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data dimension was reduced, they further transformed the data into a discrete
representation and mined
k
-motifs from the transformed time series. Agrawal
et al. proposed an algorithm to capture the shapes from historical time-series
database by using a simple translation [2]. They first transformed the differ-
ence value of every two adjacent data points into a predefined category, such
as increase, steep increase, steep decrease, decrease, no-change, and zero. The
same time series may be labeled more than one category. In other words, the
intervals among these categories have overlapped a little. The transformed
symbolic series were then used for querying desired results.
Most of the above approaches, however, usually require predefined crisp
intervals for each category. It thus needs domain knowledge and depends on
applications. Udechukwu et al. thus proposed a domain-independent trend-
encoding method to mine frequent trends [13]. They transformed the difference
value between two adjacent data points into an angle, instead of the difference
value itself. The angles lay within the range
90
0
to 90
0
, and were partitioned
into 52 predefined angular categories, represented by letters. They then used
the data structure of su
x trees to find the maximally repeated patterns as
frequent trends. In this way, the effect of the domain knowledge could be
reduced. Their approach, however, had too many angular categories, which
might cause users hard to understand the meaning of the patterns easily.
As to fuzzy data mining, Hong et al. proposed several fuzzy mining al-
gorithms to mine linguistic association rules from quantitative data [6, 7, 10].
They transformed each quantitative item into a fuzzy set and used fuzzy oper-
ations to find fuzzy rules. Their approaches, however, focused on transaction
data. For time-series data, Song et al. proposed a fuzzy stochastic time series
and built a model by assuming the values are fuzzy sets [12]. Chen et al. pro-
posed a two-factor time-variant fuzzy time-series model to deal with forecast-
ing problems [4]. Au and Chan proposed a fuzzy mining approach to find fuzzy
rules for classifying time-series [1]. Watanabe exploited the Takagi-Sugeno
model to build a time-series model [14].
In this chapter, we thus propose a mining algorithm based on angles of
adjacent points in a time series to find linguistic trends. Several fuzzy sets
for angles are predefined to represent semantic concepts understandable to
human being. The a priori-like fuzzy mining algorithm is then used to generate
linguistic trends. Appropriate post-processing is also performed to remove
redundant patterns. Since the final results are represented by linguistic terms,
they will be friendlier to human than quantitative representation.
−
2 Mining Linguistic Trends for Time Series
The proposed fuzzy mining algorithm integrates the fuzzy sets, the a pri-
ori mining algorithm and the time-series concepts to find out appropriate
linguistic trends from a time series. The proposed approach first transforms
data values into angles, and then uses a sliding window to generate continuous
