7.2.1 Improving the Technique
7.2.1.1 Automatic Feature Representation
There are limitations to the method that should be noted. The most significant is the choice of the initial image representation. In this work we use sample vectors that effectively encode information about colour and intensity distribution on small (few pixels) scales. In principle the feature vector can be arbitrarily large, but at the cost of computation time; therefore there is a balance between performance and the sophistication of the chosen features. It is clear that the exact choice of image representation will have an impact on the ability of the algorithm to successfully segment and classify input data. It is possible that one could use an algorithm that identifies the optimal set of features to use (see unsupervised feature learning in Bengio et al. (2013), also stacked denoising autoencoders by Vincent et al. (2010) ). Initial tests using convolutional autoencoders to learn features from the data can be seen in Figure 7.1. Careful attention to rotation invariance is required as the convolutional process is not invariant. Adopting the rotational invariance technique used in (Dieleman et al., 2015b) may be the solution.
Chapter 7.Conclusion 119
FIGURE 7.1: Autoencoded reconstructions. The top row contains original image patches and the bottom row shows the reconstructions created by the convolutional autoencoder. The re- constructions provide insight into how effectively the autoencoder has learnt the structure of
the original image data.
7.2.1.2 Potential Improvements to Computational Performance
I have not fully optimized the algorithm for speed (and as noted above, performance will de- pend on the complexity of the image representations), however as a guide, the analysis of the Abell 2744 imaging took 36 msec per pixel and the analysis of the MACS 0416.1−2403 image with the model took 1.5 msec per pixel. The work was performed on a desktop computer with an Intel CPU. In my experience the amount of time spent on building the graph of the image patches takes the most time. This is why I’ve extensively tested for generalisation so that the graph can be re-used to analyse new images. These performances can clearly be dramatically improved, especially through the use of GPUs and optimal threading. The process is parallelisable making this a highly efficient algorithm to apply to large imaging data.
In addition, an approximate nearest neighbour algorithm (e.g. Muja and Lowe, 2014) could be used instead of the current approach in order to identify the patch type. This would be faster but potentially less accurate.
7.2.1.3 Improving Localisation
The technique currently makes no assumptions about object shape and size, but uses a simple threshold over the whole image to identify objects. However, the background level varies across the image and therefore a single threshold is not ideal. The introduction of a variable thresh- old that takes account of local background noise could lead to improved results. One approach
would be to partition images and calculate a background level in each partition, however, galax- ies may cross partition boundaries. The background map produced by Source Extractor (Bertin, 1996) could provide a useful example to follow.
7.2.1.4 Investigating Redshift Distributions
In Section 6.3 I discussed two possible explanations for individual clusters identifying galaxies at different redshifts. As discussed, this could be further explored by carrying out SED fitting to obtain physical parameters for galaxies in different groups. This would require multi-wavelength data for a large number of galaxies.
7.2.1.5 Investigating whether the high number of classification groups is a function of the method or a true representation of the underlying data
In Section 6.3 I discussed whether the high number of classification groups required in the CANDELS fields might be due to the underlying variation in the data (i.e. variation in colour and morphology), or whether it is a feature of the technique that a large number of groups are required to subdivide the parameter space. One method of testing this would be to create a number of dummy datasets with different degrees of variation and determine the optimum number of groups for each. If the number of groups required increases with increasing variation then this would confirm that the required number of groups depends on the underlying data.
7.2.2 Application to Future Surveys
The technique will be useful in the era of extremely large surveys such as the Large Synoptic Sky Telescope3 (Ivezic et al., 2014, LSST) and EUCLID (Laureijs et al., 2011). The LSST is a ground-based 8.4 metre optical telescope designed to have a very wide field-of-view (3.5 degrees). This, and its capability to take a pair of images every 15 seconds, enable it to image the whole sky every three days. It has six wideband filters covering 350nm-1060nm.EUCLIDis a space based telescope designed to observe the whole sky using optical (550 (green) to 920nm) and near-infrared (1000-2000nm) cameras.
Chapter 7.Conclusion 121
7.2.2.1 Unusual Objects
The unsupervised nature of the technique allows for the discovery of objects not previously known. As LSST andEUCLIDare whole sky surveys they are expected to contain larger sam- ples of unusual galaxies. I would expect the model to group these galaxies together. Alterna- tively, unusual galaxies may appear as outliers. These outliers can be found by searching at the fringe of the parameter space, for example, by looking for individual galaxies at the fringe of an identified group, or a group of galaxies that may itself be an outlier relative to other groups. One type of known rare object that could be found in future surveys is strong galaxy lenses. Lenses magnify the flux and scale of background galaxies allowing analysis of galaxies of higher redshift than would be possible by direct imaging. The model developed in this the- sis was successful in finding lenses in the CANDELS fields (see Figure 6.13 in Chapter 6). The
HSTCANDELS data has higher resolution than the LSST as the LSST is subject to the ‘seeing’ conditions provided by the atmosphere. Whereas the lensing features found in CANDELS im- ages can be clearly seen (once they have been found), similar lensing features in LSST imaging are likely to appear as blue blobs or smudges. It may be possible to change the CANDELS data to test whether the technique could find similar lenses in LSST data by degrading the resolu- tion of CANDELS data and then re-running the method to see if they are still grouped together. However, this should not be a problem forEUCLIDimages.
7.2.2.2 Transients
One of the goals of the LSST is to ‘make a high-definition colour movie of the deep Universe’ (Ivezic et al., 2014). By imaging the sky every few nights transient objects that appear and disappear over short time scales can be detected. The LSST data pipeline will provide small cutouts around potential detected transient objects. It is expected that many of the detections will be false positives4. The technique could be adapted to analyse these potential transient detections to confirm whether they are real transients, such as supernovae, or false detections due to systematics.
The technique could be applied by collating all the transients for a period of time and applying the model to these data only. The technique would classify similar transients together, creating a series of groups of false positives and a series of groups of actual transients. Once enough
transients have been acquired, the identified groups could be used to classify new transients in real time.
7.2.2.3 Application to Radio Surveys
The Square Kilometre Array is anticipated to produce Petabytes of radio data that will require automated analysis5. The technique can not easily be applied to radio intensity images as they contain so little morphology. However, it may be possible to apply the technique to combined optical and radio data.