## 2 Materials and Methods
The transmission matrix gives the output field for any arbitrary input. We used the input and output fields as the boundary conditions to further compute the intensity distributions inside the disordered waveguide for different transmission eigenchannels. The field intensity was averaged over the waveguide cross-section along \(y\) to give the evolution of the energy density along the waveguide's propagating direction \(x\). In this study, we focused on classification of the cross-section averaged intensity distributions of the first ten transmission eigenchannels. The transmission eigenchannels were chosen such that they span high, intermediate, and low transmittance. It is well known and experimentally demonstrated [26; 32] that the cross-section averaged intensities of transmission eigenchannels with high, intermediate, and low transmittance have unique spatial profiles when averaged over a large statistical ensemble of random configurations. Figure 2a shows the cross-section averaged intensity, averaged over 10,000 random configurations, of the first ten transmission eigenchannels for a disordered waveguide with \(N_{s}\) = 300. Indeed, when averaged over a large ensemble, we see different spatial profiles for different transmission eigenchannels; however, the change in spatial profile is subtle for transmission eigenchannels with similar transmittance, such as the two eigenchannels \(T_{1}\) and \(T_{2}\) with highest and second-highest transmission eigenvalues. Furthermore, this subtle difference becomes impossible to decipher when only a single configuration is considered. Figure 2b shows the calculated two-dimensional intensity distribution of a transmission eigenchannel, \(T_{1}\), with highest transmittance with \(N_{s}\) = 300. We can clearly see the very complex speckle-like intensity distribution both within the disordered region as well as in the buffer regions. Figure 2c plots the cross-section averaged intensity from the two-dimensional plot in Figure 2b overlaid on the statistically averaged spatial profiles of the transmission eigenchannels with highest and second-highest transmittance. Because of the large fluctuations that arise due to interference between the multiply scattered waves, it becomes impossible to visually determine whether the profile shown in Figure 2c corresponds to the transmission eigenchannel with highest or second-highest transmittance. Furthermore, even basic statistical analysis, such as distributions of root mean square deviation (RMSD), is not sufficient to classify and correlate the spatial profile of the intensity distribution to a specific transmission eigenchannel. In Figure 2d, we show the histogram of RMSD values of 5,000 configurations of the transmission eigenchannels with the highest (Channel 1) and second-highest transmittance (Channel 2). Both histograms have very similar spread and shape, making it difficult to correlate the intensity distribution to either of the transmission eigenchannels. To demonstrate the classification of energy density of ten transmission eigenchannels with the ten highest transmission eigenvalues, we used machine learning techniques that are known to be effective for the classification of complex data. Since transmission eigenchannels dictate not only the intensity distribution inside the disordered region but also the transmitted light through these structures, we looked at the cross-section averaged intensity of the disordered region as well as the intensity pattern both in the front and back empty buffer regions of the waveguides. All of the data for the different disordered waveguides with different numbers of scatterers were combined. The resulting dataset consisted of 750,000, 451-component vectors.