distance matrix.

Error Indicators and Warnings

"NE_BAD_PARAM"

On entry, argument dist had an illegal value.

"NE_IDEN_ELEM_COND"

On entry, or , and , for , for some with .

"NE_INT_ARG_LE"

On entry, m must not be less than or equal to 0: .

"NE_INT_ARG_LT"

On entry, n must not be less than 2: .

"NE_INTARR"

On entry, . Constraint: , for at least one .

"NE_INTERNAL_ERROR"

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please consult NAG for assistance.

"NE_REALARR"

On entry, . Constraint: , when .

	Accuracy
	The computations are believed to be stable.

	Further Comments
	g03ecc (nag_mv_hierar_cluster_analysis) can be used to perform cluster analysis on the computed distance matrix.

Examples

update := "Nag_NoMatUp":
dist := "Nag_DistSquared":
scale := "Nag_NoVarScale":
n := 5:
m := 3:
tdx := 3:
x := Matrix([[1, 1, 1], [2, 1, 2], [3, 6, 3], [4, 8, 2], [5, 8, 0]], datatype=float[8], order='C_order'):
isx := Vector([0, 1, 1], datatype=integer[kernelopts('wordsize')/8]):
s := Vector([1, 1, 1], datatype=float[8]):
d := Vector([0, 0, 0, 0, 0, 0, 0, 0, 0, 0], datatype=float[8]):
NAG:-g03eac(update, dist, scale, x, isx, s, d, 'n' = n, 'm' = m, 'tdx' = tdx):

	See Also
	Everitt B S (1974) Cluster Analysis Heinemann Krzanowski W J (1990) Principles of Multivariate Analysis Oxford University Press g03 Chapter Introduction. NAG Toolbox Overview. NAG Web Site.