machine learning additions. sublinear README.

The Fast Johnson-Lindenstrauss Transform
A Sparse Johnson-Lindenstrauss Transform
Towards a unified theory of sparse dimensionality reduction in Euclidean space

machine_learning/README.md

@@ -7,5 +7,23 @@ Important machine learning papers
 * [Random Forests](http://oz.berkeley.edu/~breiman/randomforest2001.pdf) - The initial paper on random forests
 * [Conditional Random Fields: Probabilistic Models for Segmenting and Labeling Sequence Data](http://repository.upenn.edu/cgi/viewcontent.cgi?article=1162&context=cis_papers) - The paper introducing conditional random fields as a framework for building probablistic models.
 * [Support-Vector Networks](http://rd.springer.com/content/pdf/10.1007%2FBF00994018.pdf) - The initial paper on support-vector networks for classification.
+* [The Fast Johnson-Lindenstrauss Transforms](https://www.cs.princeton.edu/~chazelle/pubs/FJLT-sicomp09.pdf)
 
+    The Johnson-Lindenstrauss transform (JLT) prescribes that there exists a matrix of size `k x d`, where `k = O(1/eps^2 log d)` such that with high probability, a matrix A drawn from this distribution preserves pairwise distances up to epsilon (e.g. `(1-eps) * ||x-y|| < ||Ax - Ay|| < (1+eps) ||x-y||`). This paper was the first paper to show that you can actually compute the JLT in less that `O(kd)` operations (e.g. you don't need to do the full matrix multiplication). They used their faster algorithm to construct one of the fastest known approximate nearest neighbor algorithms.
+
+    *Ailon, Nir, and Bernard Chazelle. "The fast Johnson-Lindenstrauss transform and approximate nearest neighbors." SIAM Journal on Computing 39.1 (2009): 302-322. Available: https://www.cs.princeton.edu/~chazelle/pubs/FJLT-sicomp09.pdf*
+
+## Hosted Papers
+
+* :scroll: **[A Sparse Johnson-Lindenstrauss Transform](https://github.com/papers-we-love/papers-we-love/blob/master/machine_learning/dimensionality_reduction/a-sparse-johnson-lindenstrauss-transform.pdf)**
+
+    The JLT is still computationally expensive for a lot of applications and one goal would be to minimize the overall operations needed to do the aforementioned matrix multiplication. This paper showed that a goal of a `O(k log d)` algorithm (e.g. `(log(d))^2)` may be attainable by showing that very sparse, structured random matrices could provide the *JL* guarantee on pairwise distances.
+
+    *Dasgupta, Anirban, Ravi Kumar, and Tamás Sarlós. "A sparse johnson: Lindenstrauss transform." Proceedings of the forty-second ACM symposium on Theory of computing. ACM, 2010. Available: [arXiv/cs/1004:4240](http://arxiv.org/abs/1004.4240)*
+
+* :scroll: **[Towards a unified theory of sparse dimensionality reduction in Euclidean space](https://github.com/papers-we-love/papers-we-love/blob/master/machine_learning/dimensionality_reduction/toward-a-unified-theory-of-sparse-dimensionality-reduction-in-euclidean-space.pdf)**
+
+    This paper attempts to layout the generic mathematical framework (in terms of convex analysis and functional analysis) for sparse dimensionality reduction. The first author is a Fields Medalist who is interested in taking techniques for Banach Spaces and applying them to this problem. This paper is a very technical paper that attempts to answer the question, "when does a sparse embedding exist deterministically?" (e.g. doesn't require drawing random matrices).
+
+    *Bourgain, Jean, and Jelani Nelson. "Toward a unified theory of sparse dimensionality reduction in euclidean space." arXiv preprint arXiv:1311.2542; Accepted in an AMS Journal but unpublished at the moment  (2013). Available: http://arxiv.org/abs/1311.2542*
 

sublinear_algorithms/README.md

@@ -0,0 +1,16 @@
+Important Sublinear Algorithm papers
+
+## Hosted Papers
+
+* :scroll: **[Probablistic Counting Algorithms for Database Applications](https://github.com/papers-we-love/papers-we-love/blob/master/sublinear_algorithms/1985-Flajolet-Probabilistic-counting.pdf)**
+
+    This paper introduces a class of probabilistic counting algorithms with which one can estimate the number of distinct elements in a large collection of data (typically a large file stored on disk) in a single pass using only a small additional storage (typically less than a hundred binary words) and only a few operations per element scanned. The algorithms are based on statistical observations made on bits of hashed values of records. They are by construction totally insensitive to the replicative structure of elements in the file; they can be used in the context of distributed systems without any degradation of performances and prove especially useful in the context of data bases query optimisation
+
+    *Flajolet, Philippe, and G. Nigel Martin. "Probabilistic counting algorithms for data base applications." Journal of computer and system sciences 31.2 (1985): 182-209.*
+
+* :scroll: **[An Elementary Proof of a Theorem of Johnson and Lindenstrauss](https://github.com/papers-we-love/papers-we-love/blob/master/sublinear_algorithms/An-Elementary-Proof-of-a-Theorem-of-Johnson-and-Lindenstrauss.pdf)**
+
+    A result of Johnson and Lindenstrauss shows that a set of n points in high dimensional Euclidean space can be mapped into an `O(log n/ϵ2)-dimensional` Euclidean space such that the distance between any two points changes by only a factor of `(1 ± ϵ)`. In this note, we prove this theorem using elementary probabilistic techniques.
+
+    *Dasgupta, Sanjoy, and Anupam Gupta. "An elementary proof of a theorem of Johnson and Lindenstrauss." Random Structures & Algorithms 22.1 (2003): 60-65.*
+