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In general, a set of terminal nodes is given and the objective is to find a connected subgraph, spanning all the terminals with minimal aggregate weights for all.
The aggregate weights calculated by employing Eqs. 1, 2, 3 and 4, which are listed in the fuzzy, mean column of Table 11.
This is equivalent to the local resampling step in Algorithm 2. Island level: the aggregate weights (W_{t}^{(m)}) are used to resample the particle subsets, or islands, assigned to the individual PFs.
In a practical implementation, the aggregate weights (W_{t}^{(m)*}) should be monitored and additional particle exchange steps should be triggered when the weight of any subset increases beyond some prescribed threshold.
Similar to the DRNA-based PFs of Section 3.2, the algorithms proposed in [13] are based on running M parallel PFs, each one on a disjoint subset of particles, namely (big { x_{t}^{(m,n)} big }_{1 le n le N}) for the mth filter, and keep track of the non-normalised aggregate weights (W_{t}^{(m)*}) defined in Eq. (14).
M bootstrap filters (as Algorithm 1 in this paper) are run in parallel and an aggregate weight is computed for each one of them, denoted (W_{t}^{(m)}); When the coefficient of variation (CV) of these aggregate weights is greater than a given threshold, the M bootstrap filters are resampled (some filters are discarded and others are replicated using a multinomial resampling procedure).
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The particles in the nth PE will tend to degenerate when its aggregate weight becomes negligible relative to the aggregated weights of the other PEs.
At a guess — from their dimensions and specific gravity — the aggregate weight of the two rocks was a hundred and sixty tons.
For a tree in graph, the aggregate weight is defined as (2).
where Q ˜ i is an aggregate weighting matrix of size (M - 1) × (M - 1) as well.
Note that Q ˜ i, j is also an aggregate weighting matrix of size (M - 1) × (M - 1).
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