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from PIL import Image,ImageDraw
def readfile(filename):
lines=[line for line in file(filename)]
# First line is the column titles
colnames=lines[0].strip().split('\t')[1:]
rownames=[]
data=[]
for line in lines[1:]:
p=line.strip().split('\t')
# First column in each row is the rowname
rownames.append(p[0])
# The data for this row is the remainder of the row
data.append([float(x) for x in p[1:]])
return rownames,colnames,data
from math import sqrt
def pearson(v1,v2):
# Simple sums
sum1=sum(v1)
sum2=sum(v2)
# Sums of the squares
sum1Sq=sum([pow(v,2) for v in v1])
sum2Sq=sum([pow(v,2) for v in v2])
# Sum of the products
pSum=sum([v1[i]*v2[i] for i in range(len(v1))])
# Calculate r (Pearson score)
num=pSum-(sum1*sum2/len(v1))
den=sqrt((sum1Sq-pow(sum1,2)/len(v1))*(sum2Sq-pow(sum2,2)/len(v1)))
if den==0: return 0
return 1.0-num/den
class bicluster:
def __init__(self,vec,left=None,right=None,distance=0.0,id=None):
self.left=left
self.right=right
self.vec=vec
self.id=id
self.distance=distance
def hcluster(rows,distance=pearson):
distances={}
currentclustid=-1
# Clusters are initially just the rows
clust=[bicluster(rows[i],id=i) for i in range(len(rows))]
while len(clust)>1:
lowestpair=(0,1)
closest=distance(clust[0].vec,clust[1].vec)
# loop through every pair looking for the smallest distance
for i in range(len(clust)):
for j in range(i+1,len(clust)):
# distances is the cache of distance calculations
if (clust[i].id,clust[j].id) not in distances:
distances[(clust[i].id,clust[j].id)]=distance(clust[i].vec,clust[j].vec)
d=distances[(clust[i].id,clust[j].id)]
if d<closest:
closest=d
lowestpair=(i,j)
# calculate the average of the two clusters
mergevec=[
(clust[lowestpair[0]].vec[i]+clust[lowestpair[1]].vec[i])/2.0
for i in range(len(clust[0].vec))]
# create the new cluster
newcluster=bicluster(mergevec,left=clust[lowestpair[0]],
right=clust[lowestpair[1]],
distance=closest,id=currentclustid)
# cluster ids that weren't in the original set are negative
currentclustid-=1
del clust[lowestpair[1]]
del clust[lowestpair[0]]
clust.append(newcluster)
return clust[0]
def printclust(clust,labels=None,n=0):
# indent to make a hierarchy layout
for i in range(n): print ' ',
if clust.id<0:
# negative id means that this is branch
print '-'
else:
# positive id means that this is an endpoint
if labels==None: print clust.id
else: print labels[clust.id]
# now print the right and left branches
if clust.left!=None: printclust(clust.left,labels=labels,n=n+1)
if clust.right!=None: printclust(clust.right,labels=labels,n=n+1)
def getheight(clust):
# Is this an endpoint? Then the height is just 1
if clust.left==None and clust.right==None: return 1
# Otherwise the height is the same of the heights of
# each branch
return getheight(clust.left)+getheight(clust.right)
def getdepth(clust):
# The distance of an endpoint is 0.0
if clust.left==None and clust.right==None: return 0
# The distance of a branch is the greater of its two sides
# plus its own distance
return max(getdepth(clust.left),getdepth(clust.right))+clust.distance
def drawdendrogram(clust,labels,jpeg='clusters.jpg'):
# height and width
h=getheight(clust)*20
w=1200
depth=getdepth(clust)
# width is fixed, so scale distances accordingly
scaling=float(w-150)/depth
# Create a new image with a white background
img=Image.new('RGB',(w,h),(255,255,255))
draw=ImageDraw.Draw(img)
draw.line((0,h/2,10,h/2),fill=(255,0,0))
# Draw the first node
drawnode(draw,clust,10,(h/2),scaling,labels)
img.save(jpeg,'JPEG')
def drawnode(draw,clust,x,y,scaling,labels):
if clust.id<0:
h1=getheight(clust.left)*20
h2=getheight(clust.right)*20
top=y-(h1+h2)/2
bottom=y+(h1+h2)/2
