Duong Tuan Anh

An Improvement of PAA for Dimensionality Reduction in Large Time Series Databases

Many dimensionality reduction techniques have been proposed for effective representation of time series data. Piecewise Aggregate Approximation (PAA) is one of the most popular methods for time series dimensionality reduction. While PAA approach allows a very good dimensionality reduction, PAA minimizes dimensionality by the mean values of equal sized frames. This mean value based representation may cause a high possibility to miss some important patterns in some time series datasets. In this work, we propose a new approach based on PAA, which we call Piecewise Linear Aggregate Approximation (PLAA). PLAA is the combination of a mean-based and a slope-based dimensionality reduction. We show that PLAA can improve representation preciseness through a better tightness of lower bound in comparison to PAA.

Combining SAX and Piecewise Linear Approximation to Improve Similarity Search on Financial Time Series

Efficient and accurate similarity searching on a large time series data set is an important but non- trivial problem. In this work, we propose a new approach to improve the quality of similarity search on time series data by combining symbolic aggregate approximation (SAX) and piecewise linear approximation. The approach consists of three steps: transforming real valued time series sequences to symbolic strings via SAX, pattern matching on the symbolic strings and a post-processing via Piecewise Linear Approximation.

Time Series Discord Discovery Based on iSAX Symbolic Representation

Among several algorithms have been proposed to solve the problem of time series discord discovery, HOT SAX is one of the widely used algorithms. In this work, we employ state-of-the-art iSAX representation in time series discord discovery. We propose a new time series discord discovery algorithm, called HOTiSAX, by employing iSAX rather than SAX representation in discord discovery algorithm. The incorporation requires two new auxiliary functions to handle approximate non-self match search and exact non-self match search in the discord discovery algorithm. Besides, we devise a new heuristic to offer a better ordering for examining subsequences in the outer loop of HOTiSAX algorithm. We evaluate our algorithm with a set of experiments. Experimental results show that the new algorithm HOTiSAX outperforms the previous HOT SAX.

An efficient method for motif and anomaly detection in time series based on clustering

Motifs and anomalies are two important representative patterns in a time series. Existing approaches usually handle motif discovery and anomaly detection in time series separately. In this paper, we propose a new efficient clustering-based method for discovering motif and detecting anomaly at the same time in large time series data. Our method first extracts motif/anomaly candidates from a time series by using significant extreme points and then clusters the candidates by using BIRCH algorithm. The proposed method computes anomaly scores for all sub-clusters and discovers the top motif based on the sub-cluster with the smallest anomaly score and detects the top anomaly based on the sub-cluster with the largest anomaly score. Experimental results on several benchmark datasets show that our proposed method can discover precise motif and anomaly with high time efficiency on large time series data.

Motif-based method for initialization the k -means clustering for time series data

Time series clustering by k -Means algorithm still has to overcome the dilemma of choosing the initial cluster centers. In this paper, we present a new method for initializing the k -Means clustering algorithm of time series data. Our initialization method hinges on the use of time series motif information detected by a previous task in choosing k time series in the database to be the seeds. Experimental results show that our proposed clustering approach performs better than ordinary k -Means in terms of clustering quality, robustness and running time.

An Improvement of PIP for Time Series Dimensionality Reduction and Its Index Structure

In this paper, we introduce a new time series dimensionality reduction method, IPIP. This method takes full advantages of PIP (Perceptually Important Points) method, proposed by Chung et al., with some improvements in order that the new method can theoretically satisfy the lower bounding condition for time series dimensionality reduction methods. Furthermore, we can make IPIP index able by showing that a time series compressed by IPIP can be indexed with the support of a multidimensional index structure based on Skyline index. Our experiments show that our IPIP method with its appropriate index structure can perform better than to some previous schemes, namely PAA based on traditional R*- tree.

Generating complete university course timetables by using local search methods

The course timetabling problem of large-scale size in realistic applications is considered very hard and cannot be solved by exact methods. In this paper, we present a solution method for this timetabling problem using local search methods. The solution method consists of two phases: the first phase to provide an initial solution that satisfies all hard constraints and the second phase using a local repair method with tabu mechanism to produce high quality solution, taking the soft constraints into account. We perform preliminary experiments of the method on real data set and the results are quite promising.

Similarity search for numerous patterns over multiple time series streams under dynamic time warping which supports data normalization

A huge challenge in nowadays’ data mining is similarity search in streaming time series under Dynamic Time Warping (DTW). In the similarity search, data normalization is a must to obtain accurate results. However, data normalization on the fly and the DTW calculation cost a great deal of computational time and memory space. In the paper, we present two methods, SUCR-DTW and ESUCR-DTW, which conduct similarity search for numerous prespecified patterns over multiple time-series streams under DTW supporting data normalization. These two methods utilize a combination of techniques to mitigate the aforementioned costs. The efficient methods inherit the cascading lower bounds introduced in UCR-DTW, a state-of-the-art method of similarity search in the static time series, to admissibly prune off unpromising subsequences. To be adaptive in the streaming setting, SUCR-DTW performs incremental updates on the envelopes of new-coming time-series subsequences and incremental data normalization on time-series data. However, like UCR-DTW, SUCR-DTW retrieves only similar subsequences that have the same length as the patterns. ESUCR-DTW, an extension of SUCR-DTW, can find similar subsequences whose lengths are different from those of the patterns. Furthermore, our proposed methods exploit multi-threading to have a fast response to high-speed time-series streams. The experimental results show that SUCR-DTW obtains the same precision as UCR-DTW and has lower wall clock time. Besides, the experimental results of SUCR-DTW and ESUCR-DTW reveal that the extended method has higher accuracy in spite of longer wall clock time. Also, the paper evaluates the influence of incremental z-score normalization and incremental min–max normalization on the obtained results.

Efficient Subsequence Join Over Time Series Under Dynamic Time Warping

Joining two time series in their similar subsequences of arbitrary length provides useful information about the synchronization of the time series. In this work, we present an efficient method to subsequence join over time series based on segmentation and Dynamic Time Warping (DTW) measure. Our method consists of two steps: time series segmentation which employs important extreme points and subsequence matching which is a nested loop using sliding window and DTW measure to find all the matching subsequences in the two time series. Experimental results on ten benchmark datasets demonstrate the effectiveness and efficiency of our proposed method and also show that the method can approximately guarantee the commutative property of this join operation.

From Cluster-Based Outlier Detection to Time Series Discord Discovery

Anomalous patterns or discords are just the kind of outliers in time series. In this paper, we present a new approach for time series discord discovery which is based on cluster-based outlier detection. In this approach, first, subsequence candidates are extracted from the time series using a segmentation method, then these candidates are transformed into the same length and are input for an appropriate clustering algorithm, and finally, we identify discords by using a measure suggested in the cluster-based outlier detection method given by He et al. 2003. The experimental results show that our approach is much more efficient than the HOTSAX algorithm in detecting time series discords while the anomalous patterns discovered by the two methods perfectly match with each other.