SAX符号化序列范例源码

SAX符号化序列范例源码 -------------------- timeseries2symbol.m: -------------------- This function takes in a time series and convert it to string(s). There are two options: 1. Convert the entire time series to ONE string 2. Use sliding windows, extract the subsequences and convert these subsequences to strings For the first option, simply enter the length of the time series as "N" ex. We have a time series of length 32 and we want to convert it to a 8-symbol string, with alphabet size 3: timeseries2symbol(data, 32, 8, 3) For the second option, enter the desired sliding window length as "N" ex. We have a time series of length 32 and we want to extract subsequences of length 16 using sliding windows, and convert the subsequences to 8-symbol strings, with alphabet size 3: timeseries2symbol(data, 16, 8, 3) Input: data is the raw time series. N is the length of sliding window (use the length of the raw time series instead if you don't want to have sliding windows) n is the number of symbols in the low dimensional approximation of the sub sequence. alphabet_size is the number of discrete symbols. 2 <= alphabet_size <= 10, although alphabet_size = 2 is a special "useless" case. Output: symbolic_data: matrix of symbolic data (no-repetition). If consecutive subsequences have the same string, then only the first occurrence is recorded, with a pointer to its location stored in "pointers" pointers: location of the first occurrences of the strings N/n must be an integer, otherwise the program will give a warning, and abort. The variable "win_size" is assigned to N/n, this is the number of data points on the raw time series that will be mapped to a single symbol, and can be imagined as the "compression rate". The symbolic data is returned in "symbolic_data", with pointers to the subsequences ---------- min_dist.m ---------- This function computes the minimum (lower-bounding) distance between two strings. The strings should have equal length. Input: str1: first string str2: second string alphabet_size: alphabet size used to construct the strings compression_ratio: original_data_len / symbolic_len Output: dist: lower-bounding distance usage: dist = min_dist(str1, str2, alphabet_size, compression_ratio) This distance measure is not the best measure to use for comparing strings, if you are NOT going to follow up with access to the original data. This is because it cannot discriminate between two strings that differ only in the ith place, by consecutive symbols. For example the min_dist between 'abba' and 'abbb' is zero. However, in practice, the min_dist function works very well for classification and clustering, even when you do not follow up with access to the original data. See [1]. --------- sax_demo: --------- This code demonstrates the first case described in timeseries2symbol.m (for the second case, see the example below). It provides a step-by-step demo of SAX (Symbolic Aggregate approXimation). Press enter for the next step. usage: [str] = sax_demo [str] = sax_demo(data) -------------- mindist_demo.m -------------- This function demonstrates that min_dist lower-bounds the true Euclidean distance. Suppose there are two time series A and B. The demo shows the euclidean distance and the mindist. >> mindist_demo sax_version_of_A = 3 4 2 1 1 3 4 2 sax_version_of_B = 1 1 3 4 3 1 1 4 euclidean_distance_A_and_B = 10.9094 ans = 5.3600 ---> This is the mindist ----------------- symbolic_visual.m ----------------- This demo presents a visual comparison between SAX and PAA and shows how SAX can represent data in finer granularity while using the same, if not less, amount of space as PAA. The input parameter [data] is optional. The default # of PAA segments is 16, and the alphabet size is 4. -------- Examples: -------- You can type this up in your matlab: Recall that there are two options for timeseries2symbol. The first option is demonstrated in sax_demo.m Now here is an example of the latter. We are going to convert time series of length 50, with a sliding window of 32, into 8 symbols, with and alphabet size of 3. >> [symbolic_data, pointers] = timeseries2symbol(long_time_series,32,8,alphabet_size) symbolic_data = 1 1 3 3 3 3 1 1 1 2 3 3 3 2 1 1 1 3 3 3 3 1 1 1 2 3 3 3 2 1 1 1 3 3 3 3 1 1 1 1 3 3 3 2 1 1 1 2 3 3 3 1 1 1 1 3 3 3 2 1 1 1 2 3 3 3 1 1 1 1 3 3 3 2 1 1 1 2 3 3 pointers = 1 2 5 6 9 10 13 14 17 18 Note that each row corresponds to a subsequence (with overlap) The SAX word at 3 and 4 were omitted, since they where the same as the word at 2, same for 7 and 8, which were the same as 6 etc (look at the pointers) It might be helpful to view the data this way >> [pointers symbolic_data ] ans = 1 1 1 3 3 3 3 1 1 2 1 2 3 3 3 2 1 1 5 1 3 3 3 3 1 1 1 6 2 3 3 3 2 1 1 1 9 3 3 3 3 1 1 1 1 10 3 3 3 2 1 1 1 2 13 3 3 3 1 1 1 1 3 14 3 3 2 1 1 1 2 3 17 3 3 1 1 1 1 3 3 18 3 2 1 1 1 2 3 3 So the first word is (1 1 3 3 3 3 1 1) , the 9th word is (3 3 3 3 1 1 1 1) , the 14 word is (3 3 2 1 1 1 2 3)