Sequence pattern mining on continuous dataset

Question

I have a dataset on broadband usage and bills for a set of customers for an year. For every metric, like Upload usage, I have 12 values corresponding to each month. Below are the columns and the format.

CustomerId,Upload_Jan,Upload_Feb...Upload_Dec, Download_Jan,Download_Feb....Download_Dec, bill_Jan....bill_Dec

The values in all columns are continuous. I want to see if there are some sequences appearing in the data frequently.

1. Can we do sequential mining on continuous data set?
2. Is it mandatory to bin each column to separate bins? How to decide the number of bins?
3. What is the best way of pre processing the data set for tools like SPMF which requires transactionized data?

I looked at TraMineR package in R and wrote a few scripts, but I could not make out much from the sequences generated.

Answer 1

The established procedure is called symbolic aggregate approximation or SAX in which you first first do piecewise aggregate approximation (PAA), namely send non-overlapping mean (boxcar) windows of width $w$ over the data, and then transform the obtained values into symbols by equal-frequency-splitting the resulting data distribution into $k$ letters of the alphabet.

How to determine appropriate $w$ and $k$? They are a tradeoff between dimensionality reduction and information loss. One way to adapt $w$ is to look at window' data points variance; if the variance is too large, reduce the window size, and vice versa. Another information-theoretic is MDL as explained in this question.

Since you only have 12 values in a series, the windowing step may not be necessary.

Alternatively, you could try reshaping the data into three series:

$$Dd_1^{(c_1)}\dots{}d_{12}^{(c_1)}Dd_1^{(c_2)}\dots{}d_{12}^{(c_2)}D\dots$$

$$Uu_1^{(c_1)}\dots{}u_{12}^{(c_1)}Uu_1^{(c_2)}\dots{}u_{12}^{(c_2)}U\dots$$

$$Bb_1^{(c_1)}\dots{}b_{12}^{(c_1)}Bb_1^{(c_2)}\dots{}b_{12}^{(c_2)}B\dots$$

where D, U, and B are string literals (used as start markers) and $d_m^{(c_i)}$, $u_m^{(c_i)}$, and $b_m^{(c_i)}$ are the values of download, upload and billed, for customer $c_i$ in month $m$. Then you could use one of the frequent subsequence mining algorithms on those three sequences (separately) to find any prevaling patterns.