Notes 1. Similarity function is used to evaluate the similar degree of point k related to the system of i and j. 

2. Offset function calculates the real distance between k and system of i and j.

3. wij is the weight of system of ij, denotes relative effective degree. 

4. Relative deviant degree combines two measurements: similarity and real distance.

By Algorithm 1, we get RDD values for problem 1 in Table 1. Points at 8, 9, 10, 11 and 12 have high values. We will present method to identify them later.

## Table 1

| Position   | 1      | 2      | 3      | 4      | 5      |
|------------|--------|--------|--------|--------|--------|
| RDD        | 0.001  | 0.025  | 0.061  | 0.018  | 0.031  |
| Position   | 6      | 7      | 8      | 9      | 10     |
| RDD        | 0.067  | 0.138  | 17.956 | 27.693 | 23.879 |
| Position   | 11     | 12     | 13     | 14     | 15     |
| RDD        | 18.482 | 14.609 | 0.021  | 0.003  | 0.005  |
| Position   | 16     | 17     | 18     | 19     |        |
| RDD        | 0.006  | 0.008  | 0.010  | 0.002  |        |

Though RDD algorithm has commons in form with robust regression, it differs from robust ones at the point that we approach from the inside structure of the pattern and stress on the whole effect, thus with more balance. Note that RDD algorithm is same as robust regression, can be possible with a highest breakdown point (50%). Now we modify our Algorithm 1 to a general form. First, we introduce definition of view V.

Definition 3: Given a time series data S, a sub-series of S is also a time series where each element of it is an element of S. We denote eS when e is a sub-series of S.

Definition 4: A view of S, Vα, is a set of sub-series of S of same length, that is Vα = { e | eS, 
|e| = }. 

## Algorithm 1': Rdd Algorithm

Input: data set S Output: RDDs of S