Fix bug in change point; update document

Author: joseph-hellerstein

docs/changepoint_detector.md

@@ -63,8 +63,8 @@ The inputs to the algorithm are:
 
 The algorithm proceeds as follows.
 
-1. Calculate the evaluation sum for minimal partitions for each $n \in S$, where $n$ is the first index in the second partition.
-   1. $y^{\prime}_n = y_n - y_{f_S}$
+1. For $n \in [f_S, l_S]$, calculate the signal for the partition, $A_{S_{n,1}} + A_{S_{n,2}}$.
+   1. $y^{\prime}_n = y_n - y_{f_S-1}$
    2. $z^{\prime}_n = z_n - y_N + y_{l_S}$
-   3. $v_n = \frac{y_{n-1}^{\prime}y^{\prime}_{n-1}}{n} + \frac{z_n^{\prime}z_n^{\prime} }{(|S|-n)}$
-2. $n^{\star} = argmax_n v_n$
+   3. $s_n = \frac{y_{n-1}^{\prime}y^{\prime}_{n-1}}{n} + \frac{z_n^{\prime}z_n^{\prime} }{(N-n)}$
+2. Find the change point: $n^{\star} = argmax_n s_n$

src/piecewise_system_discovery.py

@@ -87,7 +87,7 @@ def _computeChangePointSignalDifference(self, timecourse_df: pd.DataFrame,
         diff_arr = norm_jacobian_arr[1:] - norm_jacobian_arr[:-1]
         raw_signal_arr = np.linalg.norm(
                 diff_arr.reshape(diff_arr.shape[0], -1), axis=1) / (num_species ** 2)
-        return raw_signal_arr
+        return np.sqrt(raw_signal_arr)
         #split_time_arr = timecourse_df.index.to_numpy(dtype=float)[1:]
         #return self._gaussianSmooth(split_time_arr, raw_signal_arr, self.fit_kernel_bandwidth)
 
@@ -108,7 +108,7 @@ def _computeChangePointSignalMedian(self, timecourse_df: pd.DataFrame,
                 for j in norm_jacobian_arr])/(num_species ** 2)
         #split_time_arr = timecourse_df.index.to_numpy(dtype=float)
         #return self._gaussianSmooth(split_time_arr, raw_signal_arr, self.fit_kernel_bandwidth)
-        return raw_signal_arr
+        return np.sqrt(raw_signal_arr[1:])
 
 
     def _detectChangePoints(self, signal_arr: np.ndarray, num_point: int) -> List[int]: