Programmatically finding "significant" data points

[erikcw]

Hi all,

I have a collection of ordered numerical data in a list. The numbers
when plotted on a line chart make a low-high-low-high-high-low (random)
pattern. I need an algorithm to extract the "significant" high and low
points from this data.

Here is some sample data:
data = [0.10, 0.50, 0.60, 0.40, 0.39, 0.50, 1.00, 0.80, 0.60, 1.20,
1.10, 1.30, 1.40, 1.50, 1.05, 1.20, 0.90, 0.70, 0.80, 0.40, 0.45, 0.35,
0.10]

In this data, some of the significant points include:
data[0]
data[2]
data[4]
data[6]
data[8]
data[9]
data[13]
data[14]
.....

How do I sort through this data and pull out these points of
significance?

Thanks for your help!

Erik

[Jeremy Sanders]

erikcw wrote:

I have a collection of ordered numerical data in a list. The numbers
when plotted on a line chart make a low-high-low-high-high-low (random)
pattern. I need an algorithm to extract the "significant" high and low
points from this data.

....

>
How do I sort through this data and pull out these points of
significance?

Get a book on statistics. One idea is as follows. If you expect the points
to be centred around a single value, you can calculate the median or mean
of the points, calculate their standard deviation (aka spread), and remove
points which are more than N-times the standard deviation from the median.

Jeremy

--
Jeremy Sanders
http://www.jeremysanders.net/

[Fredrik Lundh]

"erikcw" wrote:

I have a collection of ordered numerical data in a list. The numbers
when plotted on a line chart make a low-high-low-high-high-low (random)
pattern. I need an algorithm to extract the "significant" high and low
points from this data.

Here is some sample data:
data = [0.10, 0.50, 0.60, 0.40, 0.39, 0.50, 1.00, 0.80, 0.60, 1.20,
1.10, 1.30, 1.40, 1.50, 1.05, 1.20, 0.90, 0.70, 0.80, 0.40, 0.45, 0.35,
0.10]

silly solution:

for i in range(1, len(data)-1):
if data[i-1] < data[i] data[i+1] or data[i-1] data[i] < data[i+1]:
print i

(the above doesn't handle the "edges", but that's easy to fix)

</F>

[Philipp Pagel]

erikcw <er***********@gmail.comwrote:

I have a collection of ordered numerical data in a list. The numbers
when plotted on a line chart make a low-high-low-high-high-low (random)
pattern. I need an algorithm to extract the "significant" high and low
points from this data.

I am not sure, what you mean by 'ordered' in this context. As
pointed out by Jeremy, you need to find an appropriate statistical test.
The appropriateness depend on how your data is (presumably) distributed
and what exactly you are trying to test. E.g. do te data pints come from
differetn groupos of some kind? Or are you just looking for extreme
values (outliers maybe?)?

So it's more of statistical question than a python one.

cu
Philipp

--
Dr. Philipp Pagel Tel. [phone]
Dept. of Genome Oriented Bioinformatics Fax. [phone]
Technical University of Munich
http://mips.gsf.de/staff/pagel

[Peter Otten]

erikcw wrote:

Hi all,

I have a collection of ordered numerical data in a list. The numbers
when plotted on a line chart make a low-high-low-high-high-low (random)
pattern. I need an algorithm to extract the "significant" high and low
points from this data.

Here is some sample data:
data = [0.10, 0.50, 0.60, 0.40, 0.39, 0.50, 1.00, 0.80, 0.60, 1.20,
1.10, 1.30, 1.40, 1.50, 1.05, 1.20, 0.90, 0.70, 0.80, 0.40, 0.45, 0.35,
0.10]

In this data, some of the significant points include:
data[0]
data[2]
data[4]
data[6]
data[8]
data[9]
data[13]
data[14]
....

How do I sort through this data and pull out these points of
significance?

