Research goals in 2015

Having finished writing the draft for T-RO, I guess now is an appropriate time for seeking for this year's research goals. So far, I have focussed on doing, 

 - deep learning in RO-MAN 2013

 - sensor network using GP in CDC 2013

 - navigation using GP in ICRA 2014

 - leveraged GP in ICRA 2015

 - Gaussian random path in IROS 2015 (submitted).

Gaussian processes are heavily used, and I think the portion of GPs must decrease. 

Whatsoever, I should move on to other topics and belows are some possible topics:

 1. Somehow extend the leverage GP so that the leverage value can be estimated from the data. Interpretation can be done using correlation between random processes. (Function correlation clustering)

 2. Find way to set appropriate anchoring points in Gaussian random path framework. (Path stamping) - computation can be parallelized! 

 3. Motion primitives as graph: Given sequences of motion states, cluster them somehow, and generate a graph from sequences. 

 4. Depth image reconstruction using denoising auto-encoder. 

 5. Biomimetic Recognition Technology for Agency for Defence Development (BMRR)

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1. Leverage estimation 

- Leverage can be interpreted as a process-specific value that characterizes the random process. Processes with similar leverage indicate that those are highly correlated, meaning that those processes are similar. Using this property, one can cluster functions from the training data with input and output. 

 There is an analogy between leverage estimation and Gaussian latent variable model (GPLVM) which is a nonlinear dimension algorithm. 

Above is a graphical model of a GPLVM where the objective is to find a low dimensional representation, X, of given (high dimensional) data Y. 

Above is a graphical model of a leverage optimization model where the objective is to find proper '$\gamma$' based on input-output data, {X, Y}. 

Graphical model above is a function mixture model where '$\gamma$' indicates a function-specific value which defines correlation between different processes. 

We assume that each data consists of input and output pair comes from a finite number of functions (processes). The purpose is to cluster the data which come from same function. 

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2. Gaussian random paths (GRP)

 - One important property of GRP is that it can 'stamp out' diverse paths in a very rapid speed. However, for the resulting paths to be feasible, appropriate anchoring points are required. So, the problem of finding paths now turns into the problem of selecting proper anchoring points. 

 The easiest (?) option would be use a RRT to set some anchoring points. 

 We can construct a 'tube' of path even with some anchoring points by varying the '$\sigma^2_w$' parameter of anchoring points. 

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3. Motion primitives as a Graph

 - Maintaining the stability is always a hard thing control in robotics. So, instead of modeling stability using center of method or zero moment point, we manually collect sequences of feasible states in the configuration space (full body) and represent them as a graph, where nodes indicate change points and edges indicate sequence of states connecting nodes. 

 But I guess it is not that interesting idea.. 

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4. Depth image reconstruction

 - Denoising autoencoder can be used for this. 

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5. BMRR - Human detection

 - Main purpose of this work is to detect a pedestrian using a small number of distance measuring sensors based on following criterion. 

 Criteria 1- Sensor placement: Find the sensor placement which maximize the KL-divergence between Normal distributions modelled by positive and negative training data. 

KL-divergence of two multivariate Gaussians

$$KL = \frac{1}{2}[\log \frac{|\Sigma_2|}{|\Sigma_1|} - d + tr(\Sigma^{-1}_2\Sigma_1) + (\mu_2-\mu_1)^T\Sigma_2^{-1}(\mu_2-\mu_1)]$$

1. Always non-negative.

2. KL=0 indicates given distributions are almost the same. 

 Criteria 2- Classification performance: The criteria is to maximize the number of points inside the bounding box of given training images.

 If we can somehow show that it has submodularity property..? 

Once the optimal or sub-optimal sensor placement is given, we can use existing classifier, such as  SVM or GPC.