# Line length
ll=clust.distance*scaling
# Vertical line from this cluster to children
draw.line((x,top+h1/2,x,bottom-h2/2),fill=(255,0,0))
# Horizontal line to left item
draw.line((x,top+h1/2,x+ll,top+h1/2),fill=(255,0,0))
# Horizontal line to right item
draw.line((x,bottom-h2/2,x+ll,bottom-h2/2),fill=(255,0,0))
# Call the function to draw the left and right nodes
drawnode(draw,clust.left,x+ll,top+h1/2,scaling,labels)
drawnode(draw,clust.right,x+ll,bottom-h2/2,scaling,labels)
else:
# If this is an endpoint, draw the item label
draw.text((x+5,y-7),labels[clust.id],(0,0,0))
def rotatematrix(data):
newdata=[]
for i in range(len(data[0])):
newrow=[data[j][i] for j in range(len(data))]
newdata.append(newrow)
return newdata
import random
def kcluster(rows,distance=pearson,k=4):
# Determine the minimum and maximum values for each point
ranges=[(min([row[i] for row in rows]),max([row[i] for row in rows]))
for i in range(len(rows[0]))]
# Create k randomly placed centroids
#clusters=[[random.random()*(ranges[i][1]-ranges[i][0])+ranges[i][0]
#for i in range(len(rows[0]))] for j in range(k)]
clusters = [rows[int(random.random()*len(rows))] for i in range(k)]
lastmatches=None
for t in range(100):
print 'Iteration %d' % t
bestmatches=[[] for i in range(k)]
# Find which centroid is the closest for each row
for j in range(len(rows)):
row=rows[j]
bestmatch=0
for i in range(k):
d=distance(clusters[i],row)
if d<distance(clusters[bestmatch],row): bestmatch=i
bestmatches[bestmatch].append(j)
# If the results are the same as last time, this is complete
if bestmatches==lastmatches: break
lastmatches=bestmatches
# Move the centroids to the average of their members
for i in range(k):
avgs=[0.0]*len(rows[0])
if len(bestmatches[i])>0:
for rowid in bestmatches[i]:
for m in range(len(rows[rowid])):
avgs[m]+=rows[rowid][m]
for j in range(len(avgs)):
avgs[j]/=len(bestmatches[i])
clusters[i]=avgs
return bestmatches
def tanamoto(v1,v2):
c1,c2,shr=0,0,0
for i in range(len(v1)):
if v1[i]!=0: c1+=1 # in v1
if v2[i]!=0: c2+=1 # in v2
if v1[i]!=0 and v2[i]!=0: shr+=1 # in both
return 1.0-(float(shr)/(c1+c2-shr))
def scaledown(data,distance=pearson,rate=0.01):
n=len(data)
# The real distances between every pair of items
realdist=[[distance(data[i],data[j]) for j in range(n)]
for i in range(0,n)]
# Randomly initialize the starting points of the locations in 2D
loc=[[random.random(),random.random()] for i in range(n)]
fakedist=[[0.0 for j in range(n)] for i in range(n)]
lasterror=None
for m in range(0,1000):
# Find projected distances
for i in range(n):
for j in range(n):
fakedist[i][j]=sqrt(sum([pow(loc[i][x]-loc[j][x],2)
for x in range(len(loc[i]))]))
# Move points
grad=[[0.0,0.0] for i in range(n)]
totalerror=0
for k in range(n):
for j in range(n):
if j==k: continue
# The error is percent difference between the distances
errorterm=(fakedist[j][k]-realdist[j][k])/realdist[j][k]
# Each point needs to be moved away from or towards the other
# point in proportion to how much error it has
grad[k][0]+=((loc[k][0]-loc[j][0])/fakedist[j][k])*errorterm
grad[k][1]+=((loc[k][1]-loc[j][1])/fakedist[j][k])*errorterm
# Keep track of the total error
totalerror+=abs(errorterm)
print totalerror
# If the answer got worse by moving the points, we are done
if lasterror and lasterror<totalerror: break
lasterror=totalerror
# Move each of the points by the learning rate times the gradient
for k in range(n):
loc[k][0]-=rate*grad[k][0]
loc[k][1]-=rate*grad[k][1]
return loc
def draw2d(data,labels,jpeg='mds2d.jpg'):
img=Image.new('RGB',(2000,2000),(255,255,255))
draw=ImageDraw.Draw(img)
for i in range(len(data)):
x=(data[i][0]+0.5)*1000
y=(data[i][1]+0.5)*1000
draw.text((x,y),labels[i],(0,0,0))
img.save(jpeg,'JPEG')