Apriori algorithm
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The Apriori algorithm is used for frequent itemset mining and discovering association rules between variables in a transactional database. It uses a "bottom up" approach, where frequent subsets are extended one item at a time and candidate itemsets are tested against the database to determine which itemsets meet the minimum support threshold. The algorithm performs multiple passes over the database and joins itemsets from the previous pass to generate candidates to test for the next pass.
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Dust suppressants operate primarily through three interrelated mechanisms: wetting, coagulation, and consolidation.
Wetting: This mechanism involves the application of dust suppressants to reduce the surface tension of water, allowing it to penetrate and coat dust particles. This increases the weight and cohesion of the particles, causing them to settle quickly. Surfactants and hygroscopic agents are commonly used in this approach.
Coagulation: Dust particles are brought together to form larger aggregates through electrostatic interactions or binding agents, which helps in accelerating their settling.
Consolidation: A more long-term effect where the suppressant forms a crust or mesh-like structure over the dust-prone surface, physically stabilizing it and preventing re-entrainment of particles by wind or vehicle movement.
Bio-Organic Materials in Dust Suppressants
The shift toward natural, renewable, and biodegradable components has led to extensive research on the use of various bio-organic substances, including:
Polysaccharides: Starch, cellulose derivatives, and chitosan can form gels or films that stabilize surfaces.
Lignin: A byproduct of the paper industry, lignin offers strong binding capacity and is naturally water-resistant.
Proteins: Derived from agricultural waste, proteins like casein and soy protein can enhance binding and wetting.
Microorganisms: Certain bacteria and fungi can produce biofilms or exopolysaccharides that trap dust particles.
Agricultural and Forestry Wastes: Residues su
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Apriori algorithm
- 1. DEFINITION OF APRIORI ALGORITHM • The Apriori Algorithm is an influential algorithm for mining frequent itemsets for boolean association rules. • Apriori uses a "bottom up" approach, where frequent subsets are extended one item at a time (a step known as candidate generation, and groups of candidates are tested against the data. • Apriori is designed to operate on database containing transactions (for example, collections of items bought by customers, or details of a website frequentation).
- 2. KEY CONCEPTS Frequent Itemsets: All the sets which contain the item with the minimum support (denoted by 𝐿𝑖 for 𝑖𝑡ℎ itemset). Apriori Property: Any subset of frequent itemset must be frequent. Join Operation: To find 𝐿𝑘 , a set of candidate k-itemsets is generated by joining 𝐿𝑘−1 with itself.
- 4. MARKET BASKET ANALYSIS Provides insight into which products tend to be purchased together and which are most amenable to promotion. Actionable rules Trivial rules • People who buy chalk-piece also buy duster Inexplicable • People who buy mobile also buy bag
- 6. The Apriori Algorithm : Pseudo Code • Join Step: 𝐶𝑘 is generated by joining 𝐿𝑘−1 with itself • Prune Step: Any (k-1)-itemset that is not frequent cannot be a subset of a frequent k-itemset • Pseudo-code :𝐶𝑘: Candidate itemset of size k 𝐿𝑘: frequent itemset of size k L1 = {frequent items}; for (k = 1; Lk !=null; k++) do begin Ck+1 = candidates generated from Lk; for each transaction t in database do increment the count of all candidates in Ck+1 that are contained in t Lk+1 = candidates in Ck+1 with min_support end return k Lk;
- 7. LIMITATIONS Apriori algorithm can be very slow and the bottleneck is candidate generation. For example, if the transaction DB has 104 frequent 1- itemsets, they will generate 107 candidate 2-itemsets even after employing the downward closure. To compute those with sup more than min sup, the database need to be scanned at every level. It needs (n +1 ) scans, where n is the length of the longest pattern.
- 8. METHODS TO IMPROVE APRIORI’S EFFICIENCY Hash-based itemset counting: A k-itemset whose corresponding hashing bucket count is below the threshold cannot be frequent Transaction reduction: A transaction that does not contain any frequent k- itemset is useless in subsequent scans Partitioning: Any itemset that is potentially frequent in DB must be frequent in at least one of the partitions of DB. Sampling: mining on a subset of given data, lower support threshold + a method to determine the completeness Dynamic itemset counting: add new candidate itemsets only when all of their subsets are estimated to be frequent
- 9. APRIORI ADVANTAGES/DISADVANTAGES Advantages • Uses large itemset property • Easily parallelized • Easy to implement Disadvantages • Assumes transaction database is memory resident. • Requires many database scans