# Pattern Recognition of Gene Expression with Singular Spectrum Analysis

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Singular Spectrum Analysis (SSA)

#### 2.1. LS and MV Estimators

#### 2.2. LS Estimate of $\mathbf{S}$

#### 2.3. MV Estimate of $\mathbf{S}$

#### 2.4. Weight Matrix **W**

## 3. Empirical Results

#### 3.1. Simulated Series

Parameter | Original Value | Average | S.D | Ratio | ||
---|---|---|---|---|---|---|

before | after | before | after | |||

A | 200 | 204.2 | 202.6 | 4.19 | 2.64 | $\frac{2.64}{4.19}=0.63$ |

λ | 20 | 19.57 | 19.76 | 0.41 | 0.26 | $\frac{0.26}{0.41}=0.62$ |

**Figure 2.**Distribution of the estimated parameters of A and λ for noisy Bcd and noise-reduced Bcd (thick line).

**X**, 50 eigentriples were obtained, ordered by their contribution (share) in the decomposition stage. We shall say that the series ${Y}_{N}$ is not complex if ${Y}_{N}$ is well approximated by a series with small rank d. For example, series ${y}_{i}={e}^{\alpha i}$ (i = 1, ... , N) has rank 1. For all $2\le L\le N-1$, ${y}_{i}=b{y}_{i-1}$ where $b={e}^{\alpha}$. It should be noted that the number of eigentriples selected as corresponding to the series ${S}_{N}$ has to be at least d. For example, if ${y}_{i}={e}^{\alpha}+{\u03f5}_{i}$ then the window length L should be at least 2 and the first eigentriple is enough for reconstructing the original series if $\left|\right|{S}_{N}\left|\right|\gg \left|\right|{E}_{N}\left|\right|$. Accordingly, the first eigentriple is selected for filtering andtrend extraction.

Simulation Run | RMSE | RRMSE ($\frac{\mathit{SSA}}{\mathit{SDD}}$) | |
---|---|---|---|

SSA | SDD | ||

1 | 2.72 | 4.87 | 0.55 |

2 | 2.71 | 4.83 | 0.56 |

3 | 2.69 | 3.98 | 0.54 |

4 | 2.72 | 4.68 | 0.58 |

5 | 2.73 | 4.96 | 0.54 |

#### 3.2. The Bicode Data

#### 3.2.1. Data Description

#### 3.2.2. The Results

Time Class | w-Correlation | Time Class | w-Correlation |
---|---|---|---|

10 | 0.008 | 14(3) | 0.001 |

11 | 0.005 | 14(4) | 0.002 |

12 | 0.007 | 14(5) | 0.001 |

13 | 0.003 | 14(6) | 0.001 |

14(1) | 0.001 | 14(7) | 0.001 |

14(2) | 0.001 | 14(8) | 0.001 |

**Figure 3.**Temporal dynamics of Bcd expression, cleavage cycles 10 to 13. Red and green lines show the trend extracted by SSA

_{MV}and SDD, respectively.

**Figure 4.**Temporal dynamics of Bcd expression, cleavage cycles 14. Red and green lines show the trend extracted by SSA

_{MV}and SDD, respectively.

## 4. Conclusions

## Conflicts of Interest

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**MDPI and ACS Style**

Hassani, H.; Ghodsi, Z.
Pattern Recognition of Gene Expression with Singular Spectrum Analysis. *Med. Sci.* **2014**, *2*, 127-139.
https://doi.org/10.3390/medsci2030127

**AMA Style**

Hassani H, Ghodsi Z.
Pattern Recognition of Gene Expression with Singular Spectrum Analysis. *Medical Sciences*. 2014; 2(3):127-139.
https://doi.org/10.3390/medsci2030127

**Chicago/Turabian Style**

Hassani, Hossein, and Zara Ghodsi.
2014. "Pattern Recognition of Gene Expression with Singular Spectrum Analysis" *Medical Sciences* 2, no. 3: 127-139.
https://doi.org/10.3390/medsci2030127