I think you are looking for "extrema":

def w3(items):
items = iter(items)
view = None, items.next(), items.next()
for item in items:
view = view[1:] + (item,)
yield view

for i, (a, b, c) in enumerate(w3(data)):
if a b < c:
print i+1, "min", b
elif a < b c:
print i+1, "max", b
else:
print i+1, "---", b

Peter

[Alan J. Salmoni]

If the order doesn't matter, you can sort the data and remove x * 0.5 *
n where x is the proportion of numbers you want. If you have too many
similar values though, this falls down. I suggest you check out
quantiles in a good statistics book.

Alan.

Peter Otten wrote:

erikcw wrote:

Hi all,

I have a collection of ordered numerical data in a list. The numbers
when plotted on a line chart make a low-high-low-high-high-low (random)
pattern. I need an algorithm to extract the "significant" high and low
points from this data.

Here is some sample data:
data = [0.10, 0.50, 0.60, 0.40, 0.39, 0.50, 1.00, 0.80, 0.60, 1.20,
1.10, 1.30, 1.40, 1.50, 1.05, 1.20, 0.90, 0.70, 0.80, 0.40, 0.45, 0.35,
0.10]

In this data, some of the significant points include:
data[0]
data[2]
data[4]
data[6]
data[8]
data[9]
data[13]
data[14]
....

How do I sort through this data and pull out these points of
significance?

I think you are looking for "extrema":

def w3(items):
items = iter(items)
view = None, items.next(), items.next()
for item in items:
view = view[1:] + (item,)
yield view

for i, (a, b, c) in enumerate(w3(data)):
if a b < c:
print i+1, "min", b
elif a < b c:
print i+1, "max", b
else:
print i+1, "---", b

Peter

[Roberto Bonvallet]

erikcw wrote:

I have a collection of ordered numerical data in a list. The numbers
when plotted on a line chart make a low-high-low-high-high-low (random)
pattern. I need an algorithm to extract the "significant" high and low
points from this data.

In calculus, you identify high and low points by looking where the
derivative changes its sign. When working with discrete samples, you can
look at the sign changes in finite differences:

>>data = [...]
diff = [data[i + 1] - data[i] for i in range(len(data))]
map(str, diff)

['0.4', '0.1', '-0.2', '-0.01', '0.11', '0.5', '-0.2', '-0.2', '0.6',
'-0.1', '0.2', '0.1', '0.1', '-0.45', '0.15', '-0.3', '-0.2', '0.1',
'-0.4', '0.05', '-0.1', '-0.25']

The high points are those where diff changes from + to -, and the low
points are those where diff changes from - to +.

HTH,
--
Roberto Bonvallet

[Ganesan Rajagopal]

>>>>Jeremy Sanders <je*******************@jeremysanders.netwrites:

>How do I sort through this data and pull out these points of
significance?

Get a book on statistics. One idea is as follows. If you expect the points
to be centred around a single value, you can calculate the median or mean
of the points, calculate their standard deviation (aka spread), and remove
points which are more than N-times the standard deviation from the median.

Standard deviation was the first thought that jumped to my mind
too. However, that's not what the OP is after. He's seems to be looking for
points when the direction changes.

Ganesan

--
Ganesan Rajagopal

[Roy Smith]

"erikcw" <er***********@gmail.comwrote:

I have a collection of ordered numerical data in a list. The numbers
when plotted on a line chart make a low-high-low-high-high-low (random)
pattern. I need an algorithm to extract the "significant" high and low
points from this data.

I think you want a control chart. A good place to start might be
http://en.wikipedia.org/wiki/Control_chart. Even if you don't actually
graph the data, understanding the math behind control charts might help you
with your analysis.

Wow. I think this is the first time I'm actually used something I learned
by sitting though those stupid Six Sigma training classes :-)

[Beliavsky]

erikcw wrote:

Hi all,

I have a collection of ordered numerical data in a list.

Called a "time series" in statistics.

The numbers
when plotted on a line chart make a low-high-low-high-high-low (random)
pattern. I need an algorithm to extract the "significant" high and low
points from this data.

Here is some sample data:
data = [0.10, 0.50, 0.60, 0.40, 0.39, 0.50, 1.00, 0.80, 0.60, 1.20,
1.10, 1.30, 1.40, 1.50, 1.05, 1.20, 0.90, 0.70, 0.80, 0.40, 0.45, 0.35,
0.10]

In this data, some of the significant points include:
data[0]
data[2]
data[4]
data[6]
data[8]
data[9]
data[13]
data[14]
....

How do I sort through this data and pull out these points of
significance?

The best place to ask about an algorithm for this is not
comp.lang.python -- maybe sci.stat.math would be better. Once you have
an algorithm, coding it in Python should not be difficult. I'd suggest
using the NumPy array rather than the native Python list, which is not
designed for crunching numbers.

[robert]

erikcw wrote:

Hi all,

I have a collection of ordered numerical data in a list. The numbers
when plotted on a line chart make a low-high-low-high-high-low (random)
pattern. I need an algorithm to extract the "significant" high and low
points from this data.

Here is some sample data:
data = [0.10, 0.50, 0.60, 0.40, 0.39, 0.50, 1.00, 0.80, 0.60, 1.20,
1.10, 1.30, 1.40, 1.50, 1.05, 1.20, 0.90, 0.70, 0.80, 0.40, 0.45, 0.35,
0.10]

In this data, some of the significant points include:
data[0]
data[2]
data[4]
data[6]
data[8]
data[9]
data[13]
data[14]
....

How do I sort through this data and pull out these points of
significance?

Its obviously a kind of time series and you are search for a "moving_max(data,t,window)>data(t)" / "moving_min(data,t,window)<data(t)": an extremum within a certain (time) window. And obviously your time window is as low as 2 or 3 or so.

Unfortunately a moving_max func is not yet in numpy and probably not achievable from other existing array functions. You have to create slow looping code.
Robert

[Paul McGuire]

"robert" <no*****@no-spam-no-spam.invalidwrote in message
news:ej**********@news.albasani.net...

erikcw wrote:

>Hi all,

I have a collection of ordered numerical data in a list. The numbers
when plotted on a line chart make a low-high-low-high-high-low (random)
pattern. I need an algorithm to extract the "significant" high and low
points from this data.

Here is some sample data:
data = [0.10, 0.50, 0.60, 0.40, 0.39, 0.50, 1.00, 0.80, 0.60, 1.20,
1.10, 1.30, 1.40, 1.50, 1.05, 1.20, 0.90, 0.70, 0.80, 0.40, 0.45, 0.35,
0.10]

In this data, some of the significant points include:
data[0]
data[2]
data[4]
data[6]
data[8]
data[9]
data[13]
data[14]
....

How do I sort through this data and pull out these points of
significance?

Using zip and map, it's easy to compute first and second derivatives of a
time series of values. The first lambda computes

[Paul McGuire]

.... dang touchy keyboard!

Here is some sample data:
data = [0.10, 0.50, 0.60, 0.40, 0.39, 0.50, 1.00, 0.80, 0.60, 1.20,
1.10, 1.30, 1.40, 1.50, 1.05, 1.20, 0.90, 0.70, 0.80, 0.40, 0.45, 0.35,
0.10]

In this data, some of the significant points include:
data[0]
data[2]
data[4]
data[6]
data[8]
data[9]
data[13]
data[14]

Using the first derivative, and looking for sign changes, finds many of the
values you marked as "significant".

-- Paul
data = [0.10, 0.50, 0.60, 0.40, 0.39, 0.50, 1.00, 0.80, 0.60, 1.20,
1.10, 1.30, 1.40, 1.50, 1.05, 1.20, 0.90, 0.70, 0.80, 0.40, 0.45, 0.35,
0.10]

delta = lambda (x1,x2) : x2-x1
dy_dx =[0]+map(delta,zip(data,data[1:]))
d2y_dx2 = [0]+map(delta,zip(dy_dx,dy_dx[1:]))

sgnChange = lambda (x1,x2) : x1*x2<0
sigs = map(sgnChange,zip(dy_dx,dy_dx[1:]))
print [i for i,v in enumerate(sigs) if v]
[2, 4, 6, 8, 9, 10, 13, 14, 15, 17, 18, 19, 20]