Define clustering. Differentiate between single linkage and complete linkage method of clustering.
(b) Consider the following partitioned sample variance-covariance matrix S, obtained from a sample of size 10.$
If , then test for the independence of the sub-vectors
and
.
(Use
)
---
Clustering is a technique in multivariate statistics where objects are grouped based on similarity, so that objects within a cluster are more similar to each other than to objects in other clusters. Difference between single linkage and complete linkage methods: * Single linkage: The distance between two clusters is defined as the minimum distance between any pair of objects, one from each cluster. It tends to produce elongated clusters. * Complete linkage: The distance between two clusters is defined as the maximum distance between any pair of objects, one from each cluster. It tends to ___ ___ ____ ___ ________ _________ ____ ____ _______ _________.
______ ____ ________ ______ __________ ________ _______ ____ ____ _____ _________.
______ ____ ___ ________ ____ _______ ______ __________.
______ ____ _________ ____ _____ _______ __________ ______ __________ ____ ____ ________.
________ _________ ___ __________ _________ ____ ______ ___ ________ _________ __________.
______ _________ ____ ___ _____ ___ ______ _____ _______ _______ _____ ___.
___ __________ _______ _____ __________ __________ ____ _______ __________ _____ _______ ______.
______ __________ _________ ___ _____ __________ ___ ________ _____.
______ _____ ______ ______ _______ ____ _________ ______ ______ ____ _____.
_____ __________ ________ _________ __________ _________.
_______ _______ ____ ________ __________ __________.
_________ ________ _______ ______ ____ _________ _________ _____ __________ __________ ______ ______.
_______ ____ _______ ______ ____ ____.
_________ _________ ___ _______ ________ _________ _____ _________ __________ ______ _____ ____.
___ ____ _______ _______ ______ ______ ____ _______.
_____ _________ ______ ____ _________ _____ ___ ________ __________ ___ ______ ______.
_________ ___ ____ ___ ___ __________ __________ ____ __________.
__________ ____ ________ ____ ________ _____ ____ ________ ______ ______ ___.
_______ __________ _____ _________ ___ _______ _________.
__________ _________ _______ _________ _______ _________.
________ _____ ____ _____ ___ _________ __________ ______.
_______ ___ ___ __________ ________ ___ ________ ___ _______ ___ _______.
___ ________ ___ ______ _________.
________ ________ ______ _______ _____ ___.
___ ___ _________ __________ ________.
___ ________ _____ _________ _________ _________ _____.
___ ________ _________ ____ ____ _____.
___ ___ _______ _____ __________ ____ ______ ____ ___.
____ _____ ______ _________ ___ _____.
_______ ________ _____ _____ _______ ______ _________ ______ ___ __________.
_________ ________ ___ _________ ______ ___.
_________ ______ ______ __________ _____ ______ ____ _____ ___ ___ _________.
__________ ________ __________ ________ _____ _____ ______.
Get Full Answer on WhatsApp
Let two independent samples of size and
from trivariate normal populations have following mean vectors and variance-covariance matrices:
and
and
, respectively.
---$
$
samples are significantly different from each other at 5% level of significance or not.$
Let , where
and
.
Then find and
.
Let ,
and
be partitioned as
,
and
. Then derive the conditional distribution of
.
Obtain the square root matrix corresponding to a matrix . Also
verify that .
If with
and
. Then find the joint distribution
of X1 + 2X2, 2X1 - X2 and X3.
Define clustering. Differentiate between single linkage and complete linkage method of clustering.
(b) Consider the following partitioned sample variance-covariance matrix S, obtained from a sample of size 10.$
If , then test for the independence of the sub-vectors
and
.
(Use
)
---
State whether the following statements are True or False. Give reasons in support of your answer: 5×2=10
(a) The eigenvalues of a positive definite matrix are less than zero.
(b) is an orthogonal and idempotent matrix.
(c) A factor model postulates that a random vector is linearly dependent upon a few observable common factors.
(d) A given px1 vector is a plausible value for the mean of a multivariate normal distribution can be tested using Student's t test.
(e) In single linkage method, we find the minimum distance in the distance matrix and merge the minimum distanced clusters