Entity Matching is an essential part of all real-world systems that take in structured and unstructured data coming from different sources. Typically no common key is available for connecting records. Massive data cleaning and integration processes require completion before any data analytics, or further processing can be performed. Although record linkage is frequently regarded as a somewhat tedious but necessary step, it reveals valuable insights, supports data visualization, and guides further analytic approaches to the data. Here, we focus on organization entity matching. We introduce CompanyName2Vec, a novel algorithm to solve company entity matching (CEM) using a neural network model to learn company name semantics from a job ad corpus, without relying on any information on the matched company besides its name. Based on a real-world data, we show that CompanyName2Vec outperforms other evaluated methods and solves the CEM challenge with an average success rate of 89.3%.

We show that given two bases $A$ and $B$ of a matroid $\mathcal M$ and any given partition $\bigcup_{i=1}^kB_i$ of $B$ there exists a partition $\bigcup_{i=1}^kA_i$ of $A$ such that $(A- A_i)\cup B_i$ and $(A- \bigcup_{j=1}^i A_j)\cup (\bigcup_{j=1}^i B_j)$ are bases for all $i=1,\ldots,k$. We also give a new proof, not relying on Hall's theorem, of a theorem of Donald and Tobey stating that for each $k=1,\dots,n$, there exists a bijection $\tau_k$ from $k$-subsets $I$ of $A$ to $k$-subsets of $B$ such that $(A- I)\cup\tau_k(I)$ is always a basis.

Let $f(n)$ be the smallest number such that every collection of $n$ matchings, each of size at least $f(n)$, in a bipartite graph, has a full rainbow matching. Generalizing famous conjectures of Ryser, Brualdi, and Stein, Aharoni and Berger [ Electron. J. Combin., 16 (2009), R119] conjectured that $f(n)=n+1$ for every $n>1$. Clemens and Ehrenmüller proved that $f(n) \le \frac{3}{2}n +o(n)$. We show that the $o(n)$ term can be reduced to a constant, namely, $f(n) \le \lceil \frac{3}{2}n \rceil+1$.