Grafico 2. Diagrama del Sistema Económico Social y Solidario
2.1 Reseña histórica de la compra Pública en el Ecuador
The major advantage of using convolutional layers over fully-connected ones is that they retain the spatial information of the local image patterns. A convolutional layer generates a tensor of activationsX in RH⇥W ⇥D, where (H, W ) is the spatial dimension of the feature maps and D the total number of feature maps. Xi,j,krefers to
an activation located in the spatial location (i, j) in the feature map k. As discussed in Section 3.4.1, the volume of activations can be reinterpreted as N = H⇥ W local descriptors f (i, j)2 RD arranged in a 2D space. Before aggregating the activations
into a single representation, it is possible to apply a weighting scheme wi,j,k to weight
the contribution of each activation, so that weighted activationsX0
i,j,k are computed
by X0
i,j,k = wi,j,kXi,j,k.
6.2.1 Types of weighting
We can distinguish three types of weighting: weights applied across feature maps of dimension D, weights across the spatial dimension (H, W ) of the feature maps, or hybrid approaches.
6.2.1.1 Feature weighting k
Each dimension of a local descriptor f (i, j) represents the response associated with a particular feature detector. Di↵erent weights can be applied to the features of the local vectors, so that the weighting is uniform across the spatial dimensions of the feature maps wi,j,k= k. For instance in [? ], k is a weighting scheme that weights
the contribution of each dimension according to the sparsity associated with their global feature map k in X . The proposed scheme up-weights the contribution of rare-features (dimensions corresponding to feature maps with higher sparsity levels) before aggregation. This procedure is similar to the traditional tf-idf weighting scheme [114], that also boosts the importance of the most distinctive and rare visual
6.2.1.2 Spatial weighting ↵i,j
In this approach di↵erent weights are applied to f (i, j) depending on its spatial location. In this case the final weighting is uniform across di↵erent feature maps wi,j,k= ↵i,j. For instance, ↵i,j is defined using a Gaussian weighting scheme in [8]
and, similarly, in [? ] each local feature is weighted with its associated L2 norm.
6.2.1.3 Hybrid weighting wi,j,k
In this approach activations are weighted by combining k and ↵i,j schemes. An
example of this is the Cross-Dimensional Weighting scheme (CroW) [? ] where the weighting is defined as wi,j,k = ↵i,j k. The weight assigned to a particular activation
is a combination of the weights derived from the channel sparsity and the weights associated to the strength (L2-norm) of each local descriptor.
More specifically, subsections (6.2.1.2) and (6.2.1.1) describe a weighting types can be seen as a particular case of the hybrid weighting CroW, where ↵i,j = 1 in the
case of feature weighting and k= 1 for the spatial weighting types.
6.2.2 Spatial weighting schemes
Spatial weighting ↵i,j weights the contribution of each local feature f (i, j) before
the aggregation stage. We can further classify four di↵erent schemes for this type of weighting: fixed, image-dependent, query-dependent, and hybrid weighting schemes.
6.2.2.1 Fixed weighting schemes
In this approach, the weighting is a function that does not depend on the image content (or local descriptors). Examples include global sum-pooling of unweighted activations (↵i,j = 1) or global sum-pooling with spatial weighting following a
Gaussian centre-prior is defined by:
↵i,j = exp (i H2)2+ (j W 2 )2 2 2 ! . (6.1)
These schemes do not depend on the image content (as can be seen from Equa- tion 6.1): the weighting only depends on the image resolution.
6.2.2.2 Image-dependent weighting schemes
Here weights are a function of the image content. Schemes can be classified into two main categories:
1. Non-parametric image-dependent weighting where weights do not depend on any learned parameters. For instance, in global sum-pooling of features spatially weighted with the contribution of the local L2-norms [? ], weights are defined as
↵i,j =kf(i, j)k2 (6.2)
where ↵i,j is a non-parametric function that depends on the local descriptor.
Similarly, in the same spirit as R-MAC [125], local sum-pooling of di↵erent regions followed by L2 region normalization and global pooling is also an example of this scheme, where each region is inversely weighted according to its associated L2-norm (as will be shown in Section 6.4.2).
2. Parametric image-dependent weighting where the weighting function is para- metric and fit using supervised learning. One example is the local sum-pooling of regions obtained from a learned region proposal algorithm followed by L2 re- gion normalization and global pooling, as in the fine-tuned R-MAC version [39]. Another example is the saliency weighting of convolutional activations. This scheme is particularly interesting because saliency models are trained to directly up-weight parts of the image that humans consider important. The saliency weighting scheme is furthered discussed in Section 6.6.
The above categorization ignores PCA whitening for the sake of simplicity. PCA whitening performs an additional linear transformation of the weights that equalizes
but rather a projection of the features onto an alternative basis. It can be added to any of the above approaches as a post-processing step, either after local pooling or global pooling.
6.2.2.3 Query-dependent weighting schemes
In this case the spatial weighting is a function of the query image (or its repre- sentation). As with the image-dependent weighting schemes, the weighting can be non-parametric or parametric.
An example of this weighting is described in [17], where the authors propose a query-adaptive image search re-ranking where convolutional activations are locally pooled within di↵erent regions similarly to [125]. However, instead of directly pooling all the regions via sum-pooling into a final representation, a soft merging function of the set of regions is optimized for each query. The function up-weights the contribution of the regions that are more related to the query. Due to the fact that the total amount of dataset regions can be prohibitively large for the optimization algorithm, the method is only applied as a re-ranking step, considering the regions from the top retrieved images obtained from an initial search.
Although this weighting scheme represents a potentially interesting avenue of research, its main drawback is that it needs to be optimized at query time, adding a significant computational computational load as well as memory demand, since all region descriptors need to be stored, making the system less scalable.
6.2.2.4 Hybrid schemes
This type of scheme involves both image-dependent and query-dependent weighting. Although this is theoretically possible, the scheme would su↵er from the same drawbacks as the query-dependent schemes. Again, it could be an interesting avenue of future research.