Search Efficient Binary Network Embedding

Traditional network embedding primarily focuses on learning a dense vector representation for each node, which encodes network structure and/or node content information, such that off-the-shelf machine learning algorithms can be easily applied to the vector-format node representations for network analysis. However, the learned dense vector representations are inefficient for large-scale similarity search, which requires to find the nearest neighbor measured by Euclidean distance in a continuous vector space. In this paper, we propose a search efficient binary network embedding algorithm called BinaryNE to learn a sparse binary code for each node, by simultaneously modeling node context relations and node attribute relations through a three-layer neural network. BinaryNE learns binary node representations efficiently through a stochastic gradient descent based online learning algorithm. The learned binary encoding not only reduces memory usage to represent each node, but also allows fast bit-wise comparisons to support much quicker network node search compared to Euclidean distance or other distance measures. Our experiments and comparisons show that BinaryNE not only delivers more than 23 times faster search speed, but also provides comparable or better search quality than traditional continuous vector based network embedding methods

End-to-End Cross-Modality Retrieval with CCA Projections and Pairwise Ranking Loss

Cross-modality retrieval encompasses retrieval tasks where the fetched items are of a different type than the search query, e.g., retrieving pictures relevant to a given text query. The state-of-the-art approach to cross-modality retrieval relies on learning a joint embedding space of the two modalities, where items from either modality are retrieved using nearest-neighbor search. In this work, we introduce a neural network layer based on Canonical Correlation Analysis (CCA) that learns better embedding spaces by analytically computing projections that maximize correlation. In contrast to previous approaches, the CCA Layer (CCAL) allows us to combine existing objectives for embedding space learning, such as pairwise ranking losses, with the optimal projections of CCA. We show the effectiveness of our approach for cross-modality retrieval on three different scenarios (text-to-image, audio-sheet-music and zero-shot retrieval), surpassing both Deep CCA and a multi-view network using freely learned projections optimized by a pairwise ranking loss, especially when little training data is available (the code for all three methods is released at: https://github.com/CPJKU/cca_layer).Comment: Preliminary version of a paper published in the International Journal of Multimedia Information Retrieva

Ramified rectilinear polygons: coordinatization by dendrons

Simple rectilinear polygons (i.e. rectilinear polygons without holes or cutpoints) can be regarded as finite rectangular cell complexes coordinatized by two finite dendrons. The intrinsic $l_1$-metric is thus inherited from the product of the two finite dendrons via an isometric embedding. The rectangular cell complexes that share this same embedding property are called ramified rectilinear polygons. The links of vertices in these cell complexes may be arbitrary bipartite graphs, in contrast to simple rectilinear polygons where the links of points are either 4-cycles or paths of length at most 3. Ramified rectilinear polygons are particular instances of rectangular complexes obtained from cube-free median graphs, or equivalently simply connected rectangular complexes with triangle-free links. The underlying graphs of finite ramified rectilinear polygons can be recognized among graphs in linear time by a Lexicographic Breadth-First-Search. Whereas the symmetry of a simple rectilinear polygon is very restricted (with automorphism group being a subgroup of the dihedral group $D_4$), ramified rectilinear polygons are universal: every finite group is the automorphism group of some ramified rectilinear polygon.Comment: 27 pages, 6 figure