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We tabulate bounds on the optimal number of mutually unbiased bases in R. For most dimensions d, it can be shown with relatively simple methods that either there are no real orthonormal bases that are mutually unbiased or the optimal number is at most either 2 or 3. We discuss the limitations of these methods when applied to all dimensions, shedding some… (More)

- Mohamad Tarifi, Meera Sitharam, Jeffery Ho
- BICA
- 2011

This paper introduces an elemental building block which combines Dictionary Learning and Dimension Reduction (DRDL). We show how this foundational element can be used to iteratively construct a Hierarchical Sparse Representation (HSR) of a sensory stream. We compare our approach to existing models showing the generality of our simple prescription. We then… (More)

- Meera Sitharam, Mohamad Tarifi, Menghan Wang
- CCCG
- 2014

We study Dictionary Learning (aka sparse coding). By geometrically interpreting an exact formulation of Dictionary Learning, we identify related problems and draw formal relationships among them. Dictionary Learning is viewed as the minimum generating set of a subspace arrangement. This formulation leads to a new family of dictionary learning algorithms.… (More)

- Meera Sitharam, Mohamad Tarifi, Menghan Wang
- ArXiv
- 2016

Given a hypergraph H with m hyperedges and a set Q of m pinning subspaces, i.e. globally fixed subspaces in Euclidean space R, a pinned subspace-incidence system is the pair (H,Q), with the constraint that each pinning subspace in Q is contained in the subspace spanned by the point realizations in R of vertices of the corresponding hyperedge of H . This… (More)

Besides being of independent interest in understanding the structure of (partial) MUB collections and their conjugacy classes, satisfactory answers to these questions will help the following investigations: – the search for lower bounds on the number of MUBs and specifically for efficient constructions; – the search for upper bounds on the number of MUBs… (More)

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