Protein sequence comparison remains a challenging work for the researchers owing to the computational complexity due to the presence of 20 amino acids compared with only four nucleotides in Genome sequences. Further, protein sequences of different species are of different lengths; it throws additional changes to the researchers to develop methods, specially alignment-free methods, to compare protein sequences. In this work, an efficient technique to compare protein sequences is developed by a graphical representation. First, the classified grouping of 20 amino acids with a cardinality of 4 based on polar class is considered to narrow down the representational range from 20 to 4. Then a unit vector technique based on a two-quadrant Cartesian system is proposed to provide a new two-dimensional graphical representation of the protein sequence. Now, two approaches are proposed to cope with the varying lengths of protein sequences from various species: one uses Dynamic Time Warping (DTW), while the other one uses a two-dimensional Fast Fourier Transform (2D FFT). Next, the effectiveness of these two techniques is analyzed using two evaluation criteria—quantitative measures based on symmetric distance (SD) and computational speed. An analysis is performed on five data sets of 9 ND4, 9 ND5, 9 ND6, 12 Baculovirus, and 24 TF proteins under the two methods. It is found that the FFT-based method produces the same results as DTW but in less computational time. It is found that the result of the proposed method agrees with the known biological reference. Further, the present method produces better clustering than the existing ones.

对于研究人员来说，蛋白质序列比较仍然是一项具有挑战性的工作，因为与基因组序列中仅存在 4 个核苷酸相比，存在 20 个氨基酸，导致计算复杂性。进一步地，不同物种的蛋白质序列长度不同；它给研究人员带来了额外的改变，以开发方法，特别是免比对方法，来比较蛋白质序列。在这项工作中，通过图形表示开发了一种比较蛋白质序列的有效技术。首先，考虑基于极类对基数为4的20个氨基酸进行分类分组，将表示范围从20缩小到4。然后提出基于二象限笛卡尔系统的单位向量技术，以提供一种新的方法。蛋白质序列的二维图形表示。现在，提出了两种方法来应对不同物种的不同长度的蛋白质序列：一种使用动态时间扭曲（DTW），另一种使用二维快速傅里叶变换（2D FFT）。接下来，使用两个评估标准——基于对称距离（SD）和计算速度的定量测量来分析这两种技术的有效性。在两种方法下对 9 ND4、9 ND5、9 ND6、12 杆状病毒和 24 TF 蛋白的五个数据集进行了分析。结果发现，基于 FFT 的方法产生与 DTW 相同的结果，但计算时间更少。发现所提出的方法的结果与已知的生物学参考一致。此外，本方法产生比现有方法更好的聚类。