Article Contents
Article Contents

# Using distribution analysis for parameter selection in repstream

• * Corresponding author: Ross Callister
• One of the most significant challenges in data clustering is the evolution of the data distributions over time. Many clustering algorithms have been introduced to deal specifically with streaming data, but common amongst them is that they require users to set input parameters. These inform the algorithm about the criteria under which data points may be clustered together. Setting the initial parameters for a clustering algorithm is itself a non-trivial task, but the evolution of the data distribution over time could mean even optimally set parameters could become non-optimal as the stream evolves. In this paper we extend the RepStream algorithm, a combination graph and density-based clustering algorithm, in a way which allows the primary input parameter, the $K$ value, to be automatically adjusted over time. We introduce a feature called the edge distribution score which we compute for data in memory, as well as introducing an incremental method for adjusting the $K$ parameter over time based on this score. We evaluate our methods against RepStream itself, and other contemporary stream clustering algorithms, and show how our method of automatically adjusting the $K$ value over time leads to higher quality clustering output even when the initial parameters are set poorly.

Mathematics Subject Classification: Primary: 62H30.

 Citation:

• Figure 1.  An illustration of the representative and point-level sparse graphs in the RepStream algorithm

Figure 2.  The representative vertex $R_1$ and $R_2$ share a reciprocal connection at the representative level, and are also density related. The density radius of the vertices is shown as $DR_1$ and $DR_2$ respectively, which is the average distance to neighbours at the point level, multiplied by the alpha scaling factor

Figure 3.  Intra and Inter-class edges. The Edge $E_1$ is considered an inter-class edge as it connects two vertices $R_1$ and $R_2$ that belong to different ground-truth classes. Edge $E_2$ connects two vertices belonging to the same class and thus is considered an intra-class edge

Figure 4.  An illustration of relative edge lengths of nearest neighbours in the middle of a cluster versus near the edge of a cluster

Figure 5.  Different cases for the distribution of edge lengths

Figure 6.  Visualisation of the DS1 dataset

Figure 7.  Visualisation of the DS2 dataset

Figure 8.  Two dimensional representations of the 5 classes in the SynTest dataset. The main class is always present and steadily changes shape, the smaller classes appear at various points through the dataset, as shown in Figure 9

Figure 9.  The class presence of the classes in the SynTest dataset. A marker indicates that the class is present in the dataset during the given time window

Figure 10.  The evolution of the Closer dataset, showing slices of its 3 sections

Figure 11.  Comparative purity for Tree Cover dataset

Figure 12.  Comparative purity for Tree Cover dataset

Figure 13.  Comparative purity for KDD 99' Cup dataset

Figure 14.  Comparative purity for KDD 99' Cup dataset

Figure 15.  Comparative purity for DS1 dataset

Figure 16.  The $K$ value selected by our dynamic $K$ method on the DS1 dataset

Figure 17.  Comparative purity for DS2 dataset

Figure 18.  Comparative purity for SynTest dataset

Figure 19.  Comparative purity for Closer dataset

Figure 20.  Comparative purity for Tree Cover dataset

Figure 21.  Comparative purity for KDD 99' Cup dataset

Figure 22.  The $K$ value selected by our dynamic $K$ method on the KDD Dataset

Figure 23.  F-Measure comparison vs RepStream using optimal parameters on DS1 dataset

Figure 24.  F-Measure comparison vs RepStream using optimal parameters on DS2 dataset

Figure 25.  F-Measure comparison vs RepStream using optimal parameters on SynTest dataset

Figure 26.  F-Measure comparison vs RepStream using optimal parameters on Closer dataset

Figure 27.  F-Measure comparison vs RepStream using optimal parameters on Tree Cover dataset

Figure 28.  F-Measure comparison vs RepStream using optimal parameters on KDD 99' Cup dataset

Table 1.  Table showing the input parameters used for each algorithm

 Algorithm name Density Parameters Grid Granularity Reclustering Method Decay Parameter Distance Parameter Other Parameters CluStream $k$-means $\delta$ $\alpha$, $l$ Snapshot parameters SWClustering $\beta$ $k$-means $\epsilon$, $N$ Window parameters DenStream $\mu$, $\beta$ $\epsilon$ HPStream $\lambda$ $r$ $l$ Projected Dimensions D-Stream $C_m$, $C_l$, $\beta$ $len$ $\lambda$ ExCC Grid Granularity in all dimensions MR-Stream $C_H$, $C_L$, $\beta$, $\mu$ Hierarchical $\lambda$ $\epsilon$ $H$ Heirarchical limit FlockStream $\beta$, $\mu$ $\lambda$ $\epsilon$ DeBaRa $dPts$ $f$ DBStream $\alpha$, $w\_min$ $\lambda$, $t\_gap$ $r$ SNCStream $\psi$, $\beta$ $\lambda$ $\epsilon$ $K$ Graph connectivity PASCAL Evolutionary Evolutionary EDA hyper-parameters HASTREAM $minPts$ Hierarchical $\lambda$ BEStream $\Delta$, $\tau$ $\lambda$ $\xi$ $\theta$ Direction parameter ADStream $\xi$, $\epsilon$ $\lambda$ PatchWork $ratio$, $minPoints$, $minCells$ $\epsilon$ RepStream $\lambda$ $\alpha$ $K$ Graph connectivity

Table 2.  Best and Worst $K$ values for RepStream, according to $F$ score

 Dataset Best K Best $F$ score Worst K Worst $F$ score DS1 7 0.7208 18 0.2767 DS2 7 0.6371 21 0.2594 SynTest 9 0.8614 5 0.5435 Closer 9 0.7989 5 0.4345 TreeCov 29 0.6108 5 0.2978 KDD99 30 0.7898 5 0.2636

Table 3.  Comparison of our dynamic $K$ method versus RepStream with optimal and worst $K$ values

 Dataset Best F-Measure Worst F-Measure Dynamic $K$ DS1 0.7208 0.2767 0.5153 DS2 0.6371 0.2594 0.4137 SynTest 0.7989 0.5435 0.7091 Closer 0.8614 0.4345 0.8410 TreeCov 0.6108 0.2978 0.5920 KDD99 0.7898 0.2636 0.7882
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