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A k-factor of a graph is a spanning k-regular subgraph, and a k-factorization partitions the edges of the graph into disjoint k-factors. A graph G is said to be k-factorable if it admits a k-factorization. In particular, a 1-factor is a perfect matching, and a 1-factorization of a k-regular graph is a proper edge coloring with k colors.
with a corresponding factor graph shown on the right. Observe that the factor graph has a cycle. If we merge (,) (,) into a single factor, the resulting factor graph will be a tree. This is an important distinction, as message passing algorithms are usually exact for trees, but only approximate for graphs with cycles.
This is the aim of multiple factor analysis which balances the different issues (i.e. the different groups of variables) within a global analysis and provides, beyond the classical results of factorial analysis (mainly graphics of individuals and of categories), several results (indicators and graphics) specific of the group structure.
In the tables in the following examples, the entries in the "cell" column are treatment combinations: The first component of each combination is the level of factor A, the second for factor B, and the third (in the 2 × 2 × 2 example) the level of factor C. The entries in each of the other columns sum to 0, so that each column is a contrast ...
In the example, the contribution of individuals 1 and 5 to the inertia of the first axis is 45.7% + 31.5% = 77.2% which justifies the interpretation focussed on these two points. 4. Representations of categories of qualitative variables as in MCA (a category lies at the centroid of the individuals who possess it).
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A scree plot always displays the eigenvalues in a downward curve, ordering the eigenvalues from largest to smallest. According to the scree test, the "elbow" of the graph where the eigenvalues seem to level off is found and factors or components to the left of this point should be retained as significant. [3]
The data include quantitative variables =, …, and qualitative variables =, …,.. is a quantitative variable. We note: . (,) the correlation coefficient between variables and ;; (,) the squared correlation ratio between variables and .; In the PCA of , we look for the function on (a function on assigns a value to each individual, it is the case for initial variables and principal components ...
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