P-values ​​in pvclust and hclust results

Question

I am running some cluster analysis and I am trying to figure out two main things:

1) What is the best way to interpret the results of p-values ​​in pvclust (what is the zero that they set?)

2) How to translate these results in hclust

I am using a dataset mtcarsas an example ...

First use the function pvclust(using Euclidean distance and full coupling):

d.pv <- pvclust(t(mtcars), method = "euclidean", 
            method.hclust = "complete", nboot = 10)

Then I create my dendrogram, and for red boxes put around significant clusters (alpha = 0.95)

plot(d.pv)
pvrect(d.pv, alpha = 0.95)

I get this figure:

I can also trigger important observations:

pvpick(team.clus.pv, alpha = 0.95)

But what is the significance of these results? We see two clusters in the dendrogram, is it a significant discovery (p = 0.02) that these two clusters are different? It's simple?

/ , , hclust , , 3 ?

d <- dist(mtcars, method = "euclidean")
hc <- hclust(d, method = "complete")
plot(hc)
rect.hclust(hc, k = 3, border = "red")

:

3 , pvclust, 3 ? , , , pvclust? ?

, pvclust, , , ( hclust), p-. ?

Answer 1

, Cross Validated, ?

, , pvclust - , . , , pvclust .
, , .

NB: mtcars . ( ) .

pvclust

pvclust , node ( - node) print:

• - Bootstrap Probability * 100 (BP)
• - Approximately Unbiased p-value * 100 (AU) BP

(BP)

BP . pvclust - - ( , ), . nboot * length(r) (length(r) = 10 ), , .

BP = 0,31, , 9 (Maserati Bora, Chrysler Imperial,..., Pontia Firebird) , 31 100 .
, ( ?), 31% . NB: . - , - .

, BP node, . , middel, hclust ( 7 : Homet 4 drive,..., AMC Javelin), BP = 0,39, , .

pvclust ()?

, . , , , , . / , , /. pvclust (), (). , hclust .

, pvclust, , . . / ( ), // - , , . , , .

(= ) x species (= variables). . , , ... , .

p "(AU)

AU , BP, . , , ... , , , BP , , , , , , , ( , , ).

BP . , Paradis (2011) , BP , . , , - . Efron . (Efron et al., 1996) , , , BP . p- " " " ". Suzuki Shimodaira , pvclust AU.

, . 11 , 11 nboot ( = 1000, nboot = 10). 1000 * 10 ( ), 5, 6, 7, 8, 9, 11, 12, 13, 14 15. r , ( = 11) ( 5 15). pvclust: Bootstrap (r = 0.45)... Done. (.. = 0.45*11 = 5).

Efron B. et al. (1996) , Proc. Natl Acad. Sci. 93: 13429-13434

Paradis, E. (2011) R, 1- . Springer.

Shimodaira H. (2004) ​​ , Ann. . 32: 2616-2641

Suzuki, R., Shimodaira, H., (2006) Pvclust: R . 22: 1540-1542