Using Signal Processing in Tandem With Adapted Mixture Models for Classifying Genomic Signals

Genomic (DNA) sequences can be converted to discrete signals using any numerical representation, where each of the bases is associated with a numerical value. Digital signal processing can then be applied to these discrete signals. We can assign some numerical values to each of the nucleotides in a DNA sequence without using any biological knowledge, or by using some physical or chemical properties of the nucleotides [6, 7, 8, 9]. In the baseline study [4], 13 different numerical representations were tried, and we also adopt a similar strategy; but we present results for one of the best-performing representations viz., the Purine-Pyrimidine representation (purines (A, G) = -1 and pyrimidines (T, C) = 1)).

Digital signal processing enables the study of the spectral properties of sequences. Distinct spectral properties enable classification. In the baseline, study [4], the sequences of different lengths are normalized (i.e., truncated or “anti-symmetrically” padded) to the median length of all sequences. Discrete Fourier Transform (DFT) is then applied to the length-normalized sequences to extract the corresponding magnitude spectra. The fixed-length spectra were then used to compute pairwise distance matrices using both Pearson’s Correlation Coefficient (PCC) and Euclidean distance metrics. The corresponding columns of the distance matrix were considered as feature vectors for each of the sequences for the classification task.

A Universal Background Model (UBM) is a Gaussian mixture model (GMM) that has been widely used for speaker recognition tasks [10]. We use this model in our study to obtain a fixed-length subspace representation for genomic sequences. A GMM is a generative model trained on data belonging to one particular class. A huge amount of data is required to estimate the parameters of a GMM accurately, especially when the dimension of the feature vector is quite large. UBM-GMM is employed in such cases to tackle the issue of data availability. It is built on data pooled from different classes and hence it tries to capture the properties of all of these classes. Moreover, owing to the availability of a large amount of data, the parameters of UBM-GMM are robustly estimated. Then a particular class’s data can be used to adapt a GMM from the trained UBM-GMM using maximum-a-posteriori adaptation (MAP).

We propose a novel UBM-GMM-based approach to obtain a fixed-length subspace representation for variable-length sequences, which can then be used for the genome classification task. The main contribution of our approach is that we can handle sequences of widely-varying lengths, without suffering the likely loss of information associated with length normalization (padding/truncation) of sequences done in existing studies [4, 5]. This loss of information is a serious issue when the lengths of the sequences vary quite a lot (which is the case for many classes in our application (Tables 1,2)).

The key idea behind our approach is that we take into account information across the entire sequence, by extracting features from every frame (sliding window) of the sequence (Figure 1 (a)). This yields multiple spectra from a given sequence, and we pool all such spectra corresponding to all the sequences across all the classes to build a UBM-GMM (see Figure 2) and subsequently get a fixed-length representation.

To provide more detail, we slide a window (with overlap across windows) of fixed length across the sequence, where we extract spectral features for every segment of the sequence. As discussed in [2], we experimented with a sufficiently large window of sizes ranging from 351 to a few thousand nucleotides. We considered window shifts ranging from 100 to 300 nucleotides. The magnitude spectrum is computed for each windowed sequence, with the DFT order chosen appropriately (window size rounded up to the nearest power of two). These magnitude spectra were then used to build a UBM which projects the spectra to a fixed-dimensional subspace, while primarily ensuring that the variability of the sequences across the entire sequence length is captured in the representation. The number of mixture components for UBM-GMM was empirically chosen as ten.

When adapting a GMM from the UBM-GMM using sequence data, we do mean-only adaptation using MAP, i.e., only the means of the UBM-GMM are changed depending on the feature vectors of the given sequence. The covariance matrices of the mixture components are not adapted due to insufficient data points from a sequence. The means of the adapted GMM are stacked to get a mean-supervector (Figure 2), which acts as the fixed-length subspace representation vector for the entire (untruncated/unpadded) sequence.

Once the subspace representations of sequences are obtained using our novel UBM-GMM-based approach, we can use the rest of the setup from the baseline approach for the taxonomic classification task, in order to perform a fair comparison of our and baseline representations’ classification accuracy. Specifically, our subspace representations are used to calculate a pair-wise distance matrix using PCC (as this was found to be the better metric in [4]), and the distance matrix columns used as feature vectors for the classification task. We used four different machine learning classifiers — Linear Discriminant, Linear Support Vector Machine (SVM), Quadratic SVM, and K-Nearest Nighbours (KNN) — as in the baseline study [4].

All the datasets used in this study are available from the National Center for Biotechnology Information (NCBI) and through links provided in the Suppl. material ²²2Supplementary material/codes: https://sites.google.com/view/genomic-signal-processing/. The datasets consist of mitochondrial and whole genome sequences corresponding to 8 classes. Each of these classes consists of two or more sub-classes, and classification is done at the sub-class level.

We ran the experiments on the benchmark datasets using the baseline as well as our approach. We experimented with different numerical representations, distance metrics to compute pair-wise distance matrices, window sizes, and window shifts. Based on the performances, we used the Purine-Pyrimidine representation, median length normalization (for the baseline approach), Pearson’s correlation coefficient (PCC) as a distance metric, window size as 702, window shift as 300 and FFT Order as 1024. The average accuracies computed over earlier discussed four different classifiers are mentioned in Table 2.

Our approach outperformed the baseline approach on the benchmark datasets especially when the Median Absolute Deviation (MAD) of the sequence lengths was high. It performed quite well even on unseen classes — Bacteria and Dengue — which were not used for building UBM-GMM. This suggests that UBM-GMM captures some important characteristics of the genomic data that results in discriminative properties of the adapted mixture models of a particular class. In order to interpret these results, we tried to visualize the activations per mixture components, for sequences of a given class, during the MAP adaptation process. Figure 3 (a) shows the active mixture components for Plants and Fungi classes along with their sub-classes. We can see from the figures that the active mixture components vary across sub-classes which provides the necessary discriminative properties that enable classification. Variations in active mixture components can also be observed across Plants and Fungi classes. Figure 3 (b) shows the means of the most active mixture components for two sequences belonging to the Chlorophyta and Streptophyta sub-classes of the Plant class each. The means of the active mixture components are clearly distinct across the two sub-classes.