By using 1.81 as the sensitivity threshold, we can only find -1.40 as outlier. How about +1.01? Its IIR is 1.10, which means to be detected at K=0.29. The next larger value of IIR is at 0.39, whose IIR is 0.29, and corresponding K is 0.75, which is far away from 0.29 and in a quite different "sense" level. The nearer K is to 0, the more sensitive the system is. With different sensitivity, we have different knowledge. IIR algorithm is a consistent method. About what on earth outlier is, works [8, 27] by Hsiao et al. may be referred.

Above algorithm solves the problem of two classes, how about more classes? Here we give an example to explain the application of Expanding Algorithm to multiple classes. The Ruspini data set consists of 75 points (Fig. 2) in four groups, which is 

![0_image_0.png](0_image_0.png)

popular for illustrating clustering techniques [22]. Clustering is one of the classic problems in machine learning. A popular method is k-means clustering [19, 20]. Although its simplicity and speed are very appealing in practice, it offers no accuracy guarantee. Furthermore exactly solving the problem is NP-hard [21]. Like k-means, most algorithms use center to represent a cluster, each element is classified according to the distance between it and its closest center. Real case is not always so, absolute center is not necessary (it doesn"t mean that center is useless). Based on this, a new method is presented to cluster Ruspini data. 

Given Ruspini data sets D {d1, d2, …, d75} with each point as a cell.

Oscillator Algorithm:
1. Calculate distances between any two points di and dj. 2. To any point di, arrange its distance series (with others) in a ascending order.

3. Calculate series of any i by Expanding Algorithm (Safest point is the first one and at least including three points for more than two classes exist) and get 75 clustering sets.

4. Random choose one point as a seed with firing intensity 1 (others 0). 5. Any partner (clustering member) of the firing cell can receive its stimulus thus begin to fire with same intensity, and others receive an identical negative inputs.

6. Repeat step 5 till all cells keep same or are full charged (include negative charged). 7. To all cells with positive firing, cluster them to one.