[WIP] Implement SST-based change-point detector

[myui]

This PR is based on a pending PR by @takuti that is sent before Hivemall entered Apache Incubator.

See JIRA for tracking the status of this issue.

---

Sample table

time	x
1	182.478
2	176.231
3	183.917
4	177.798
5	165.469
...	...

(14398 points from twitter data)

Usage

create temporary function sst as 'hivemall.anomaly.SingularSpectrumTransformUDF';

SELECT
  time,
  -- x is double or array<double>
  -- sst(x) AS res
  sst(x, "-th 0.005") AS res
FROM
  twitter_timeseries
ORDER BY time ASC
;

Results

7551    {"changepoint_score":0.00453049288071683,"is_changepoint":false}
7552    {"changepoint_score":0.004711244102524104,"is_changepoint":false}
7553    {"changepoint_score":0.004814871928978115,"is_changepoint":false}
7554    {"changepoint_score":0.004968089640799422,"is_changepoint":false}
7555    {"changepoint_score":0.005709056330104878,"is_changepoint":true}
7556    {"changepoint_score":0.0044279766655132,"is_changepoint":false}
7557    {"changepoint_score":0.0034694956722586268,"is_changepoint":false}
7558    {"changepoint_score":0.002549056569322694,"is_changepoint":false}
7559    {"changepoint_score":0.0017395109108403473,"is_changepoint":false}
7560    {"changepoint_score":0.0010629833145070489,"is_changepoint":false}

On the naive SVD-based implementation, elapsed time was about 20 sec. for the 14398 samples (vs. 10 sec on ChangeFinder)

Observations

The change-point scores are much more stable compared to ChangeFinder, and change-point scores are always in [0, 1]. However, since the scores are quite noisy, too many change-points are detected. Smoothing scores like ChangeFinder is practically important.

In terms of running time, the naive SVD-based implementation is clearly inefficient. So, the Lanczos-based efficient variant should be supported.

[myui]

@takuti Could you provide a markdown documentation docs/gitbook/anomaly/sst.md for user guide?

cd docs/gitbook; gitbook serve to check a user guide on a local machine.

[myui]

@takuti Could you review my changes?
e867b45

Applied refactoring based on my review comments.

[myui]

@maropu @amaya382

Support for sst UDF in Hivemall Spark module is very welcome.

[coveralls]

Coverage increased (+0.4%) to 35.951% when pulling c4de063 on myui:JIRA-22/pr-356 into 9422977 on apache:master.

[maropu]

@myui okay, I'll do.

[myui]

@maropu Thanks. anomaly/changefinder is another feature to add in v0.5.
myui/hivemall#333

The interface/functionality is similar to sst.

[takuti]

@myui Sorry for my late response to your review, and thanks for your backup. I move on to reviewing your modifications and gitbook documentation from now.

[coveralls]

Coverage increased (+0.4%) to 35.951% when pulling 0fd64e6 on myui:JIRA-22/pr-356 into 9422977 on apache:master.

[myui]

@takuti Merged this PR. When you write markdown documents, please send a PR.

Thanks.