  We present an unsupervised machine learning approach that can be employed for
estimating photometric redshifts. The proposed method is based on a vector
quantization approach called Self--Organizing Mapping (SOM). A variety of
photometrically derived input values were utilized from the Sloan Digital Sky
Survey's Main Galaxy Sample, Luminous Red Galaxy, and Quasar samples along with
the PHAT0 data set from the PHoto-z Accuracy Testing project. Regression
results obtained with this new approach were evaluated in terms of root mean
square error (RMSE) to estimate the accuracy of the photometric redshift
estimates. The results demonstrate competitive RMSE and outlier percentages
when compared with several other popular approaches such as Artificial Neural
Networks and Gaussian Process Regression. SOM RMSE--results (using
$\Delta$z=z$_{phot}$--z$_{spec}$) for the Main Galaxy Sample are 0.023, for the
Luminous Red Galaxy sample 0.027, Quasars are 0.418, and PHAT0 synthetic data
are 0.022. The results demonstrate that there are non--unique solutions for
estimating SOM RMSEs. Further research is needed in order to find more robust
estimation techniques using SOMs, but the results herein are a positive
indication of their capabilities when compared with other well-known methods.
